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Are there any examples of mathematicians have produced good research, having done poorly in mathematics exams?

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    $\begingroup$ Not an answer (not a mathematician, and false anyway). We used to hear the claim that Albert Einstein did poorly in school. But in fact that claim was due to a misunderstanding of the grading system (whether 1 is the lowest grade or the highest grade). $\endgroup$ – Gerald Edgar Oct 26 '15 at 1:19
  • $\begingroup$ Einstein actually didn't pass the university once. $\endgroup$ – Takahiro Waki May 29 '16 at 22:17
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Well Ramanujan was such a mathematician. He was not so poor in math exams but he scored somewhat unbelievable marks in mathematics. In $1907$, he appeared in FA Examination at Pachaiyappa College, after studying privately. He got $85$ out of $150$ in mathematics and failed in English, Sanskrit, Physiology and History. Now one would expect that Ramanujan would get $100\%$ by analyzing his ability to tackle hard problems, but it was not so. But as we all know, he was very good at research. The reason for his scoring low marks in examinations are discussed here by Berndt.

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The most famous case of this sort is Galois failing the entrance exam to Ecole Polytechnique.

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    $\begingroup$ Appreciate your information; would you please point out some related sources so that I can check them out myself? Thank you. $\endgroup$ – Gary Moore Oct 26 '15 at 12:36
  • $\begingroup$ I remmember reading that he failed twice and he trew the eraser at the examiners, who apperantly must have missjudged him. $\endgroup$ – MBN Oct 26 '15 at 13:12
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    $\begingroup$ Throwing an eraser at the examiners is exactly what qualifies his as "not good at taking the exams". Try it yourself and see what the result will be. $\endgroup$ – Alexandre Eremenko Oct 26 '15 at 19:41
  • $\begingroup$ @Gudson Chou: for the sources, you may begin with Wikiedia, or L. Infeld's novel on Galois. $\endgroup$ – Alexandre Eremenko Oct 26 '15 at 19:42
  • $\begingroup$ There are some details about the story in the book Fermat's Enigma, by Simon Singh. (Based on other things that Singh discusses that I know more about, I wouldn't trust Singh on every detail--the book is not a work of extremely careful scholarship--but I would guess that he's got the overall story about Galois about right. Quite entertaining, in any event.) $\endgroup$ – Mars May 15 at 15:09
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Newton somewhat infamously failed his examinations at Cambridge: he was questioned orally about the proofs in Euclid, and since he had looked at Euclid once and thought it a total waste of time, and had just rederived all the results himself, he had no idea how to answer things like "How does Euclid prove X.1?"

Somehow he was awarded the scholarship anyway - presumably someone noticed that they were dealing with Isaac Newton.

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    $\begingroup$ I am afraid that this story is made up. What is the reference? It is known from many sources that Newton studied Euclid very carefully. $\endgroup$ – Alexandre Eremenko Oct 26 '15 at 19:43
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    $\begingroup$ Whiteside reports Conduitt's account of this (The Mathematical Papers of Isaac Newton, v.1, p18), and does not dispute the story (as he frequently does with other passages of the account). Newton's detailed study of Euclid came later. $\endgroup$ – Chappers Oct 26 '15 at 22:30
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G.H. Hardy. From http://www-history.mcs.st-and.ac.uk/Biographies/Hardy.html

"While at Winchester Hardy won an open scholarship to Trinity College, Cambridge, which he entered in 1896. At Cambridge Hardy was assigned to the most famous coach R R Webb. He quickly realised that the point of the training was simply to achieve the best possible marks in the examinations by learning all the tricks of the trade. He was shocked to discover that Webb was not interested in the subject of mathematics, only in the tricks of examinations.

Hardy was placed as fourth wrangler in the Mathematical Tripos of 1898, a result which continued to annoy him for, despite feeling that the system was very silly, he still felt that he should have come out on top."

Wikipedia adds "Years later, he sought to abolish the Tripos system, as he felt that it was becoming more an end in itself than a means to an end."

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    $\begingroup$ I'm sorry, fourth wrangler is very far from not good at taking exams $\endgroup$ – Gerald Edgar Oct 26 '15 at 20:53
  • $\begingroup$ @GeraldEdgar: The question specifically clarifies "By "m was not good at taking exams" I mean that m was not the most outstanding student". I'm understanding the question to be about the failure of exams to detect the best mathematicians, and Hardy's story is a good example. $\endgroup$ – Stopple Oct 26 '15 at 21:03
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    $\begingroup$ And remember that Hardy was originally drawn to mathematics as something to be better at than the others in his school. The appeal of pure mathematics came to him at a later point, which he himself claims was when reading Jordan's Cour d'Analyse. And on an objective note, Hardy was quite right about the form of the Tripos he had sat: it was much the same as that which had been holding English mathematics back for the last hundred years. $\endgroup$ – Chappers Oct 26 '15 at 22:49

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