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So I have heard that professors doing applied work in math research have like no chance to win the big prizes in their fields, and that only the theorists win the big math prizes.

Is this true?

You might be asking "big, compared to what?"

So let's consider, for example, the Abel prize and the Fields Medal, ... or some prize of similar prestige and similar monetary award.

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    Counterexamples from my field: Peter Grunberg and Albert Fert with the giant magnetoresistance and Andre Geim and Konstantin Novoselov with the graphene got Nobel Prize for physics. – user21264 Aug 26 '17 at 6:34
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    @Magicsowon: Please don’t post answers (even partial ones) as comments. – Wrzlprmft Aug 26 '17 at 6:46
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    @Wrzlprmft When I post questions like this, they get closed by moderators for insufficient research. I'm not sure if I should answer in the first place. – user21264 Aug 26 '17 at 7:01
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    Possible duplicate of Can a theoretical physicist win a Nobel Prize anymore? – xLeitix Aug 26 '17 at 7:20
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    ...Recently I learned a little about it and got a little annoyed with the gerrymandering: it seems as "pure" as most branches of math that I know and study and more useful to my work than some. On the other hand cryptography is not usually counted as part of applied mathematics...but it seems that it should be. One notices that "pure" correlates highly with "algebra" and "applied" correlates highly with "analysis"...even though no one thinks analysis is more inherently applied than algebra. In summary: within mathematics, the distinctions seem largely artificial. – Pete L. Clark Aug 26 '17 at 23:30
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At least for the Nobel in Chemistry and Physiology this is not true and some are very applied, e.g. 2008 Chemistry Nobel for GFP and 2014 for super resolution microscopy. There are also examples in physics, as mentioned by Magicsowon.

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For the sake of brevity, I'll limit myself in answering to a few examples, but generally speaking it is not true.

The Nobel Prize has an official website, which lists all laureates:

You may choose just to look at the physics laureates during the last years:

The Nobel Prize in Physics 2015 was awarded jointly to Takaaki Kajita and Arthur B. McDonald "for the discovery of neutrino oscillations, which shows that neutrinos have mass"

The Nobel Prize in Physics 2014 was awarded jointly to Isamu Akasaki, Hiroshi Amano and Shuji Nakamura "for the invention of efficient blue light-emitting diodes which has enabled bright and energy-saving white light sources".

The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"

As already stated by Magicsowon

The Nobel Prize in Physics 2010 was awarded jointly to Andre Geim and Konstantin Novoselov "for groundbreaking experiments regarding the two-dimensional material graphene"

Although it might be true, that in some fields prestigous prizes are more likely to be awarded to theorists, the couple of examples I provided shows that at least the Nobel Prize is not just awarded to theorists.

If you take the Abel Prize: In 2005 it was awarded to Peter D. Lax

"for his groundbreaking contributions to the theory and application of partial differential equations and to the computation of their solutions." (link)

At least I would consider the work of Lax at least in parts as "applied work" as you put it in your question.

In my first year maths lecture I learned, that to falsify a (mathematical) statement you need only find one example which contradicts the statement, which I hereby did. If anyone has some statistics on the distribution of awarded Nobel Prizes among experimentalists and theorists, I'm very interested.

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