Srinivasa Ramanujan and his bachelor's degree in Creative Mathematics

[The idea]

When number-theorist Srinivasa Ramanujan wrote to G. H. Hardy, Ramanujan had already trained himself to do creative research. Is there no way that, simply by pursuing the kind of independent studies that Ramanujan was pursuing, he could have been earning some kind of recognized credentials? Or would those studies need to have been warped into something much more technical and much less creative for formal credentials to have been awarded to Ramanujan?

If we consider some creative areas in arts, such as music composition, photography, or creative writing, a student's personal portfolio of creative works is an important part of the credential, but there are formal credentials that can be earned.

Could there not be credentials for creative research in science or mathematics?

[drkitten]

Originally posted by The idea
When number-theorist Srinivasa Ramanujan wrote to G. H. Hardy, Ramanujan had already trained himself to do creative research. Is there no way that, simply by pursuing the kind of independent studies that Ramanujan was pursuing, he could have been earning some kind of recognized credentials?

What kind of "credentials" do you think would be appropriate?

And what would be the use of those "credentials"?

Assuming that by "credentials" you mean "academic degrees," the answer would vary a lot by the particular school that would be awarding the degree. In general, academic degrees are a self-perpetuating institution that got its start in the medieval guild system; a "Master's degree," in particular, was originally simply recognition that the bearer of the degree has been recognized by fellow academics as a "master" of the craft of scholarship and is now "licensed" to accept apprentice scholars under his or her own auspices. In that regard, it's not much different from someone learning to be a carpenter, plumber, or goldsmith. In either case, merely learning the skill does not grant the privilege of guild membership, in part because the guild wants to keep its valuable monopoly, and in part because the guild has a certain notion of quality control and breadth of expertise they expect from a so-called "master."

The requirements for getting a degree today tend to include at least two aspects, a breadth requirements and a depth requirement. (For example, for my Ph.D., I had to pass a series of comprehensive exams covering my chosen field at large [breadth], and then I had to do a major research project in my specific subproblem [depth].) Part of the reason for this, aside from simple tradition, is the need for a "master" academic to be able to train scholars in areas other than his/her specialized field -- I have never once had the opportunity to teach a course in my Ph.D. area, but I have enough breadth of knowledge to be able to teach more or less any course in the undergraduate catalogue in my department. It would be, for example, a poor historian (and a useless one to most schools) who could not at need teach "The History of Western Civilization" irrespective of research specialization.

I'm not sure that Ramanujan had the breadth of knowledge associated with the standard degrees. As such, I would be wary of awarding him formal degrees. If, for whatever reason, he wanted to teach, I would be inclined to require him to obtain the necessary broad-based knowledge. On the other hand, if he simply wanted to be a research mathematician, credentials are not necessary. His body of research findings would be enough to get him a job at the appropriate non-teaching think tank.

[The idea]

Originally posted by new drkitten
What kind of "credentials" do you think would be appropriate?

I'm not sure what you mean. It might be called a "diploma", "certificate", "advanced certificate", or "degree."

Originally posted by new drkitten
And what would be the use of those "credentials"?

The credentials would give some evidence regarding the abilities of applicants. For example, job advertisements might request the credentials and resumes may list the credentials.

Originally posted by new drkitten
I'm not sure that Ramanujan had the breadth of knowledge associated with the standard degrees. As such, I would be wary of awarding him formal degrees. If, for whatever reason, he wanted to teach, I would be inclined to require him to obtain the necessary broad-based knowledge. On the other hand, if he simply wanted to be a research mathematician, credentials are not necessary. His body of research findings would be enough to get him a job at the appropriate non-teaching think tank.
Maybe Ramanujan, had he lived long enough, could have taught people to do the specific kind of thing that he did, presuming that it could be taught and that there are some people who consider it to be worth learning.

Are you aware of specific institutions (whether they are called think tanks or anything else) that hire people (people who do not have academic credentials) to conduct their own self-directed research?

Here's some information from Encyclopaedia Britannica:
[...] he began a correspondence with the British mathematician Godrey H. Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge.

[Ramanujan died in 1920], generally unknown to the world at large but recognized by mathematicians as a phenomenal genius, without peer since Leonhard Euler (1707-83) and Karl Jacobi (1804-51).
Of course, special exceptions should be made in such an exceptional case. However, is that the extent of the academic community's interest in research? For researchers who don't have traditional credentials, is Ramanujan's level of ability the minimum acceptable level?

[drkitten]

Originally posted by The idea

Are you aware of specific institutions (whether they are called think tanks or anything else) that hire people (people who do not have academic credentials) to conduct their own self-directed research?


Yes, several, all over the world.

Similarly, most funding agencies make provisions for grant applications from so-called "independent scholars," that need not have any formal academic affiliations or specific credentials. All you need is a track record.

Our hypothetical mathematician of Ramanujan's aaliber (actually, he would have to be somewhat better than Ramanujan, since Ramanujan didn't bother to publish) would have no problem getting his results placed in the appropriate top-flight journals. With enough journal articles under his belt, few industrial research labs would care about a lack of degrees.

It would be much more likely, of course, that our hypothetical mathematician would be offered a scholarship at a top-flight Ph.D. program and given a chance to work toward the degree, though. This would probably be better all around for the candidate by giving him access to the resources he needs and the guidance to develop the breadth of skills to make him more useful and easier to place.

On the other hand, there's virtually no excuse today for someone of Ramanujan's caliber not getting the regular, normal, academic degrees. There are so many more scholarships and fellowships available (and so many more degree-granting institutions) than there were in 1920 that credentials are more or less a non-issue.

[The idea]

Originally posted by new drkitten
[...] there's virtually no excuse today for someone of Ramanujan's caliber not getting the regular, normal, academic degrees. There are so many more scholarships and fellowships available (and so many more degree-granting institutions) than there were in 1920 that credentials are more or less a non-issue.
According to Encyclopaedia Britannica,
In 1903 he [i.e. Ramanujan] secured a scholarship to the University of Madras but lost it the following year because he neglected all other studies in pursuit of mathematics.
Note: Ramanujan was born Dec 22, 1887.

Originally posted by new drkitten
The requirements for getting a degree today tend to include at least two aspects, a breadth requirements and a depth requirement. [...] It would be, for example, a poor historian (and a useless one to most schools) who could not at need teach "The History of Western Civilization" irrespective of research specialization.

Yes, there is a breadth requirement and there was a breadth requirement, so what has changed? It would seem that the ability to do original research is not itself valued very highly, which is odd because there would be nothing for academic institutions to teach had original research not been done in the past.

Suppose mathematical historians discovered that Lebesgue had forged fraudulent credentials for himself so that he could pursue his research interests. Would that mean that in future no one should study the Lebesgue integral?

[drkitten]

Originally posted by The idea


Yes, there is a breadth requirement and there was a breadth requirement, so what has changed? It would seem that the ability to do original research is not itself valued very highly, which is odd because there would be nothing for academic institutions to teach had original research not been done in the past.

Suppose mathematical historians discovered that Lebesgue had forged fraudulent credentials for himself so that he could pursue his research interests. Would that mean that in future no one should study the Lebesgue integral?

This posting displays such a complete misunderstanding of the nature of academia, both today, and in the past, that no further discussion is warranted -- or indeed is likely to be profitable.

[Thomas]

Originally posted by new drkitten
This posting displays such a complete misunderstanding of the nature of academia, both today, and in the past...
To the contrary. You just just made his point. But don't think too much of it, because you're properly never gonna get it anyway.

[Jeff Corey]

I have to agree with newdrkitty. Academia has many different flavors (see Moo U), but not many of those.

[Thomas]

Originally posted by Jeff Corey
I have to agree with newdrkitty. Academia has many different flavors (see Moo U), but not many of those.
The Danish government are also aware of the problem, so they have made a number of new institutes and a brand new Ministry of Science, Technology and Development. Anyone can walk in that door and get access to advice, resources and reviewers (this is the same administration who has attacked the church and the unions. I like it.).

It's coming along, and in fact, the whole idea that you don't need to prove yourself by a major innovation or follow an irrelevant class before you can get access to the proper resources, is very hot right now. So, it's coming along, but there's still work to do - worldwide.

[drkitten]

Originally posted by Thomas
To the contrary. You just just made his point. But don't think too much of it, because you're properly never gonna get it anyway.

On the contrary. You evidently don't understand academia very well either.

Let me put it simply for you. To be a "researcher," broadly defined, does not require one to hold an academic position. One does not even need to hold a job at all; for much of the 19th century, most of the groundbreaking scholarly research worldwide was done by British "gentlemen" as a form of leisure. Charles Darwin's biological observations, for example, were done while he was a passenger on a sea voyage -- technically the "captain's companion," which to modern ears is about as suggestive a title as it's possible to get. Darwin never held an academic position, or indeed any academic credentials beyond a Cambridge BA in theology.

In 1905, the year that Einstein published the three papers that established him as one of the top scientists of all time, he was working as a Swiss patent clerk without a Ph.D.

An even better case is that of Beatrix Potter, who first observed that lichens are a symbiotic combination of fungi and algae -- although she had difficulty publishing her work because of her sex, no one at the time had any issues with the idea of an amateur biologists publishing papers (and, in fact, her central paper on the idea was presented and read by her uncle, himself an amateur biologist).

Similarly, it's not necessary to have degrees or formal academic credentials in order to do research. The examples of amateur biologists is widespread -- but another interesting case is that of the so-called "Mpemba effect,' that hot water freezes faster than cold. [Mpemba and Osborne, "Cool", Physics Education vol. 4, pgs 172--5 (1969)] Mpemba was a high school student in Tanzania at the time, but his name has become immortalized in a way that few scientists can even aspire to. Greg Chaitain similarly discovered Chaitin complexity and algorithmic information theory as a high school mathematics student in the 1960s.

The "problem" you describe is a non-issue.

If you want to do research, do research. No one will stop you. No one will keep your papers from being read.

[Thomas]

Originally posted by new drkitten
On the contrary. You evidently don't understand academia very well either.

Let me put it simply for you. To be a "researcher," broadly defined, does not require one to hold an academic position.

Let me put it simply for you: Show me where I said that.

One does not even need to hold a job at all; for much of the 19th century, most of the groundbreaking scholarly research worldwide was done by British "gentlemen" as a form of leisure. Charles Darwin's biological observations, for example, were done while he was a passenger on a sea voyage -- technically the "captain's companion," which to modern ears is about as suggestive a title as it's possible to get. Darwin never held an academic position, or indeed any academic credentials beyond a Cambridge BA in theology.

Excellent example. You should be aware that the academies in those days were quite religious, and that's why Darwin waited most of his life before he published his discoveries. The academy is quite often the inertia of science, but that's exactly what you don't get.

http://www.mun.ca/biology/scarr/Darwin_as_monkey.gif

Oh, one more thing. On the very voyage with MS Beagle you refer to, Darwin was mocked and ridiculed by the Captain of the ship all the way. It discouraged Darwin for years to follow. Maybe you should go study some more history of science.


In 1905, the year that Einstein published the three papers that established him as one of the top scientists of all time, he was working as a Swiss patent clerk without a Ph.D.

Yes, everybody embraced Einstein. Especially in the book "100 Authors against Einstein", and all the open minded universities who refused to let Einstein teach. Good one, thank you for bringing up these excellent examples to justify my point.


An even better case is that of Beatrix Potter, who first observed that lichens are a symbiotic combination of fungi and algae -- although she had difficulty publishing her work because of her sex, no one at the time had any issues with the idea of an amateur biologists publishing papers (and, in fact, her central paper on the idea was presented and read by her uncle, himself an amateur biologist).

Ah! The suppressed women. That's the core isn't it Doc-K? ;)


Similarly, it's not necessary to have degrees or formal academic credentials in order to do research. The examples of amateur biologists is widespread -- but another interesting case is that of the so-called "Mpemba effect,' that hot water freezes faster than cold. [Mpemba and Osborne, "Cool", Physics Education vol. 4, pgs 172--5 (1969)] Mpemba was a high school student in Tanzania at the time, but his name has become immortalized in a way that few scientists can even aspire to. Greg Chaitain similarly discovered Chaitin complexity and algorithmic information theory as a high school mathematics student in the 1960s.

The "problem" you describe is a non-issue.

Especially when you don't get it.


If you want to do research, do research. No one will stop you. No one will keep your papers from being read.
True, but you can look forward to be ridiculed by the academies if you present a scientific revolution. Ask the Wright brothers how their "Flying machine" was recieved by the media and the academies. Let me give you a hint. They were mocked for several years. As I said, you shouldn't think too much of it, because you wouldn't understand it anyway, you could easily have been one of the 100 authors mentioned above.

Or in Max Planck's words: "An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning."

Now go study some history.

[drkitten]

Originally posted by Thomas
Ask the Wright brothers how their "Flying machine" was recieved by the media and the academies. Let me give you a hint. They were mocked for several years

Yes, quite. Because they wouldn't, and didn't, publish or demonstrate their machine, because they were concerned about secrecy while their patent went through. The mocking lasted until they started to give public demonstrations, at which point they were more or less immediately lionized.

Now go study some history.

[Thomas]

Originally posted by new drkitten
Yes, quite. Because they wouldn't, and didn't, publish or demonstrate their machine, because they were concerned about secrecy while their patent went through. The mocking lasted until they started to give public demonstrations, at which point they were more or less immediately lionized.

The chosen tactic of the flawless mind: Pick out the weakest counter-arguments and ignore everything else. But, hey, it's just too bad when the "weak argument" proves not be weak anyway isn't it?

From Wikipedia:


In January 1905, more than a year after Wilbur and Orville Wright had flown their historic first flight at Kitty Hawk on December 17, 1903, Scientific American magazine carried an article ridiculing 'alleged' flights that the Wrights claimed to have made. With somber authority, the magazine cited as its main reason for doubting the Wrights the fact that the American press had failed to cover the alleged flights. Others who joined in the skeptic outcry were the New York Herald, the US Army, and numerous American scientists. Only when President Theodore Roosevelt ordered public trials at Fort Myers in 1908 could the Wright brothers confirm their claim and compel even the most zealous skeptics to accept the reality of heavier-than-air flying machines. In actuality, the Wright brothers had been successfully flying their flying machines in public demonstrations for five years before that historic flight, beginning in December 1903.


by Doc-K
Now go study some history.
See, you're not even innovative enough to make up your own lines, and it doesn't make it any better that you have no idea what you're talking about.

[drkitten]

Originally posted by Thomas
The chosen tactic of the flawless mind: Pick out the weakest counter-arguments and ignore everything else. But, hey, it's just too bad when the "weak argument" proves not be weak anyway isn't it?



I wouldn't know. Unlike you, I try not to use weak arguments, I double check sources, and I don't take Wikipedia's unsupported word for anything.


Of course there was skepticism; the Wright's patent didn't issue until 1906. If you look at the actual history of their demonstrations, they made a few relatively unheralded demonstrations (which were not widely reported) in 1903, then basically ceased giving demonstrations at all until 1908

Wikipedia is simply wrong.

From answers.com (The original source appears to be Tom D. Crouch, The Bishop's Boys: A Life of Wilbur and Orville Wright (1989) -- this quotation is also found at Houghton-Mifflin in their Reader's Companion to American History .)


he Wrights made the world's first powered, sustained, and controlled flights with a heavier-than-air flying machine at Kitty Hawk, North Carolina, on December 17, 1903. They returned to Dayton and continued their experiments in the relative secrecy of a local cow pasture for two more years. By the close of the 1905 flying season, they had transformed the marginally successful machine of 1903 into the world's first practical airplane. They won world fame with their first public demonstration flights in Europe and America in the summer and fall of 1908.


From a more authoritative source (Scientific American, Dec. 2003):


The Wrights had developed the world's first truly practical airplane and clinched their status as aviation pioneers. But it was a laurel conferred by history alone, because the Wrights allowed so few people to observe--or photograph--the aircraft flying. It was not until 1990 that the Flyer 3 was designated as a National Historic Landmark, the sole airplane ever to receive that honor.

The Wrights offered to sell the airplane to, variously, the U.S. secretary of war, the French, the British and the Germans. But they refused to demonstrate its flight capabilities without a signed sales contract.Not surprisingly, customers balked at buying so novel a device without seeing whether it worked.

Unable to get additional information from, or about, the Wrights, Scientific American commented huffily in a January 1906 article, "It seems that these alleged experiments were made at Dayton, Ohio, a fairly large town, and that the newspapers of the United States, alert as they are, allowed these sensational performances to escape their notice."

The Wrights waited until they were close to selling airplanes to both the U.S. Army Signal Corps and to a French syndicate before showing their aircraft publicly. Starting on August 8, 1908, at a racetrack near Le Mans, France, in a Wright Model A Flyer, Wilbur astonished viewers with multiple flights of unprecedented piloting skill and technological advance, and the Wrights were hailed as heroes.




And similarly from SA

A POPULAR MYTH about the Wright brothers is that ‘they were considered cranks because everyone knew that flying was impossible.� Untrue. This fiction is based on the turn-of-the-century writings of several skeptics, principally Simon Newcomb, a prominent astronomer, who noted the difficulty of scaling up the power needed for working models to full-size aircraft. The reality is that people had been flying since 1?83, thanks to the invention in France of a practical hot-air balloon by brothers, Joseph-Michel and Jacques-Etienne Montgolfier. By 1903 powered balloon flights and glider soaring were commonplace, and engines were becoming lighter and producing more horsepower. Fitting the elements together was acknowledged as tricky, risky and expensive, but few people thought that airplane flying would always be “impossible.’ It was the Wrights’ secretiveness that made this magazine (and many others) skeptical about their accomplishment.


The demonstrations Wikipedia refers to don't seem to have existed.

[Thomas]

Originally posted by new drkitten
From a more authoritative source (Scientific American, Dec. 2003):
:dl:

So, your authoritive source on the subject is the very same magazine who ridiculed and mocked them for claiming to have invented a heavier-than-air flying machine. Oh God, this is precious.

Have it occurred to you that Scientific American are merely trying to clear up that major mistake of theirs by twisting history a little bit in their favor so they can remain the authoritive source and keep up sales?

None the less, it's not a myth that they were ridiculed. Now, if you want to put the blame on themselves by exaggerating their secrecy so Scientific American can keep up the sales, go ahead, and send me a copy of that magazine, I'm almost out of toilet paper.

It was a jolly good laugh though :)

[Thomas]

Originally posted by new drkitten
Wikipedia is simply wrong.
Is that so? Let's have a look at it shall we?


The demonstrations Wikipedia refers to don't seem to have existed.

December 17th, 1903

http://www.killdevilhills.com/graphics/wright/2a13.jpg

http://www.killdevilhills.com/graphics/wright/2a14.jpg

Source: Library of Congress (http://www.outerbanks.com/wrightbrothers/wrightlc.htm)

The only thing that doesn't exist is your knowledge of history of science and technology. Have your fun with your authoritive source popular science magazines. Bah.

[69dodge]

Originally posted by new drkitten
Darwin never held an academic position, or indeed any academic credentials beyond a Cambridge BA in theology.

In 1905, the year that Einstein published the three papers that established him as one of the top scientists of all time, he was working as a Swiss patent clerk without a Ph.D.The title page of "The Origin of Species" says it's "By CHARLES DARWIN, M.A., FELLOW OF THE ROYAL, GEOLOGICAL, LINNÆAN, ETC., SOCIETIES".

Einstein got his Ph.D. in 1905, according to the Nobel Prize people (http://nobelprize.org/physics/laureates/1921/einstein-bio.html). I don't know whether it was before or after publishing his papers.

[Jeff Corey]

Originally posted by 69dodge
The title page of "The Origin of Species" says it's "By CHARLES DARWIN, M.A., FELLOW OF THE ROYAL, GEOLOGICAL, LINNÆAN, ETC., SOCIETIES".

Einstein got his Ph.D. in 1905, according to the Nobel Prize people (http://nobelprize.org/physics/laureates/1921/einstein-bio.html). I don't know whether it was before or after publishing his papers.
Dr Kitten be right agin.
It was quite common at that time for "Natural Scientists" to be members of such societies without benefit of degrees beyond the Master's level.
And Einstein wasn't that bad in maths.

[Thomas]

Originally posted by Jeff Corey
Dr Kitten be right agin.
"Again"? Hehehe.. You're not fooling anyone you know. But you might wanna send an email to the Library of Congress about their fake pictures of the recorded lift-off in 1903, because according to Kitten: "that never took place", because it says so in a popular science magazine who ridiculed and mocked the very same inventors.

You might also want to tamper a little bit with history so Darwin and Einstein was embraced and meet absolutely no opposition, because we all know just how open minded universities are. Especially you and Kitten who has absolutely no emotional attachments to the academies must of course be the best ones to judge these matters. Especially if it says so in the popular science magazines, hahaha.

You're full of it aint ya?

Oh, and by the way, she's wrong again, as she claimed that:

by miss Kitten
Darwin never held an academic position, or indeed any academic credentials beyond a Cambridge BA in theology.

And in my version it also says M.A. on the title page. Makes you wonder if she has actually read it, doesn't it? Have you?

[drkitten]

Originally posted by Thomas


And in my version it also says M.A. on the title page. Makes you wonder if she has actually read it, doesn't it? Have you?

No, I simply know what an MA means in the Cambridge system.

It's awarded essentially as an honorary degree (I believe the official requirements for it are something like "stay out of prison for a couple of years after getting your B.A.,") and it has essentially no academic standing.

Oxford has the same system. From Wikipedia (which is not the best source, but is largely correct in this instance),


MAs in Oxford, Cambridge and Dublin

The universities of Oxford, Cambridge and Dublin award master's degrees to BAs without further examination, when a certain number of years after matriculation (7 in the case of Oxford and Cambridge) have passed, and upon payment of a nominal fee. It is commonplace for recipients of the degree to have graduated several years previously and to have had little official contact with the university or academic life since then. The only real significance of these degrees is that they historically conferred voting rights in University elections, and certain other privileges e.g. the right to dine at high table. The MAs awarded by Oxford and Cambridge are colloquially known as the Oxbridge MA. The University of Cambridge also offers an MA to senior staff both academic and non academic after five years employment with the university.

Again, a more authoritative source (Trinity College, Cambridge),


Members of the College who are Cambridge Bachelors of Arts can become Masters of Arts six years after the end of their first term of residence, provided that two years have elapsed since they took the B.A. degree. Those eligible to take the M.A. (or another degree) should write to the Junior Bursar's Clerk, College Office, Trinity College, Cambridge, CB2 1TQ, normally giving at least four weeks' notice, saying whether they wish to take the degree in person or in absence.

Wikipedia apparently got the time period wrong, or Trinity has an unusual waiting period.


.... Oh, and I never said that no flights took place in 1903. The Dayton papers dropped the ball on that one -- the Wright brothers issued a press release that the Dayton papers declined to run. However, once those flights had been done, the Wright Brothers did no more demonstration flights in '04, '05, and '06 and no well-publicized demonstratoins until August '08. Notice that your source lists no photographs after Dec. 17, 1903.

Wikipedia remains wrong in their claim that "he Wright brothers had been successfully flying their flying machines in public demonstrations for five years before that historic flight, beginning in December 1903" -- a single demonstration five years previous hardly counts as "had been successfully flying [...] in public demonstrations for five years."

... Oh, and the Universities that were apparently lining up in droves not to hire Einstein? His CV doesn't show that. If you look at his biography, he received his Ph.D. in 1905, and his "habilitation" in 1908 -- the habilitation is essentially a second, post-doctoral thesis that is required in the German (or German-based) university system to obtain a faculty position. In 1908, he became a lecturer at the University of Bern, and accepted a full professorship at Zurich the following year. For someone to get a tenured chair only four years post Ph.D. and one year past habillitation, even then, when the standards were more relaxed, is surprising and the indication of a rising star in one's chosen field. By 1914 (fewer than ten years post Ph.D., Einstein was offered a research position at the Prussian Academy of Sciences, with a full professorship, but without any mandatory teaching responsibilities, at the University of Berlin, the German MIT of its time, and the directorship of the about-to-be-established Kaiser Wilhelm Institute of Physics.

That's an unbelievably impressive job offer. I'd say that such an offfer is pretty good evidence that one has been "embraced" by the relevant academic authorities.

[Thomas]

Ah! That looks like a fairly sensible post, Kitten. I wasn't aware of the Cambridge, Oxford and Dublin Magister Artium system. Whether this counts as "academic credentials" is for you to decide with your own honesty.

I don't really have time right now, but I'll look into it later. For one thing, I remember having read some letters Einstein wrote in his youth where he tells someone that he don't think he will ever be able to get an academic career. I'll see if I can find it later or tomorrow.

I definately don't concur that one recorded flight demonstration by the Wright brothers isn't enough, and that this should be reason enough for various magazines to call them liars. They could just have looked into it. The pictures were there. Also, I don't remember the exact date, but they actually did have a demonstration with several journalists present before 08', but they exprerienced technical difficulties and that created a roar of skeptic outcries among the medias. I figure people felt cheated. On the other hand, why the heck should they have invited to a public demonstration if they were well aware that their craft couldn't fly? Sometimes journalists are very hasty in drawing conclusions.

I'll elaborate later or tomorrow, right now, deadlines are calling my name out loud.

[Jeff Corey]

[QUOTE]Originally posted by Thomas
...You're full of it aint ya?...[QUOTE]
Apparently not.

[Thomas]

Originally posted by new drkitten
No, I simply know what an MA means in the Cambridge system.

It's awarded essentially as an honorary degree (I believe the official requirements for it are something like "stay out of prison for a couple of years after getting your B.A.,") and it has essentially no academic standing.

Oxford has the same system. From Wikipedia (which is not the best source, but is largely correct in this instance),

Again, a more authoritative source (Trinity College, Cambridge),



Wikipedia apparently got the time period wrong, or Trinity has an unusual waiting period.

Ok, you don't count a Cambridge/Oxford/Dublin-MA as an academic credential. That must be on your own account.


.... Oh, and I never said that no flights took place in 1903.

Yes you did. Let me quote you.
Former statement by you
The demonstrations Wikipedia refers to don't seem to have existed.

And you based this assumption on an article from a popular science magazine. I would have thought more of you in the light of your username.


The Dayton papers dropped the ball on that one -- the Wright brothers issued a press release that the Dayton papers declined to run. However, once those flights had been done, the Wright Brothers did no more demonstration flights in '04, '05, and '06 and no well-publicized demonstratoins until August '08. Notice that your source lists no photographs after Dec. 17, 1903.

None the less, they were ridiculed and mocked on a weak basis, the photographs were there and so was the "flying machines". Bad journalism is what that was, especially from Scientific American who had no first hand knowledge of the demonstrations.


Wikipedia remains wrong in their claim that "he Wright brothers had been successfully flying their flying machines in public demonstrations for five years before that historic flight, beginning in December 1903" -- a single demonstration five years previous hardly counts as "had been successfully flying [...] in public demonstrations for five years."

And one successful flight documented with photographs hardly count as a failure.


... Oh, and the Universities that were apparently lining up in droves not to hire Einstein? His CV doesn't show that. If you look at his biography, he received his Ph.D. in 1905, and his "habilitation" in 1908 -- the habilitation is essentially a second, post-doctoral thesis that is required in the German (or German-based) university system to obtain a faculty position. In 1908, he became a lecturer at the University of Bern, and accepted a full professorship at Zurich the following year. For someone to get a tenured chair only four years post Ph.D. and one year past habillitation, even then, when the standards were more relaxed, is surprising and the indication of a rising star in one's chosen field. By 1914 (fewer than ten years post Ph.D., Einstein was offered a research position at the Prussian Academy of Sciences, with a full professorship, but without any mandatory teaching responsibilities, at the University of Berlin, the German MIT of its time, and the directorship of the about-to-be-established Kaiser Wilhelm Institute of Physics.

That's an unbelievably impressive job offer. I'd say that such an offfer is pretty good evidence that one has been "embraced" by the relevant academic authorities.
Yes, that's all very good, but this is all in the days after he had proved himself to "the court". This thread is about the originals who doesn't need to follow the common academic paths to innovate. Einstein and Ramanujan is examples of such characters. Let me show you why.

From University of St. Andrew's, Scotland
Three of Einstein's fellow students, including Grossmann, were appointed assistants at ETH in Zurich but clearly Einstein had not impressed enough and still in 1901 he was writing round universities in the hope of obtaining a job, but without success.

Einstein had to settle with a teacher job at a technical high school in Winterthur after all the refusals. And in those days he wrote:
by Albert Einstein, 1901
I have given up the ambition to get to a university ...

Source (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Einstein.html)

This is what you called a non-issue, and not a problem. Go figure what Einstein could have produced under more suitable circumstances. Maybe with the more dedicated time he could have reached his dream, to find the TOE.

On the other hand, let's not paint an unreal image. Einstein didn't have all opponents, but he did have quite a few, as evident in the book "100 authors against Einstein".

If you think it's an easy task to present a revolutionary theory to a paradigm of back-clappers, then I'm sorry, but that suggests that you have never personally made any actual revolutionary innovations or propositions yourself.

Here's a well known example:

by Thomas C. Tirado
Tradition holds that Columbus moved to Seville in 1485, and between May of 1486 and September of 1487 he was maintained at the expense of the queen. Although interested in his ideas, the king and queen were too busy fighting wars and consolidating power to give serious consideration to his plan. Finally, in 1487, Columbus presented his Atlantic project to a committee of experts called to hear the case. The so-called “Wise Men of Salamanca� raised numerous objections, asked many questions, and, in the end, rejected the plan. Among the reasons given for the rejection was that the “ocean sea" was simply too large to cross.

In his “years of great anguish,� as he called his years of petitioning the monarchs, 1491 must have seemed hopeless.

The wise men of the University of Salamanca, yes.

Source (http://muweb.millersville.edu/~columbus/columbus.html)

[Thomas]

Originally posted by Jeff Corey
Apparently not.
Apparently so. You shouldn't confuse sensibility with weakness, Jeff.

[Jeff Corey]

Originally posted by Thomas
Apparently so. You shouldn't confuse sensibility with weakness, Jeff.
I didn't.

[drkitten]

Originally posted by Thomas

Yes, that's all very good, but this is all in the days after he had proved himself to "the court". This thread is about the originals who doesn't need to follow the common academic paths to innovate. Einstein and Ramanujan is examples of such characters. Let me show you why.


Einstein had to settle with a teacher job at a technical high school in Winterthur after all the refusals. And in those days he wrote:



Let met get this straight. You're presenting Einstein as an original who doesn't need to follow the common academic path in 1901?

What had Einstein done in 1901? Had he written any papers of substance? Had he produced any interesting theories? Was there any reason at all for someone not blessed with clairvoyance to regard Einstein as anyone special, original, or particularly deserving of merit?

In order to be taken seriously as a creative thinker in academia, you need to think creatively. Or, to turn it around, if you aren't able to demonstrate that you're an especially creative thinker, then there's no reason for you to ask for any special treatment as an "original."

But, as it happens, we have some evidence from Einstein's early life that he did get a certain amount of special attention. From the Albert Einstein Collection (http://www.americagallery.com/einstein2.shtml)


Shortly after his sixteenth birthday in the spring of 1895, he dropped out of school with two years to go. Einstein hoped to enroll in the Polytechnikum (Swiss Federal Institute of Technology) in Zurich, although he was two years shy of the standard enrollment age of eighteen (which he mentions in the letter to Koch) and an uncertified school dropout. However, he was given special permission to take the entrance examinations and did well on the scientific section, but showed considerable gaps in the general section. It was arranged that he would enroll instead at the Gymnasium in Aarau, where he found a nurturing academic environment. He eventually went on to graduate in physics and mathematics from the Polytechnikum in 1900.


Already, you can see that despite having gaps in his credentials ("an uncertified high school dropout"), that was not necessarily perceived as a bar to his enrollment, and if he had managed to score better on the exams, he would have been admitted.

But the 16-year old Albert Einstein, not withstanding what he would eventually become, did not show any substantial promise at that point as a scholar.



This is what you called a non-issue, and not a problem.

And I stand by it. Einstein's brilliance as a researcher was almost immediately recognized once he started doing research. If you want to be a successful researcher, do research. Einstein, the researcher, was almost immediately recognized as a physicist of the first magnitude on the strength of his ideas alone. But he had to have those ideas, first.


On the other hand, let's not paint an unreal image. Einstein didn't have all opponents, but he did have quite a few, as evident in the book "100 authors against Einstein".


So some people wrote a book. Others offered him a dream job at three of the best universities in Europe. Big Fat Hairy Deal.



If you think it's an easy task to present a revolutionary theory to a paradigm of back-clappers, then I'm sorry, but that suggests that you have never personally made any actual revolutionary innovations or propositions yourself.

Here's a well known example:


Columbus? You're suggesting Columbus as an example of a revolutionary, now?

Um, in case you didn't know, Columbus was wrong. Completely and utterly wrong. He proposed to sail westward from Spain to the Far East, and nearly ran out of food and water someplace in the Caribbean. He misjudged the distance of his planned voyage by the entire width of the American continent and the Pacific Ocean. The wise men of Salamanca knew what the distance was between Spain and the Far East (the roundness of the Earth, and its approximate circumference, were well-known to every educated person since the 12th century) and were quite correct that 'the “ocean sea"', meaning the combined width of the Atlantic and Pacific Oceans, plus the width of America, "was simply too large to cross."

Columbus simply got lucky. Instead of running out of food and water, he bumped into a continent that he didn't know existed -- and was so dumb (and such a bad navigator) that he didn't realize he'd missed his mark by ten thousand miles!

But how is one to know who the lucky people are before they get lucky?

How is one to know who the creative thinkers are before they start thinking creatively?

If you want to be a researcher, do research. If you are successful at it, the world will beat a path to your door, and the rest of the research community make itself into your mollusc of choice. That's what, for example, Trinity College and the University of Madras did for the uncredentialed Ramanujan, but he apparently wasn't interested in the chance they gave him to acquire credentials. Einstein, who was interested in the credentials, went through normal channels and was showered with glory in the process on the basis of his research. Darwin, the uncredentialed naturalist, was nevertheless elected FRS on the basis of his research findings.

On the other hand, if you insist on doing your research in secret, as the Wright Brothers did, then you will not get credit for your ideas -- because no one knows about them. if you propose ideas that are out of the box wrong, as Columbus did, your ideas will be justly ridiculed, even if it later turns out that you serendipitously find something that you weren't looking for in the process of testing your ideas. And if you think that you're some sort of special creative "original" person, even though you've never actually done any sort of creative work worthy of the name,... well, that's just saddening.

So, let's see.


Darwin -- did creative work, was rewarded for it, despite a lack of credentials
Ramanujan -- did creative work, was rewarded for it, despite a lack of credentials
Einstein -- did creative work, was rewarded for it, despite a (temporary) lack of credentials
Columbus -- did obviously stupid work, was ridiculed for it, then lucked out and found something he wasn't looking for and didn't even recognize it.
Wright Bros. -- did creative work and didn't tell anyone about it for five years, were ridiculed in the meantime, told people about it later, and were rewarded for it, despite a lack of credentials.


I'm afraid I still don't see the problem.

ETA:

Add to the list

Mpenba -- did creative work, was rewarded for it, despite a lack of credentials
Chaitin -- did creative work, was rewarded for it, despite a lack of credentials
Potter -- did creative work, was rewarded for it, despite a lack of credentials and being a woman


I still don't see the problem.

[drkitten]

Duplicate post, hit wrong button, ignore

[Thomas]

Originally posted by new drkitten
Let met get this straight. You're presenting Einstein as an original who doesn't need to follow the common academic path in 1901?

What had Einstein done in 1901? Had he written any papers of substance? Had he produced any interesting theories? Was there any reason at all for someone not blessed with clairvoyance to regard Einstein as anyone special, original, or particularly deserving of merits?

To answer both your questions at once. It's not a matter of what he had done, but a matter of his potential which was supressed by all the refusals.

In order to be taken seriously as a creative thinker in academia, you need to think creatively. Or, to turn it around, if you aren't able to demonstrate that you're an especially creative thinker, then there's no reason for you to ask for any special treatment as an "original."

Of course not, but Einstein didn't just sloop around as you merely suggest, already from his childhood years was he specualting in theoretical physics. That should be something worth noticing alone. I know a few teachers from my time who wouldn't have paid any notice to such a kid at all.

But, as it happens, we have some evidence from Einstein's early life that he did get a certain amount of special attention. From the Albert Einstein Collection (http://www.americagallery.com/einstein2.shtml)

Exactly. First you say he showed no potential, then you say he did. No comments.

Already, you can see that despite having gaps in his credentials ("an uncertified high school dropout"), that was not necessarily perceived as a bar to his enrollment, and if he had managed to score better on the exams, he would have been admitted.

But the 16-year old Albert Einstein, not withstanding what he would eventually become, did not show any substantial promise at that point as a scholar.

That's how the story the goes for many of the originals. And it's also a popular myth among the lazy folks who need to justify their lack of studies.


And I stand by it. Einstein's brilliance as a researcher was almost immediately recognized once he started doing research. If you want to be a successful researcher, do research. Einstein, the researcher, was almost immediately recognized as a physicist of the first magnitude on the strength of his ideas alone. But he had to have those ideas, first.

Sure, but it's not as easy as you make it seem, if it was, Darwin wouldn't have waited most of his life to publish. Einstein was in a more fortunate position because his theories had no actual impact on theology. He only had to deal with the Newton fanatics.


So some people wrote a book. Others offered him a dream job at three of the best universities in Europe. Big Fat Hairy Deal.

Yea well, would you like a 100 people to write a book about why you suck? I figured not.


Columbus? You're suggesting Columbus as an example of a revolutionary, now?

Um, in case you didn't know, Columbus was wrong. Completely and utterly wrong. He proposed to sail westward from Spain to the Far East, and nearly ran out of food and water someplace in the Caribbean. He misjudged the distance of his planned voyage by the entire width of the American continent and the Pacific Ocean. The wise men of Salamanca knew what the distance was between Spain and the Far East (the roundness of the Earth, and its approximate circumference, were well-known to every educated person since the 12th century) and were quite correct that 'the “ocean sea"', meaning the combined width of the Atlantic and Pacific Oceans, plus the width of America, "was simply too large to cross."

Columbus simply got lucky. Instead of running out of food and water, he bumped into a continent that he didn't know existed -- and was so dumb (and such a bad navigator) that he didn't realize he'd missed his mark by ten thousand miles!

But how is one to know who the lucky people are before they get lucky?

That's not all correct, Columbus was well aware that the distance had to be larger than the one he presented at Salamanca, but he was ready to take the chance.

How is one to know who the creative thinkers are before they start thinking creatively?

No thinkers will suddently get a creative mind after they had made their proposals, but it is the task of the given state to make sure that it is as easy to get access to the proper resources as possible. Although you don't find that to be an issue.


If you want to be a researcher, do research. If you are successful at it, the world will beat a path to your door, and the rest of the research community make itself into your mollusc of choice. That's what, for example, Trinity College and the University of Madras did for the uncredentialed Ramanujan, but he apparently wasn't interested in the chance they gave him to acquire credentials. Einstein, who was interested in the credentials, went through normal channels and was showered with glory in the process on the basis of his research. Darwin, the uncredentialed naturalist, was nevertheless elected FRS on the basis of his research findings.

You sure make it sound easy. If you're a creative mind, then I take it that you have been growing up under quite fortunate circumstances. I personally grew up under not very fortunate circumstances despite my family background, and had to fight for common sense most of my childhood.


On the other hand, if you insist on doing your research in secret, as the Wright Brothers did, then you will not get credit for your ideas -- because no one knows about them. if you propose ideas that are out of the box wrong, as Columbus did, your ideas will be justly ridiculed, even if it later turns out that you serendipitously find something that you weren't looking for in the process of testing your ideas. And if you think that you're some sort of special creative "original" person, even though you've never actually done any sort of creative work worthy of the name,... well, that's just saddening.

I'm not sure about anything. When I was a kid I thought I was on to some pretty progressive ideas, and maybe I was. The fact is that I don't care anymore. At least I won't publish anything before I have finished the math for my ideas. The philosophy is fair, but I guess the math has to be in order before I can even begin to call it science. And untill then, I won't publish anything (and it's not just a couple of formulas, however, most of the math is already done).

Anyway, my friends are pushing me to publish all the time, so maybe I'm not all on the wrong track. But, the last time I debated this with someone, I ended up giving him an excuse because I tend to lose my temper when I debate these specifics. If my ideas are just half as innovative as they look (and hereby correct, let's not forget that), then I need some more self-control before I publish, because otherwise it will be a murder.


So, let's see.


Darwin -- did creative work, was rewarded for it, despite a lack of credentials
Ramanujan -- did creative work, was rewarded for it, despite a lack of credentials
Einstein -- did creative work, was rewarded for it, despite a (temporary) lack of credentials
Columbus -- did obviously stupid work, was ridiculed for it, then lucked out and found something he wasn't looking for and didn't even recognize it.
Wright Bros. -- did creative work and didn't tell anyone about it for five years, were ridiculed in the meantime, told people about it later, and were rewarded for it, despite a lack of credentials.


I'm afraid I still don't see the problem.
If you think I have implied otherwise, then we have seriously been talking past eachother. In fact, I was just about to nominate you for the language award for that list because it can inspire fresh thinkers to be creative.

[Thomas]

Originally posted by Jeff Corey
I didn't.
You're not exactly supporting anything with your usual empty snappy remarks.

[Thomas]

Originally posted by new drkitten

Wright Bros. -- did creative work and didn't tell anyone about it for five years, were ridiculed in the meantime, told people about it later, and were rewarded for it, despite a lack of credentials.


By the way, this is why I won't nominate you for the language award anyway. I'm not gonna nominate lies.

[Jeff Corey]

I told you once.

[Thomas]

Originally posted by Jeff Corey
I told you once.
maybe you should have someone to look at your glasses, there seem to be an issue with the objectivity.

[Jeff Corey]

Originally posted by Thomas
maybe you should have someone to look at your glasses, there seem to be an issue with the objectivity.
Now that's more inane than usual for you.

[The idea]

Perhaps I could bring this thread back to the original topic. The question is: could there be a program of study and associated credential in creative research? Such a program of study would help students learn to do creative research and such a credential would help graduates get hired.

Originally posted by new drkitten
[...] the need for a "master" academic to be able to train scholars in areas other than his/her specialized field -- I have never once had the opportunity to teach a course in my Ph.D. area, but I have enough breadth of knowledge to be able to teach more or less any course in the undergraduate catalogue in my department. It would be, for example, a poor historian (and a useless one to most schools) who could not at need teach "The History of Western Civilization" irrespective of research specialization.

I'm not sure that Ramanujan had the breadth of knowledge associated with the standard degrees. As such, I would be wary of awarding him formal degrees. If, for whatever reason, he wanted to teach, I would be inclined to require him to obtain the necessary broad-based knowledge. On the other hand, if he simply wanted to be a research mathematician, credentials are not necessary. His body of research findings would be enough to get him a job at the appropriate non-teaching think tank.
Suppose we were talking about architectural design rather than mathematical research. Would anyone make the following claims?

No one has any reason to study architecture in a school. If you want to be an architect, then simply start designing buildings. If you have the capacity to design buildings, then you will be immediately able to create designs that are good enough to get you hired as an architect.

On the other hand, if there were to be a degree or other credential in architecture, then every person who had such a credential would claim to be able to teach all architectural courses. So it would be a mistake to award any credentials to a person who has merely learned the skills required to be a practicing architect.

[drkitten]

Originally suggested as an analogy by The idea
No one has any reason to study architecture in a school. If you want to be an architect, then simply start designing buildings. If you have the capacity to design buildings, then you will be immediately able to create designs that are good enough to get you hired as an architect.

On the other hand, if there were to be a degree or other credential in architecture, then every person who had such a credential would claim to be able to teach all architectural courses. So it would be a mistake to award any credentials to a person who has merely learned the skills required to be a practicing architect.

This is truer than you realize. Architecture, like most engineering disciplines, involves a hierarchy of degrees. If you want to design buildings, there is a relatively small body of knowledge you need to master which is typically taught at the undergraduate level; if all you want to do is to design buildings, there's no need for you to do anything beyond a simple B.S. However, the people who actually teach architecture courses -- the architecture professors -- almost uniformly go on for higher degree such as the Ph.D. in Architecture. (If you're interested in US-based programs, check Michigan, Wisconsin, Georgia Tech, and even Harvard for examples).

Every person who has such an "advanced" credential would indeed be capable of teaching all architecture courses, and it would indeed be a mistake to award such credentials to "a person who has merely learned the skills required to be a practicing architect." If all you want to do is to design houses, you don't need (or want) a Ph.D. in Architecture.

So, of course, this raises the question about why anyone would want/need to take courses in architecture at all, even at the BS level. In this case, there are two main reasons. The first is that architecture is a field (unlike mathematical or many other forms of research) where licensure is required as a condition to practice, in the interests of public safety. Various government agencies want to make sure that any house you design and sell to the public isn't going to fall down and kill people -- a concern for which I congratulate them. Mathematicians in general (and Srinivasa Ramanujan in particular) are unlikely to kill people by misproving an incorrect theorem.

The second reason is that the necessary architectural knowledge is rarely taught in high school, so you can't assume that a typical high school graduate has the knowledge necessary to design the house.

However, an atypical high school graduate -- or for that matter high school dropout -- with an appropriate touch of genius could design and build a house for his own use freely. If you just want to build a house for yourself, you don't even need a B.S.

Again, I ask the question -- what use would credentials be to Ramanujan?

The program of study you ask for satisfies no need, would serve no students, and would be a waste of money, brains, and time for both the students in it and the factulty teaching it.

[The idea]

Originally posted by new drkitten
[...] if all you want to do is to design buildings, there's no need for you to do anything beyond a simple B.S. However, the people who actually teach architecture courses -- the architecture professors -- almost uniformly go on for higher degree such as the Ph.D. in Architecture. [...]

Every person who has such an "advanced" credential would indeed be capable of teaching all architecture courses [...]

Perhaps I could draw attention to the title of this thread: "Srinivasa Ramanujan and his bachelor's degree in Creative Mathematics."

Were you assuming that a bachelor's degree in Creative Mathematics would include a Ph.D. in Mathematics?

Originally posted by new drkitten
[...] The first is that architecture is a field (unlike mathematical or many other forms of research) where licensure is required as a condition to practice, in the interests of public safety. Various government agencies want to make sure that any house you design and sell to the public isn't going to fall down and kill people -- a concern for which I congratulate them. Mathematicians in general (and Srinivasa Ramanujan in particular) are unlikely to kill people by misproving an incorrect theorem.

There are academic credentials associated with activities that do not create any safety hazards. For example, there are credentials in computer animation.

Originally posted by new drkitten
The second reason is that the necessary architectural knowledge is rarely taught in high school, so you can't assume that a typical high school graduate has the knowledge necessary to design the house.

Yes, and you also can't assume that a typical high school graduate would be able to make any progress on the kinds of problems that Ramanujan made progress on. In fact, you can't assume that a typical high school graduate would be able to even work on those problems in the sense of finding a starting point that has a chance of leading somewhere and creating a stream of ideas associated with such a starting point.

Originally posted by new drkitten
However, an atypical high school graduate -- or for that matter high school dropout -- with an appropriate touch of genius could design and build a house for his own use freely. If you just want to build a house for yourself, you don't even need a B.S.

Yes, and if Ramanujan had wanted to pursue creative mathematical research purely as a hobby and without publishing any results, then he wouldn't have needed to impress anyone or communicate any mathematical ideas to anyone.

Originally posted by new drkitten
Again, I ask the question -- what use would credentials be to Ramanujan?

First of all, consider not the credential itself, but the program of study. If there had been a program in Creative Mathematics and if Ramanujan's scholarship had paid for him to study in that program, then he probably wouldn't have lost the scholarship. Instead of having been a dropout who had some mathematical interests, he would have been pursuing his interests while making progress towards obtaining formal credentials. He probably would have completed a bachelor's degree in Creative Mathematics.

Second of all, with that credential he might have obtained a job doing mathematical research. In the process of completing the degree, a student would presumably also create a personal portfolio of research results. Instead of having sought and obtained a clerical post with the Madras Port Trust, Ramanujan might have taken his credential and portfolio to an organization that employs mathematical researchers and gotten hired as a mathematical researcher.

More importantly, such a credential would help people whose abilities are not quite as high as Ramanujan's. If you think that Ramanujan had the bare minimum level of ability required to do worthwhile mathematical research, then you might be opposed to the idea of encouraging people who have less ability than Ramanujan. If, on the other hand, you think that Ramanujan had more than the minimum, then you might approve of the idea that even people with less ability than Ramanujan could be employed as mathematical researchers in the future.

Originally posted by new drkitten
The program of study you ask for satisfies no need, would serve no students, and would be a waste of money, brains, and time for both the students in it and the factulty teaching it.
Can you support that assertion?

Perhaps you believe that mathematical research methods cannot be taught? If that is what you believe, then shouldn't you say that it would be impossible to create such a program of study?

[drkitten]

Originally posted by The idea

Yes, and if Ramanujan had wanted to pursue creative mathematical research purely as a hobby and without publishing any results, then he wouldn't have needed to impress anyone or communicate any mathematical ideas to anyone.


Yes. And if Ramanujan had wanted to pursue creative mathematics mathematical research as a career, and get paid for it, he wouldn't have had that option. He would have had to publish, publications being the common currency of research of all stripes.

For a mathematician of Ramanujan's ability, publishing would not have been a problem. He would simply have had to write up some of his results (as he did for Hardy) and ship them to the appropriate journals, where they would have been published.

With a few publications under his belt, he would have been a prime candidate for any (paid) mathematical research position world-wide that didn't involve teaching.



First of all, consider not the credential itself, but the program of study. If there had been a program in Creative Mathematics and if Ramanujan's scholarship had paid for him to study in that program, then he probably wouldn't have lost the scholarship. Instead of having been a dropout who had some mathematical interests, he would have been pursuing his interests while making progress towards obtaining formal credentials. He probably would have completed a bachelor's degree in Creative Mathematics.


So what? Granting the existence of such a degree.... he wouldn't have been able to make any use of it. There's nothing that he could do with such a degree that he couldn't do without it.


Second of all, with that credential he might have obtained a job doing mathematical research.


This statement is technically true. But there is no job for which he would have been qualified with that credential for which he would not have been qualified without it. Without that credential, he still might have obtained a job doing mathematical research.

The credential would open no doors for him.

In the process of completing the degree, a student would presumably also create a personal portfolio of research results.

.... which he had already done (and submitted to Hardy). The degree would not have made a difference to his portfolio.

Ramanujan might have taken his credential and portfolio to an organization that employs mathematical researchers and gotten hired as a mathematical researcher.

He could have done that at any time, on the basis of Hardy's recommendation and his established research portfolio.


More importantly, such a credential would help people whose abilities are not quite as high as Ramanujan's. If you think that Ramanujan had the bare minimum level of ability required to do worthwhile mathematical research, then you might be opposed to the idea of encouraging people who have less ability than Ramanujan.

No. I approve entirely of supporting people who are capable of doing worthwhile research.

However, this credential you propose is not "support." It is at best irrelevant (because a graduate with that credential will have no opportunities that s/he did not have without the credential), and at worst is a scam, pure and simple.

The world is full, for example, of "modeling classes" that take young women and "teach" them to be models. In most cases -- I would venture to guess more than 95% of cases -- the classes offer little or no benefit to the students and are simply an excuse to take tuition money from the students. If you want to be a model, get someone to take some pictures of you and take them to a local agent, advertising agency, casting director, or producer -- they're all in the phone book. Agencies typically recruit through "open calls," meetings (often weekly) to which anyone and everyone with an interest is invited. Most agents won't even ask whether or not you've taken modeling classes.

For this reason, I would be deeply opposed to any school offering a degree in "modeling studies" or the like. What do you tell them after the first lecture about "go to the weekly 'open call' at the agencies you want to work for"?

My objection to degrees in "creative mathematics" is exactly analogous. If you want a job as a mathematical researcher (or researcher of any kind), the single most important attribute is your research portfolio; with it, your degree doesn't matter, and without it, your degree still doesn't matter.

So, no, such a degree would not "help people whose abilities are not quite as high as Ramanujan's."

[The idea]

Originally posted by new drkitten
For a mathematician of Ramanujan's ability, publishing would not have been a problem. He would simply have had to write up some of his results (as he did for Hardy) and ship them to the appropriate journals, where they would have been published.

Do you intend to claim that the letters Ramanujan sent to Hardy were suitable for publication in a mathematics journal?

Originally posted by new drkitten
With a few publications under his belt, he would have been a prime candidate for any (paid) mathematical research position world-wide that didn't involve teaching.

If Ramanujan had reason to believe that, then why did he get a clerical job with the Madras Port Trust?

Originally posted by new drkitten
He could have done that [gotten hired as a mathematical researcher] at any time, on the basis of Hardy's recommendation and his established research portfolio.

If you accept that Hardy's recommendation had value, why do you insist that a degree in Creative Mathematics would necessarily have no value? At the very least, wouldn't it be possible that a professor like Hardy could be teaching courses in a Creative Mathematics program and see reason to recommend a student based on the student's performance?

Originally posted by new drkitten
However, this credential you propose is [...] at best irrelevant [...] and at worst is a scam, pure and simple.

The world is full, for example, of "modeling classes" that take young women and "teach" them to be models. In most cases -- I would venture to guess more than 95% of cases -- the classes offer little or no benefit to the students and are simply an excuse to take tuition money from the students. [...]

If you want a job as a mathematical researcher (or researcher of any kind), the single most important attribute is your research portfolio; with it, your degree doesn't matter, and without it, your degree still doesn't matter.

The "scam" claim suggests two questions.

(1) Consider some undergraduate courses for which the course work consists of mainly essay writing. If essays that receive an A grade are not suitable for publication in an academic journal, then can one conclude that the courses are a scam?

(2) Consider a series of academic courses for students to learn a particular foreign language (such as Russian or Arabic, for example). The first course in the series may be designed for students who have no previous experience in that language. If the primary aim of the courses is to give students competence in the given language, then are the courses a scam?

In case it's not clear why I am asking (2), here is an explanation. If you want a job translating INTO your native language, then the single most important quality you need is competence in the language that you are translating FROM. If you have that competence, then academic credit in the language courses is an unnecessary extra. If you don't have that competence, then academic credit in the language courses will not be good enough.

[drkitten]

Originally posted by The idea


(2) Consider a series of academic courses for students to learn a particular foreign language (such as Russian or Arabic, for example). The first course in the series may be designed for students who have no previous experience in that language. If the primary aim of the courses is to give students competence in the given language, then are the courses a scam?

In case it's not clear why I am asking (2), here is an explanation. If you want a job translating INTO your native language, then the single most important quality you need is competence in the language that you are translating FROM. If you have that competence, then academic credit in the language courses is an unnecessary extra. If you don't have that competence, then academic credit in the language courses will not be good enough.

You're changing the discussion now. The opening post is specifically discussing the degrees appropriate to Srinivasa Ramanujan, whom I hope we can agree was a self-taught mathematician and a genius of the first rank. You asked what sort of formal credentials would be appropriate to be awarded to him -- my response is : "none." He needed none, had use for none, and there are none available that would be appropriate. He already had (much of) the knowledge given in a typical degree program, so taking the formal coursework would have wasted his and his teachers' time, and the credentials that he would have received would not have opened any doors for him.

As an analogy, I suggested the modeling class "scam," which offers people a chance to spend money to get a worthless piece of paper that opens no doors for them, because they already have the talents and knowledge necessary to model.

Obviously, language proficiency is a slightly different situation -- if you don't know the language(s) of interest, you can't work as a translator. But a true bilingual, someone who already knows the relevant languages fluently, typically needs no formal credentials such as a BS in "Translation Studies." Work experience -- a portfoliio of translated material -- suffices.

This is the position Srinivasa Ramanujan was in.

Now, you want to discuss those less fortunate who don't have Ramanujan's knowledge of mathematics, but who want to be research mathematicians anyway. You're right, there are formal credentials that would be useful for such people: they're called "math degrees." By definition, if you don't know enough mathematics to do research in it, you will need to learn more mathematics. But there's no reason to create a new degree in "creative mathematics" simply to duplicate the content of the existing mathematics degrees.

Your translation analogy is again apt: if I don't know German, I'm unlikely to be successful as a translator of German. But the courses I need to take are not courses in German Translation; they're simply courses in German, as taught by the existing German department.

If you want to do mathematics research, and you already know enough math, do the research. No degree is necessary.

If you want to do mathematics research, but you don't know enough math, then learn more math. If you insist, you can try learning it on your own (as did Ramanujan), or you can choose to be taught by professionals -- there are literally thousands of them in mathematics departments all over the world. You can choose to take a degree or not (once you've mastered the material), and then proceed to do the research.

But in either case, the degree is an irrelevance.

I would actually argue that your degree in "Creative Mathematics" offers negative value, in the sense that it is an equally expensive option that does not open the doors that a traditional degree would. To continue with your translation example, a typical way for me to learn German would be to take a degree in German, after which I would have mastered enough German to be able to do translations. I would also have acquired the formal credentials and recognition to let me, for example, teach German at the secondary school level (or other jobs for which a language B.S. is required).

Would a B.S. in "Translation Studies" qualify me to teach German? Possibly not (depending upon the school and district). So my specialist degree would not open the door to my chosen field (since it didn't need a degree in the first place), nor would it open the door to other fields as fall-back contingency career choices. I've paid just as much money for a degree that isn't as useful as a traditional one. A very dumb choice, from an economic point of view. (I should note that there are, in fact, a
few such degrees available. But if you look in detail at them, they're not actually degrees in "translation studies"; they're traditional language degrees with a few pre-chosen electives that focus on translation skills, and they're almost all run out of the relevant language departments. The faculty who run such programs are well aware of this problem with specialty focus, and are specifically setting this kind of program up as a wrapper around and including a traditional degree so as to not limit students' career options.)

I keep getting back to the same central question : "What would be the use of these `credentials'?"

Ramanujan couldn't have used them, ashe had a self-generated research portfolio that was more effective.

More typical students couldn't use them, as they don't have the necessary skills to generate such a portfolio -- and in order to get those skills, they will have to take a courseload that largely duplicates existing mathematics programs.

There is no student I can imagine for whom, if I were shown your "creative mathematics" program, I would not instead, without hesitation, recommend either "just skip this program and work on publishing your portfolio" or "this isn't an appropriate program for you; you should take a general mathematics course instead."

[The idea]

(1) No appropriate program exists

Originally posted by new drkitten
[...] The opening post is specifically discussing the degrees appropriate to Srinivasa Ramanujan, [...] You asked what sort of formal credentials would be appropriate to be awarded to him -- my response is : "none." [...] there are none available that would be appropriate.

Yes, exactly. Now, given that no existing program would be appropriate, why not consider the possibility that an appropriate program could be created in the future?

(2) Ramanujan learned what, when, and why?

I don't know what you mean by this statement:

Originally posted by new drkitten
He already had (much of) the knowledge given in a typical degree program, so taking the formal coursework would have wasted his [...] time [...].


In particular, I don't know what moment in time you have in mind when you use the word "already."

Perhaps you mean something like this:

Posted here for the first time, but not asserted by anyone
During a period of six months, Ramanujan taught himself much of the material in a typical mathematics degree program. During those six months, he only worked on standard assigned problems that have known solutions. Then, at the end of those six months, for the first time in his life, Ramanujan decided to attempt to solve a problem that no mathematician had yet solved.

He spent a week working on it and then almost gave up entirely on such pursuits because it seemed that he didn't have enough knowledge. Of course, if he had not had enough knowledge, then it would have been entirely appropriate for him to give up on such pursuits. However, he suddenly remembered a method he had learned during his six months of studying standard material. He applied the method, solved the problem, and at that moment he became a research mathematician.


(3) The need for knowledge: motivated learning

Originally posted by new drkitten
By definition, if you don't know enough mathematics to do research in it, you will need to learn more mathematics.


Suppose a student is at the beginning of learning to do mathematical research or in the middle of learning to do mathematical research. Let's suppose that, in the process of pursuing some particular research investigation, the student becomes convinced that, in order for the research to proceed smoothly, it is either essential or very important for the student to learn some particular topic in the body of existing mathematics.

Do you assert that if the topic is not covered in the standard undergraduate or graduate school curriculum, but is only covered in journal articles, then the student should feel free to study those articles? If, on the other hand, the topic is covered in the standard curriculum, then do you assert that the student should put aside the research and study everything in the standard curriculum that comes before the topic of interest?

Why should the student care so much where a topic is covered? Why should a student react in that manner based on where a topic is covered?

Suppose the student could learn all the really essential prerequisites in two weeks and learn the topic itself in a couple of days. Suppose a request for the teaching of that kind of two weeks and two days of material would be considered a normal request in a Creative Mathematics program. Would that be a bad thing?

(4) Collaboration to produce papers suitable for publication

If a person is actually doing research that has value, does it follow that the results obtained by the person who is working in isolation will be considered suitable for publication?

For example, suppose Ramanujan's reading told him that no known formula gets a certain job done. Suppose Ramanujan found a formula that seemed to get the job done. Ramanujan may have been far from having an actual proof that the formula does what it was supposed to do. Such explanations and justifications as Ramanujan produced might not have been suitable for publication.

Perhaps it would have been possible to publish a statement describing the formula and challenging people to prove or disprove that the formula works, but such a challenge might have been extremely short and not necessarily something that a math journal would consider worth publishing. However, if Hardy considered the formula to be interesting and the challenge to be worthwhile and if Hardy found a proof, then Hardy and Ramanujan could publish a paper together.

Would it be wrong for students in a Creative Mathematics program to collaborate with their instructors to produce papers suitable for publication?

(5) Early efforts and later efforts: increasing quality

Perhaps a student in a Creative Mathematics program might be producing papers that are not good enough to be published in a mathematics journal. This is particularly likely to be true in the student's first year or first two years in the program. The question is: would that indicate that the program is a scam? If the answer is "yes", then we might ask whether we have similarly demanding standards when it comes to other programs of study. Thus we arrive at a question already asked but not yet answered:

Originally posted by The idea
Consider some undergraduate courses for which the course work consists of mainly essay writing. If essays that receive an A grade are not suitable for publication in an academic journal, then can one conclude that the courses are a scam?

[drkitten]

Originally posted by The idea


Yes, exactly. Now, given that no existing program would be appropriate, why not consider the possibility that an appropriate program could be created in the future?

I have. And I have concluded that no such program can be created because there is no use for the credential such a program would offer.




Suppose a student is at the beginning of learning to do mathematical research or in the middle of learning to do mathematical research. Let's suppose that, in the process of pursuing some particular research investigation, the student becomes convinced that, in order for the research to proceed smoothly, it is either essential or very important for the student to learn some particular topic in the body of existing mathematics.

Do you assert that if the topic is not covered in the standard undergraduate or graduate school curriculum, but is only covered in journal articles, then the student should feel free to study those articles?


Yes. A student should be free to study anything at any time for their own personal enrichment.

If, on the other hand, the topic is covered in the standard curriculum, then do you assert that the student should put aside the research and study everything in the standard curriculum that comes before the topic of interest?


See above.

Suppose a request for the teaching of that kind of two weeks and two days of material would be considered a normal request in a Creative Mathematics program. Would that be a bad thing?


Yes -- it would be a bad thing, because it presupposes a) that a program in Creative Mathematics exists (which is in and of itself a bad thing), and b) that such a request would not be considered normal outside a Creative Mathematics program, which is false. Requests like this are normal and appropriate in any competently-taught program.






For example, suppose Ramanujan's reading told him that no known formula gets a certain job done. Suppose Ramanujan found a formula that seemed to get the job done.



By the way you phrase the supposition, Ramanujan's hypothetical finding is not appropriate for a pure mathematics forum, but for an applied one.

Ramanujan may have been far from having an actual proof that the formula does what it was supposed to do.

Doesn't matter in an applications forum. Electrical engineers used frequency domain analysis for decades before someone came up with the "proof" that it worked -- it even made it into textbooks.



Perhaps it would have been possible to publish a statement describing the formula and challenging people to prove or disprove that the formula works, but such a challenge might have been extremely short and not necessarily something that a math journal would consider worth publishing.


Your "perhaps" is unsupported by the facts.



Would it be wrong for students in a Creative Mathematics program to collaborate with their instructors to produce papers suitable for publication?


Yes, for the same two reasons cited above.

You have still failed to demonstrate either an area in which traditional mathematical education is deficient or an area in which your hypothetical Creative Mathematics provides any advantages whatsoever. Since the deficiencies of your Creative Mathematics program are pretty well established (it doesn't give the breadth of education necessary for non-research careers), I still can only conclude that it's a scam.

My central points remain





Anything you can do with a (hypothesized) Creative Mathematics degree, you can do without a degree. The degree adds nothing, creates no opportunities, and opens no doors.
The proposed Creative Mathematics degree is demonstrably inferior to the standard degrees in terms of employability outside of the research arena. The Creative Mathematics degree, in fact, closes a number of doors that would otherwise be open.
There is no part of the teaching of "Creative Mathematics" that is not already a standard part of the teaching of mathematics in general.

[The idea]

Instead of considering a separate Creative Research degree program, we could consider undergraduate science or mathematics COURSES in creative research.

For example, perhaps it could be arranged so that any math or science major would have the option of being enrolled in a creative research course in every semester of the program, just as a music major who wishes to focus on music composition might have the option of learning to compose, as part of a program of studies, in every semester.

[drkitten]

Originally posted by The idea
Instead of considering a separate Creative Research degree program, we could consider undergraduate science or mathematics COURSES in creative research.

Sigh. Been there, done that, bought the T-shirt. The course is usually entitled "independent study," and it's not confined merely to science and mathematics programs. I don't think there's a single post-secondary school with which I'm familiar that does not offer such courses as a matter, er, of course.

There are extensive national-level programs in place specifically to encourage this sort of this -- see, for example, this NSF link (http://www.nsf.gov/funding/education.jsp?org=NSF&fund_type=1), which lists nearly thirty programs supporting specifically undergraduate research or the incorporation of research into the undergraduate curriculum.

Check out the specific wording of the REU (Research Experiences for Undergraduates) program

NSF:
The Research Experiences for Undergraduates (REU) program supports active research participation by undergraduate students in any of the areas of research funded by the National Science Foundation. REU projects involve students in meaningful ways in ongoing research programs or in research projects designed especially for the purpose. This solicitation features two mechanisms for support of student research.

Of course, not all students want to do this sort of research for credit, which is why a lot of places also offer REU-style programs as work-study programs, where students work (on faculty-directed research programs) for wages instead of for credits, which can be a useful way to spend the summer.

At my department, more than fifty percent of our undergraduates are involved in such a REU over the course of their studies.

Which returns me to my central point, since the beginning of this thread:

"There is no part of the teaching of "Creative Mathematics" that is not already a standard part of the teaching of mathematics in general."