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See at least Emmy Noether :
was a German mathematician known for her contributions to abstract algebra and theoretical physics. She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading mathematicians of her time, she developed ...
73
The other answer is correct. In addition, there is significant evidence that Fermat did not have a proof of the theorem now known as Fermat's Last Theorem.
First, we should note that Fermat was not a professional mathematician, only an amateur. He never published any mathematics himself. With just that, it would not seem strange that he did not publish his ...
56
It seems ball lightning was disbelieved by scientists until around 1960. See Wikipedia .
I knew a geologist who told us how his eye-witness account of ball lightning had been ridiculed. He had learned not to mention it when he interviewed for jobs as a professor of geology.
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In 1726's Gulliver's Travels, Jonathan Swift mocked the learned scientists of Britain for not having solved the Longitude problem: Figure out a way to keep track of one's east-west location to within a mile after making a round-trip across the Atlantic. This was one of the most important scientific challenges of the 18th century. The British Parliament ...
48
Maryam Mirzakhani, the first Iranian and first woman to win the Fields medal, died of breast cancer in July 2017. She was only 40 years of age.
43
Évariste Galois (1811 - 1832), aged 20, was killed in a duel. He is known for Galois theory and he wrote his most notable results down in the night before the duel. You can also find more information about him and why he was killed in this question.
Niels Henrik Abel (1802 - 1829), aged 26, died of tuberculosis. He is mainly known for proving the Abel-...
41
An immediate motivation of Cantor to work on what became set theory was his earlier work on trigonometric series. To solve a problem in that domain he considered the set (a closed set) of zeros of such a function, then the derived set of this set, the derived set of this set and so on. This is all still classical, but then had to go a step beyond that to ...
41
Perhaps because of its youth, the mathematical end of Computer Science has several notable women in its history.
Sheila Greibach was a pioneer in the field of formal language theory, particularly in the area of context-free languages. At the time, that would have been considered more a branch of mathematics, as Computer Science wasn't really a thing of its ...
37
Srinivasa Ramanujan (1887 - 1920) died at the age of $32$, according to Wikipedia the cause was:
A 1994 analysis of Ramanujan's medical records and symptoms by Dr. D.A.B. Young concluded that it was much more likely he had hepatic amoebiasis, a parasitic infection of the liver widespread in Madras, where Ramanujan had spent time. He had two episodes of ...
36
Lagrange enrolled to the university at the age of 14, to study law. But he quickly switched to mathematics. According to his biography, his mother was surprised when the French ambassador presented himself to congratulate her and give her the prize of the Paris Academy which Lagrange won in a public competition (by correspondence).
(His mother was surprised ...
33
Yes, it is true. Fermat's own copy was used in the publication
of Diophantus by Fermat's son Samuel,
and he included Fermat's notes. The original with Fermat's handwriting is lost.
https://www.joh.cam.ac.uk/library/special_collections/early_books/fermat.htm#:~:text=When%20reviewing%20his%20copy%20of,to%20fit%20in%20the%20margin.
(The page with his most ...
31
That's John von Neumann, about whom George Pólya wrote:
There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the ...
30
Bernhard Riemann (1826–1866) died at the age of 39. Paraphrasing the following from Wikipedia:
The son of a poor pastor, he enrolled at age 19 at the University of Göttingen to obtain a degree in Theology. There Gauss urged him to become a mathematician. When he was 31, there was an attempt to promote him to extraordinary professor status. When he was 33, ...
30
This isn't a topic I'm familiar with, just something I've read on Quanta, but according to this article, Richard Kershner of Johns Hopkins claimed to have a complete classification of convex pentagon tilings in 1968, though he notably said that "The proof that the list in Theorems 1 and 2 is complete is extremely laborious and will be given elsewhere" and ...
30
It is a play of words by Charles Babbage. Deism was a religious belief or rather a movement promoting the idea that God exists but it does not interfere with whatever happens in this world. This old philosophy according to the Wikipedia "...asserts God's existence as the cause of all things, and admits its perfection (and usually the existence of ...
29
There is no way that Fermat could have had anything approaching the now commonly-accepted proof. Almost none of the concepts in that proof were known in any form in Fermat's time.
Further, Fermat is known for publishing very few of his proofs; almost none survive today, and even in the 1800s there was significant doubt in the mathematical community that he ...
29
First hand testimony and insightful thoughts on Ramanujan's background and way of doing mathematics can be found in Hardy's lecture Indian Mathematician Ramanujan. Hardy is the British mathematician who first appreciated the full extent of Ramanujan's talent, knew him well personally, and had a fruitful mathematical collaboration with him.
Here is Hardy's ...
28
According to an American Scientist article (Gauss' day of reckoning by Brian Hayes, Volume 94 p. 200) mentioned in the comments, the original source for this story, or at least a story very similar to it, was Gauss zum Gedächtnis, a memorial written very soon after Gauss' death by Wolfgang Sartorius, a colleague of his at Göttingen (however, I am not sure if ...
27
There is Sophie Germain's theorem, a theorem in number theory, related to Fermat's last theorem and proved by the French mathematician Sophie Germain (1776-1831).
27
There is the work by Ada Lovelace.
In the annotations, which were called "Notes", Ada Lovelace described how the analytical engine could be programmed and gave what many consider to be the first ever computer program.
In particular, she found and corrected a bug in Babbage's algorithm for computing Bernoulli numbers:
We discussed together the ...
26
Karatsuba's own report can be found in his 1995 paper Сложность вычислений (Complexity of computations). The phrasing he uses is "сильно взволновалo", which Google does translate as "very excited" or "greatly agitated". But we can see the usual dynamic of an anecdote in the making on the Reddit thread, where Kolmogorov is "...
25
This is a common claim which has been repeated enough times that one can find many sources claiming it to be true. However, this doesn't seem to be corroborated by accounts of the time or serious biographies. Indeed, Helen M. Walker, in her 1934 biography of De Moivre in Scripta Mathematica Volume II, Number 4, August 1934, (reproduced here freely on Google ...
25
I think a famous example is the Monty Hall problem` https://en.wikipedia.org/wiki/Monty_Hall_problem about switching doors.
The problem was answered correctly by Marilyn vos Savant, but she got
baskets of letters from experts that she is wrong.
25
The man is Paul Erdős. As pointed out by the OP in the comments, his "nomadic" lifestyle is briefly mentioned in the Brown Numbers - Numberphile video, 3.05-3.30. It is also concisely described in Currey's book Daily Rituals read in this YouTube video that refers to Hoffman's popular biography The Man Who Loved Only Numbers, which is featured in ...
23
The issue is thorny ...
According to Morris Kline, Mathematical Thought from Ancient to Modern Time. Volume I (1972), page 272 [only entry of the Subject Index regarding : mathematical Induction] :
The method was recognized explicitly by Maurolycus in his Arithmetica of 1575 and was used by him to prove, for example, that $1+3+5+ \ldots + (2n+1)=n^2$. ...
23
How To Solve It was originally published in English in 1945 by Princeton University Press in English, after being rejected by three other U.S. publishers.
However, the original text at least started out in German as a draft. Pólya began writing the draft prior to 1940, while he was living in Zürich, and presumably initially intended for the text to be ...
23
Mikhail Yakovlevich Suslin (1894-1919).
Known for "Suslin sets" and the "Suslin hypothesis".
He died of typhus following the Russian Revolution. He was 25.
LINK
I recently read a very interesting book Naming Infinity about the Moscow school of mathematics.
23
Eugenio Elia Levi (1883-1917), the one of Levi decomposition in Lie algebras, was killed in action during WWI to which he participated as a volunteer. It is often said that his early death played a role in the Italian school of geometry leavng largely unexplored the subject of Lie algebras and Lie groups.
Andreas Floer (1956-1991) who introduced what is ...
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