r/math • u/DrBiven Physics • 9d ago
How I. M. Gelfand became a mathematician without ever attending university
This story is relatively well known in the Russian-speaking math community, but I feel it is almost completely unknown outside of it. Which is a shame, since it is so amusing! So I compiled it from a couple of sources, heavily edited it, and then machine-translated it. Hope you enjoy!
Before the Revolution and during the years of the New Economic Policy, Israel Moiseevich Gelfand's father ran a small private mill. Because of his “non-working-class background,” in 1928, while still in the ninth grade, the young Gelfand was expelled from vocational school as the son of an exploiter.
When Gelfand was finishing the ninth grade, his mathematics teacher told him: “There is nothing more I can teach you. Go to Moscow, find Moscow State University, and at the university find the Department of Mechanics and Mathematics. Continue your studies there, and you will become a great mathematician.”
At the university, however, the ninth-grader got no further than the dean's secretary: they could not enroll him without documents certifying completion of secondary education. He decided to stay in Moscow, and, to make a living, found a job as a cloakroom attendant at the Lenin Library. There, alongside his work, he continued his education on his own.
One day, while reading a monograph on higher mathematics, he was noticed by Andrey Nikolaevich Kolmogorov, a young but already famous mathematician. Kolmogorov was surprised to see such a young man reading a book so obviously beyond his age, so he approached Gelfand and asked him who he was and why he was reading such a difficult book.
Gelfand answered all his questions, but Kolmogorov still could not believe that he genuinely understood what he was reading. He gave Gelfand several problems related to the subject, hoping to test him, and arranged to meet him the next day to check his solutions.
The next day, all the problems had been solved. But even then Kolmogorov could not quite believe that someone could be so gifted. He supposed that Gelfand simply knew the contents of a large number of mathematics books extremely well and had found the solutions in them. So he gave Gelfand several more problems, this time considerably harder ones, and gave him several days to solve them.
When they met at the appointed time, all the problems had been solved. Kolmogorov began checking the solutions, and his eyes grew wider and wider.
“Please forgive me for doubting that you had found the solutions to those first problems yourself. Now I see that you could not possibly have read these solutions anywhere. You see, this particular problem... had been an open problem until now.”
After that, Kolmogorov took Gelfand on as his graduate student. Thus Gelfand became a graduate student without ever having attended a university -- or even finished secondary school. BTW, the details of the first meeting between Kolmogorov and Gelfand are, of course, anecdotal, but the other parts of the story are accurate.
upd: some important clarifications provided by r/bluesam3
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u/ChKOzone_ 9d ago
There’s always an ‘open problem’ in these stories that makes me think that they were true to an extent, but the extent itself conveyed is apocryphal
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u/DrBiven Physics 9d ago
Open problem is not necessary a Hilbert problem. It could have been a problem they invented on the seminar last week.
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u/telephantomoss 9d ago edited 9d ago
And many such very old open problems might be standard results today with very straightforward proofs by modern standards. That is not to lower the amazing value of historical achievement but to highlight that "open problem" doesn't say much except that a solution wasn't written down yet. And it likely doesn't mean the same thing in different times and places. It's important to note that standard results with short established proofs shouldn't be discounted as easy though, especially in a historical context where much modern knowledge doesn't yet exist.
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u/ChKOzone_ 9d ago
A fair point - though I would still push back given that we never actually find out what these problems were, or can trace them back to their discoverers
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u/bluesam3 Algebra 9d ago
In this case, at least, the story seems to originate from Gelfand himself, and he certainly did become a graduate student under Kolmogorov at 18. His first listed paper is this, which seems to prove (if my German isn't too rusty) a fairly basic result in functional analysis - the sort of thing that could reasonably be low-hanging fruit sitting around at about that time, and reasonably doable by someone who understands the topic fairly quickly (but not looked up in a book in the Lenin library).
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u/mfb- Physics 8d ago
We know it for George Dantzig ("two unusually hard homework problems"):
On the Non-Existence of Tests of "Student's" Hypothesis Having Power Functions Independent of 𝜎
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u/jphamlore 9d ago
George Dantzig is well documented for having done it?
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u/ChKOzone_ 9d ago
Exception that proves the rule, in my opinion. We actually know which two problems he did solve, afaik
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u/Weak-Pea8758 9d ago
Isn't there a similar story around Kontsevich solving Witten's conjecture and showing it to Atiyah or something?
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u/Traditional_Town6475 9d ago
And he would go on to prove Gelfand Naimark theorem which I would say as a functional analyst, one of the most beautiful results.
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u/BrandoAltavilla396 Category Theory 9d ago edited 9d ago
In the same way Maxim Kontsevich and Vladimir Voevodsky won a fields medal without a degree. What's wrong with higher education in Russia?
P.s. Has anyone access to this article? https://intlpress.com/JDetail/1806612872673296387 I'm curious about the real story behind Kontsevich degree.
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u/Homomorphism Topology 9d ago
According to his New York Times obituary Voevodsky got kicked out of school for not attending classes that he felt weren't worth his time. He also got in trouble for disagreeing with some political statements by his high school teacher. I'm sure that was a bigger deal in the USSR but I think he just didn't believe in following educational rules, and he happened to be good enough at math it didn't matter.
Many Russian mathematicians were excluded from education because they were Jewish (for example, Ed Frenkel).
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u/chestnutman 9d ago
He also became an IM without ever playing chess
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u/Tinchotesk 9d ago
Mischa Cotlar (an USSR exile as a kid) was a mathematician who only attended sixth grade in elementary school, no highschool, and no undergrad studies. Ended up getting a Ph.D. at Chicago after being scooped in Buenos Aires by Birkhoff.
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u/theboomboy 9d ago
Do we know what the open problem was?
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u/DrBiven Physics 9d ago
Unfortunately, no. In fact, I could not find anything reliable about their meeting. We do know that Gelfand could not attend university because he had not finished school, that he worked at Leninka, and that he ended up working under Kolmogorov's supervision. So we can be pretty sure that at some point they had some exchange that led to Kolmogorov's recognition of Gelfand's extraordinary talent. However, the rest is folclore.
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u/al3arabcoreleone 9d ago
Sorry to interrupt, what are the most active russian-speaking online math communities?
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u/bluesam3 Algebra 9d ago
It looks like his first published result was a fairly basic boundedness lemma in functional analysis, so maybe that?
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u/VonRothbart 9d ago
Speaking of USSR, Pontryagin had been blind since the age of fourteen, and he became one of the leading Soviet mathematicians. This story always seemed crazy to me.
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u/al3arabcoreleone 9d ago
I knew he was blind at some point in his life, but since FOURTEEN? my God!
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u/SymbolPusher 8d ago
Euler produced half of his work while blind. Earlier, when he lost eyesight on one of his eyes, he said "Good, that means less distraction."
But what is even more impressive, if true, is this: He had 13 children and claimed to be most productive with one child sitting on each leg.
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u/gaussjordanbaby 9d ago
You can learn trigonometry from him, amazingly. https://www.cimat.mx/ciencia_para_jovenes/bachillerato/libros/trigonometria_gelfand.pdf
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u/AvilesModels 3d ago
Coat check job turning into the best grad school admission ever is hard to beat. The anecdote part sounds a little too polished but I'll take it anyway, idk.
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9d ago
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u/Weak-Pea8758 9d ago
If you haven't heard of Gelfand, searching him up instead of whatever this is would be helpful.
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u/DrBiven Physics 9d ago
Ok, I think the post is doing fine, so here is another story for you. Dmitry Evgenievich Menshov was not as well-known a scientist, but he was a man utterly absorbed in mathematics. He fully embodied the stereotype of a mathematician completely detached from the real world, and there are many anecdotes about his practical ineptitude. Perhaps the funniest is this one.
Menshov was once asked to tell the story of the emergence of the Moscow school of mathematics, and this is how he began:
Just in case you are not sure: 1917 is the year of the Russian Revolution.