As in the movie “Good Will Hunting” have any math super geniuses ever been discovered in real life who had little if any formal math background?
I ask because mastering complex math seems to be highly dependent on building on prior work and not someone anyone, regardless of intelligence, could come to cold and be a superstar.
Srinivasa Ramanujan was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Living in India with no access to the larger mathematical community, which was centred in Europe at the time, Ramanujan developed his own mathematical research in isolation. As a result, he sometimes rediscovered known theorems in addition to producing new work. Ramanujan was said to be a natural genius by the English mathematician G. H. Hardy, in the same league as mathematicians such as Euler and Gauss. He died at the age of 32.
A truly extraordinary individual.
The only example I can think of off the top of my head is Srinivasa_Ramanujan
Edit: Ninja’d by Blake
I read at least one case of a primary school student who was discovered to be using his own brand of calculus to solve 5th grade math problems. Well, that’s not so strange. Straight division IS differentiation.
The Ramanujan story gets somewhat to massively exaggerated, depending on whose doing the telling. He studied mathematics in High-school and College, he certainly doesn’t count as someone with “no mathematical education”.
He had far les formal education than the character in Good Will Hunting, who also had high school level education. Ramanujan however had just 6 years of school education, compared to the ~16 years of the character in the movie.
His tertiary education was undertaken peicemeal after his talents were already well proven.
He certainly counts as a mathematics prodigy who had little formal math background.
George Green (of Green’s Theorem fame) fits the bill. According to the Wiki article, he had but one year of formal education, and that at age 8! In terms of mathematics, he was entirely self-taught.
According to this biography of Green (from the excellent MacTutor site), Green commenced his undergraduate education at age 40 by which time his talents had become more widely appreciated and he had been encouraged to do so.
Intrigued. How’s that?
Ramanujan was not brought up in a poor family. His family were Brahmins, so they were relatively high in the caste structure. His father was a clerk. Look, even being able to read in that time and place meant that you were above average in status. At that time being a clerk was a relatively good job. It was then the sort of thing that one could get use to get promoted to higher level jobs. Ramanujan was recognized even as a child as being brilliant. He went to college. He tried college twice. Each time he only spent a year there because he spent all his time on studying math and ignored his other courses, so they wouldn’t continue his scholarship.
Other mathematicians found him a job as a clerk where he could do mathematics in his free time, since they all recognized that he was brilliant. He had already published one paper before he tried to contact G. H. Hardy at Cambridge. Other Indian mathematicians suggested that he contact Hardy because they thought that his work was similar to that of Hardy’s.
He did not have just 6 years of formal education.
He had lots of formal training in math.
His brilliance had been recognized many times by other Indian mathematicians before he wrote to Hardy.
Read the Wikipedia entry. It’s all there.
So what you’re saying is that he was a completely self taught genius who grew up in poverty with less than 6 years of formal education, completely unknown before his letters to G.H. Hardy introduced him to the civilized world? What a fascinating story!
And, if I understand correctly, he hung around with a bunch of neighborhood kids, getting into fights and drinking beer, until a funny-but-wise teacher (with his own demons) inspired him to take the plunge and write to Hardy.
I guess there are no real examples, but if it is going to happen it will be in combinatorics where it is conceivable that an uneducated person might have a unusual insight. It seemed clear to me that what Will Hunting was purported to have done is in combinatorics.
Speaking of which you might want to check out the biography of Mary Celine Fasenmyer, whose PhD thesis was rediscovered by Herb Wilf and Doron Zeilberger and sort of revolutionized the summation of hypergeometric series, one branch of combinatorics. While obviously not uneducated, her methods were entirely unprecedented. See Mary Celine Fasenmyer - Wikipedia. Also see the Wilf-Zeilberger book A=B (it is available free online) to read about it.
The one whose first sentence includes the words “with almost no formal training in pure mathematics”?
Maybe it’s a question of how you define “formal training in math.” In any case, the “no math education” of the thread title certainly doesn’t apply literally to Ramamnujan.
It appears that what Will Hunting is supposed to be working on is something in graph theory, but I guess you could consider that to be part of combinatorics:
http://www.ams.org/news/math-in-the-media/mmarc-hunting-review
According to that, the following reference is approximately what he was working on:
Frank Harary and Geert Prins, The number of homeomorphically irreducible trees, and other species, Acta Math. 101 (1959), 141-162.
It might be worth pointing out that a Will Hunting-like incident really happened to mathematician George Dantzig, though he certainly didn’t qualify as having no mathematical training.
The Wikipedia entry is inconsistent or muddled in its terminology, I think. It talks about the fact that he studied math in college. It also claims that he had “almost no training in pure mathematics.” I don’t know what it means by that. Perhaps it means that anything up to second-year calculus is not pure mathematics. It also makes it clear that up through high school he taught himself the math he would have learned in his classes years before he would have studied it in school. Big deal. I taught myself a lot of math up to high school. I went to a worthless high school. I still didn’t even make it to a Ph.D.
An current American equivalent of Ramanujan would be somebody who went to a lousy high school and who taught himself all the math he was supposed to be learning there years before taking it in classes. All his teachers in elementary and high school recognized how smart he was. He then went to college, where his math professors recognized how smart he was. He flunked out because he didn’t do any work on his other classes. He went to another college and flunked out again for the same reason.
This by itself is, to be honest, no big deal. A few people do this every year, and they are not generally child prodigies. Some of them turn out to be burnouts. Some of them eventually go back to college and even get Ph.D.'s. What’s different about Ramanujan is that he then started turning out brilliant theorems, which nearly all those people didn’t do. Being thought utterly brilliant up through graduating from college doesn’t mean that you’re going to be a Fields medalist or a Nobel Prize winner (for those subjects that have Nobel Prizes) or anything else at the top of your field. You may like to think that that brilliant kid who went to your high school who seemed to be so much smarter than everyone else will surely win a Nobel Prize or something, but there are a lot of brilliant people out there, so the chances that the one you know is the best is pretty small.
Describing it as a ‘Good Will Hunting-like incident’ seems a bit of an exaggeration to me. The solver was a PhD student in mathematics (and the son of a math professor), who was taking the class, not some unknown prodigy of a janitor. (And the student only solved the two problems because he mistakenly thought they were homework assignments).
For fuck’s sake, if you want to have a purely semantic debate do it in another thread. Ramanujan had essentially no formal training in math theory and independently derived a number of existing theorems as well as producing a large quantity of novel theorems, identities, and conjectures, the vast majority of which were later determined to be correct. While Ramanujan is not the only self-taught mathematician to have made significant contributions to modern mathematics theory (in addition to the already mentioned George Greene I would add Oliver Heaviside, Carl Gauss, and Pierre de Fermat as being essentially self-trained in math theory) the breadth of his contributions are basically unmatched by any self-taught mathematicians, and rival the entire body of work of many significant mathematicians who practiced for decades. He may not be unique, but he is certainly the best documented case of a self-taught mathematical genius.
As for math being largely built upon prior work, that is entirely true, and why Ramanujan’s work is so impressive. However, the holes in his education also showed; he re-derived many basic theorems and made a number of wrong steps that a comprehensive basic education in math theory would have avoided. He could doubtless have done even better work with a proper foundation.
Stranger
One other point that has been made about Ramanujan’s career (I saw it in a Numberphile video) is that due to his uneven and delayed education (as indicated by the number of wrong or duplicative results he produced, and his unconventional presentation), he did not have any consistent professorial guidance until he went to Cambridge at the age of 25 – the age at which most mathematicians have already done their most original work. While Ramanujan might have been one of those exceptions who never stopped doing his best work, it’s likely that he wasted some of the best years of his life on work that would have been weeded out by a competent adviser.
I say this, of course, as a man who has forgotten most of calculus, and who couldn’t follow the most elementary of Ramanujan’s results if he tried.
He was 40320 years old?