A perfect example would be Srinivasa Ramanujan.

It is known that the conventional community throughout history have been close-minded towards great men of science and mathematics (e.g., Galileo).

Srinivasa Ramanujan being one of them. Einstein is another one.

A lot of history's math and science problems were solved in what would have been considered heresy.

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    $\begingroup$ Ramanujan was not ignored. He was invited to England, where he did some outstanding work with Hardy. $\endgroup$ – Alexandre Eremenko Mar 29 '19 at 1:45
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    $\begingroup$ This is way too broad for a reasonable answer. Ignored when and by whom? For how long? They were, obviously, not ignored forever, if we now remember their names as the "top". There are innumerable examples of mathematicians who were "ahead of their time" in some or all of their work, e.g. Madhava, Leibniz, Galois, Bolzano, even Euler (non-standard analysis, graph theory) and Poincare (algebraic topology). $\endgroup$ – Conifold Mar 29 '19 at 10:02
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    $\begingroup$ Einstein was ignored? In what alternate universe (which he may or may not have agreed could exist)? $\endgroup$ – Carl Witthoft Mar 29 '19 at 12:56
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    $\begingroup$ Bernhard Bolzano did not get very far during his life. But I think this was not because his ideas were un-conventional. His ideas were ignored because they were unknown. And that was partly because he got on the bad side of his government (the Austro-Hungarian Empire) and could not publish. $\endgroup$ – Gerald Edgar Mar 30 '19 at 12:50
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    $\begingroup$ Einstein was not ignored and recognized rather quickly. His work on special relativity was published in 1905 and was recognized after 1905. He became international renowned after the solar eclipse experiment in 1919. $\endgroup$ – hermes Mar 31 '19 at 2:15

Georg Cantor was a German mathematician who created set theory that has become a fundamental theory in mathematics. However, his original work on infinity and ordinal number was considered unconventional or even unorthodox, which was under heavy attacks from some of the famous contemporary mathematicians for a long time.

Another example is Charles Sanders Pierce, an American philosopher and logician who made important contributions to logic, relation theory, pragmatism, semiotics and so on. But his work was largely ignored in his lifetime and he could not even find an academic position. Only after 1920s, his original work was rediscovered that he is recognized as one of the most original and versatile of American philosophers and America's greatest logicians.

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    $\begingroup$ Cantor's work was criticized but certainly not IGNORED. $\endgroup$ – Alexandre Eremenko Nov 22 '19 at 2:06
  • $\begingroup$ Yes, it was initially ignored because Cantor's papers could not be published in major journals at that time. But fortunately, his work was widely accepted after 1897, when Cantor received high praises in the first ICM. So his work was recognized before his death which is a good fortune. $\endgroup$ – hermes Nov 22 '19 at 17:53

Hermann Cäsar Hannibal Schubert invented what is called "Schubert calculus" (publ. in 1879). His highly original method was not sufficiently justified. One of the Hilbert problems (1900) was to justify Schubert Calculus. This was achieved in principle in the 1920s and the interest to the Schubert Calculus declined, and it was never very strong before that.

It experienced a strong revival in the 1970s when mathematicians started to check and re-compute Schubert's results sometimes using computers. Nowadays it is a vigorously developing area of mathematics with many applications inside and outside mathematics. Schubert's book has been recently reprinted. Schubert himself was not sufficiently recognized in his lifetime and worked as a high school (gymnasium) teacher.

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    $\begingroup$ OK, but what is unconventional, and what evidence is there that it was ignored on those grounds, rather than simply not being complete, or not having a known application? $\endgroup$ – Carl Witthoft Mar 29 '19 at 12:57

Not necessarily ignored, but A. Robinson's non standard analysis wasn't much well-received either, most probably because he relied on metamathematical machinery to set it up

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  • $\begingroup$ Non standard analysis is not recognized as today, and probably will not forever. $\endgroup$ – hermes Apr 18 '19 at 17:33
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    $\begingroup$ @MathWizard: To the contrary, NSA is a well-established and recognized area of mathematics, just it requires too much background in logic (model theory) to be taught to undergraduates in most places. It is also occasionally useful even for proving theorems in "standard" areas of mathematics such as group theory. See for instance, "The Nonstandard Treatment of Hilbert's Fifth Problem", by Joram Hirschfeld, Transactions of AMS, Vol. 321, No. 1 (1990), pp. 379-400. Or: "Gromov's theorem on groups of polynomial growth and elementary logic", by L. van den Dries and A. Wilkie. $\endgroup$ – Moishe Kohan Nov 8 '19 at 14:16
  • $\begingroup$ @Moishe Kohan, I disagree with you on NSA is a well-established and recognized area of mathematics. Except for a few proofs as you mentioned, it has found no use in Calculus in general. The reason could be that infinitesimal is fundamentally different from number, and so can not be put into an extended field of number. Even one of its biggest contributors, Jerome Keisler acknowledged this fact. $\endgroup$ – hermes Nov 8 '19 at 18:05
  • $\begingroup$ Of course, one can so easily add few answers to each claim, but to save the space links were provided in order that historian people understand those simple facts first, get convinced that the true mathematics is basically discovery and not simply human definitions based on the axiom of choices where the axioms are in clear contradictions with greater elementary theorems and fundamental principles of mathematics that is purely based upon true understanding for real numbers that can never be created from chosen definitions that are no different from being wrong decisions nowaday, so what is ..? $\endgroup$ – Bassam Karzeddin Jan 8 at 14:26
  • $\begingroup$ I think my answers are better viewed here in many thousands of views as a public publication since this is impossible to be official at this early stage of their older history where so many others have truly well-understood them with quora.com/content?content_types=answers and p people would ultimately go every were including this site that hides them aimlessly to know their simplest truth $\endgroup$ – Bassam Karzeddin Jan 13 at 18:49

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