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First, let me attempt to semi-rigorously define "non-prestigious". A "non-prestigous" mathematician has at least three of the following attributes:

  1. Has never received any significant awards at the national or international level at any age (i.e. no olympiads, math olympics, etc.).

  2. Did not do Phd at an "elite" university (top 20?)

  3. Did not work under a prestigious advisor in grad school.

  4. Either did not attend a prestigious undergrad institution or at a minimum did not excel in undergrad at a prestigious undergrad institution.

  5. Has never been published in a well known journal or other such medium.

Obviously this is a very flawed attempt at a definition so take it more as a guideline.

Anyways, I'm just curious to see some examples because I am probably looking at a "non-prestigious" path to becoming a mathematician (I actually dropped out of school for two years). I am hoping that there are at least a few relevant examples of some underrated talent making significant contributions to their respective fields. I definitely do math purely because I love it (i.e. intrinsic value) but if I am going to make it my life's work, I'd like to know that there is some chance I can make a dent (however small) in whatever field it is I choose to work in.

Edit: As for what constitutes a "significant" contribution, let's say that it would be defined as a contribution that an expert in a given field would immediately recognize the significance of.

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    $\begingroup$ You seem to think that "pedigree" is relevant... $\endgroup$ – John B Dec 6 '16 at 18:14
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    $\begingroup$ I think the vast majority of mathematicians fall into that category. You should probably also define what a "significant" contribution is. $\endgroup$ – tilper Dec 6 '16 at 18:15
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    $\begingroup$ But anyways two outstanding examples are José Luis Massera and Pat Moran. None of them ever got a PhD, but their influence was immeasurable. $\endgroup$ – John B Dec 6 '16 at 18:17
  • $\begingroup$ @tilper Fair point, think something that an expert in a given field would immediately recognize as relevant but not necessarily something that a non-expert would be familiar with. Still vague but it's something. $\endgroup$ – TheLaughingAlgebrist Dec 6 '16 at 18:19
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    $\begingroup$ How about Pythagoras? $\endgroup$ – barak manos Dec 6 '16 at 18:25
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Two French examples:

Évariste Galois: utterly ignored during his life.

Roger Apéry: virtually unknown until his proof of the irrationality of $\zeta(3)$.

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Yitang Zhang's breakthrough toward the twin prime conjecture.

https://en.wikipedia.org/wiki/Yitang_Zhang

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