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What recent discoveries have amateur mathematicians made?

Dear overflowers

Out of curiosity: do you know any famous papers and/or results by non professional mathematicians? (I realize that 'non professional mathematicians' is quite vague, so let's also say 'amateur'?) Thank you for your answers!

Edit: I meant of course math papers. Also, I am interested in somewhat recent examples, say the last 2 centuries.

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  • $\begingroup$ I assume the OP means famous math papers/results by amateurs.... $\endgroup$
    – Barry Cipra
    Commented May 31, 2013 at 13:13
  • $\begingroup$ Could we limit the discussion to somewhat recent (say 20th century and later)? If not there are many "half-way" examples. $\endgroup$
    – user9072
    Commented May 31, 2013 at 13:14
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    $\begingroup$ just found this link en.wikipedia.org/wiki/List_of_amateur_mathematicians Some really famous names popped up in the list (Pascal, Heaviside, Ramanujan, and even Napoleon...) $\endgroup$
    – leo monsaingeon
    Commented May 31, 2013 at 13:16
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    $\begingroup$ mathoverflow.net/questions/44244/… $\endgroup$
    – José Hdz. Stgo.
    Commented May 31, 2013 at 13:22
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    $\begingroup$ @leo: Sadly for Math history buffs, Napoleon's Theorem was not discovered by Napoleon... See Grünbaum, Branko, "Is Napoleon's Theorem Really Napoleon's Theorem?", American Mathematical Monthly 119 (2012), 495–501 $\endgroup$
    – Rodrigo A. Pérez
    Commented May 31, 2013 at 13:37

7 Answers 7

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Let's start with all time classics.

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  • $\begingroup$ An answer given to a question (already) in CW mode is automatically CW, however once given the CW-status of the answer is independent of that of the question. So CW is "inherited" but only at the time of "birth" of the answer. However, and this is why this is confusing, when a moderator turns a question into CW they typically in addition turn all answers into CW at the same time (causing wrong impression this change is inherited, too). [To be precise: they do not need to do this manually for each, but still they also can just change Q and not A in addition.] $\endgroup$
    – user9072
    Commented May 31, 2013 at 17:26
  • $\begingroup$ @fedja Notifier: you wrote in comment to my question: " the conjecture is, indeed, true for every symmetric distribution." please can you say more on that ? I would accept answer proving it. I am very interested. $\endgroup$
    – Alexander Chervov
    Commented Jun 1, 2013 at 9:02
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Ramanujan was an autodidact and a clerk, so perhaps not really a professional mathematician. His "results" are famous, and without any doubt extraordinary contributions to mathematics.

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E.T. Bell, of course, dubbed Fermat the "prince of amateurs."

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Robert Ammann (from Wikipedia):

Robert Ammann [...] was an amateur mathematician who made several significant and groundbreaking contributions to the theory of quasicrystals and aperiodic tilings.

Ammann attended Brandeis University, but generally did not go to classes, and left after three years. He worked as a programmer for Honeywell. After ten years, his position was eliminated as part of a routine cutback, and Ammann ended up working as a mail sorter for a post office.

He discovered several new aperiodic tilings, each among the simplest known examples of aperiodic sets of tiles. He also showed how to generate tilings using lines in the plane as guides for lines marked on the tiles, now called "Ammann bars".

Ammann's discoveries came to notice only after Penrose had published his own discovery and gained priority.

He published one paper with Grünbaum and Shephard.

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Kurt Heegner is a nice example. Sadly he died before the mathematical community realized that his proof of the class number 1 problem was essentially correct.

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The text below is quoted from a 1990 article in Scientific American dealing with the discovery of the Mandelbrot set. The emphasis at the end is mine, and the point (subject to debate) is that although Mandelbrot had a PhD in Mathematics, he did not do serious research related to his discovery of fractal structures. He is of course given due credit for the paradigm change he created.

Sullivan, who has also been acclaimed for his studies of the Mandelbrot set, calls himself "sort of a defender of Mandelbrot." Mandelbrot deserves to have the set named after him, Sullivan says, because his efforts brought the set to the attention of both the public and of the pure-mathematics community.

The fact that it was only "by coincidence" that the set proved later to be mathematically significant, Sullivan says, in no way diminishes Mandelbrot's achievement. "That's the wonderful thing about mathematics," he adds. "Even amateurs can make important contributions."

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  • $\begingroup$ I agree with M. Greenblatt, the fact that his discovery was unrelated to his field of research is irrelevant. Mandelbrot was definitely not an amateur! $\endgroup$
    – leo monsaingeon
    Commented May 31, 2013 at 13:37
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    $\begingroup$ Mandelbrot was a Yale math professor, had a PhD in math, and had numerous math publications, including many before his work on fractals. Working primarily in other branches of math doesn't make someone an amateur or another kind of "non professional mathematician". $\endgroup$
    – Michael Greenblatt
    Commented May 31, 2013 at 13:38
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Edward Witten is a theoretical physicist who has made important contributions to mathematics. The controversial question may be whether to consider him a professional mathematician. (Witten's Wikipedia entry quotes Michael Atiyah saying "Although he is definitely a physicist, his command of mathematics is rivaled by few mathematicians.")

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    $\begingroup$ I would think that by any reasonable standard Edward Witten is both a professional physicist and a professional mathematician. $\endgroup$
    – Jeff Harvey
    Commented May 31, 2013 at 13:41

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