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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 ...
48
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.
45
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 ...
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 ...
32
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.
29
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-...
27
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 natural law ...
26
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
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 ...
25
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).
25
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 ...
24
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 ...
23
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.
22
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 ...
21
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 ...
21
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 ...
21
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 $1+3+5+ \ldots + (2n+1)=n^2$. ...
21
Take meteorites, for instance. By the end of the XVIIIth century, educated people “knew” that no rock found on Earth could possibly have fallen from the sky, in spite of the evidence (eyewitnesses included) for their existence. As science journalist Kat Eshner wrote, “eighteenth-century rationalists […] thought the stories of rains ...
20
I found an existence theorem for the Cauchy Problem in partial differential equations which has been proven by Sofia Vasilyevna Kovalevskaya.
19
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.
19
Let me clarify a couple of things. No student of Pythagoras discovered irrational numbers, although this is a common misconception, Pythagoreans and even Euclid did not associate numbers with geometric points or segments, the only numbers available were positive integers. Instead they had magnitudes of different dimensions (segments, areas, volumes), and ...
19
Just warning not to include pre-1920s medicine (and a lot of medical mantra thru the 20th century), as there was little to no science involved amongst physicians. Just look at how difficult it was for Lister et. al. to convince hospitals, midwives, etc. to wash their hands and sterilize operating theatres.
There are dozens of incorrect anecdotes ...
18
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 ...
18
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, ...
17
The first evidence of zero is from the Sumerian culture in Mesopotamia, some 5000 years ago (source: Robert Kaplan, The Nothing that is: a natural History of Zero).
It is interesting to note that different cultures discovered the concept of "zero" independently. The Babylonians, the Mayans, the Chinese and the Hindus all introduced symbols for zero. They ...
17
I was originally looking for the first documented reference of another contemporary mathematician calling Gauss the prince to no avail. What we do know is that he was considered, by at least many of his contemporaries (by some accounts all), to be the greatest among them.
I do see in The Beginnings and Evolution of Algebra, Volume 19 I. G. Bashmakova, G. S....
17
Really, it's because that was the social protocol at the time.
From the Wikipedia article on polymaths,
Many notable polymaths lived during the Renaissance period, a cultural movement that spanned roughly the 14th through to the 17th century and that began in Italy in the late Middle Ages and later spread to the rest of Europe. These polymaths had a ...
17
Scientists and mathematicians rarely self-report on psychological circumstances of their creative process, at best presenting a rationalization of their path to discovery. Kekule's dream and Kepler's vivid struggles described in Astronomia Nova are exceptions (and there are doubts that Kepler's descriptions are factual, see How did Kepler "guess" ...
17
Michael Ventris, an amateur philologist, (he was an architect) managed to decipher the Mycenean script known as Linear B, a problem that professional specialists had been trying to solve for decades.
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