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There are some prizes in Mathematics nowadays that may be considered probably as hard to win, like the Abel Prize, but they were established quite recently. Looking back to a few years ago, the Fields Medal was the most prestigious award in Mathematics and the Nobel Prize the most prestigious award in many others, with no age limit to get one...

My question is why there is a limit age for the 'hardest' award in mathematics and no age limit for the 'hardest' award in science (physics or chemistry, ...)?

If someone under 40 years old in mathematics is assumed to be a 'genius' we don't see such ideology in for instance the Nobel Prize.

Putting it another way: why does someone less than 40 years old 'deserve' a great reward but not someone older? It doesn't seem fair to me!

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    $\begingroup$ "If you haven't done ground-breaking research by age 40, chances are you never will". This argument is true, it is also true if we change 40 for any other integer. The chances someone make a Ground Breaking contribution in today's world are very slim regardless their age. $\endgroup$ – Jorge Fernández Hidalgo Jun 22 '15 at 7:11
  • $\begingroup$ In case of the unlikely event that I ever stumble over something ground-breaking I will post the result here first just to pester the Fields committee. $\endgroup$ – mvw Jun 22 '15 at 7:53
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    $\begingroup$ There have been many ground-breaking researchers, even 80 years old ones. See some mobels: 90 years Leonid Hurwicz Economic Sciences 2007, 89 years Lloyd Shapley Economic Sciences 2012, 88 years Raymond Davis Jr. Physics 2002 , 87 years Yoichiro Nambu Physics 2008, 87 Vitaly L. Ginzburg Physics 2003 and so on. I think it's not fair to limit the age. Many people don't have the opportunity to research when they are young. $\endgroup$ – skan Feb 12 '17 at 0:54
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Fields wanted the award to encourage recipients' further achievement and stimulate others' renewed effort.

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    $\begingroup$ I understand the first part, how does he achieve stimulating other's renewed effort? $\endgroup$ – Jorge Fernández Hidalgo Jun 22 '15 at 7:12
  • $\begingroup$ @Gamamal Hmm, maybe others would work very hard just to try to win the award? LOL. $\endgroup$ – please delete me Jun 22 '15 at 7:15
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    $\begingroup$ Re emulation, age limits are irrelevant, no? $\endgroup$ – Did Jun 22 '15 at 7:18
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    $\begingroup$ @did I guess it makes them work harder, just like it makes people type fast on SE to be the first to post an answer. $\endgroup$ – please delete me Jun 22 '15 at 7:25
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    $\begingroup$ @JasperLoy Interesting conjecture -- which seems refuted by the level of competition in quite a few non-maths scientific fields. $\endgroup$ – Did Jun 22 '15 at 7:27
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I am guessing that the age-restriction is put there to award "young" mathematicians. In most awards most people who receive it are pretty old. I think that until recently the Fields Medal was the most prestigious math award, now it is the Abel prize. If you look at the people who won the Abel prize, they are all "old" mathematicians. Even though there is no age restriction on the Abel prize, it seems you have to be minimum 70 years old to get it (perhaps, because it is awarded for lifetime achievement). Many people who win the Nobel prize are "old" also. Thus, perhaps Fields wanted his award prize to specifically target the young community so they get a piece of the action.

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Here's the short version: When the award was proposed, those involved were specifically worried about lingering rivalry between mathematicians from opposite sides of World War I (especially French v German), a rivalry which at that point had basically sunk the first attempt at an International Mathematical Union. Fields's proposal (adopted after his death) tried to sidestep the problem of "invidious comparisons" by inserting fuzzy language about future achievement (which is hard to measure and debate) as vs just past accomplishments (which can be debated more easily and thus lead to conflict). Early Fields Medal committees interpreted this as saying that the Fields Medal should be something like an early/mid-career award for someone not already decorated with other prizes and career milestones. A big motive for doing this was to avoid getting into debates over who was really the top mathematician, especially since they had so many top mathematicians (including many they knew personally and who might be offended) to choose from. Before 1966, when the limit was codified, there were people under 40 who were ruled out as being too advanced in their careers, and also people over 40 who were seriously considered even past the stage of initial nomination.

Working on an article that explains the bigger story, but if you're around Cambridge, MA on March 6, 2017, you can see me give a preview at MIT: http://events.mit.edu/event.html?id=16503559

Also important is that the Fields Medal wasn't really in the same conversation as the Nobel Prize until 1966, and at the beginning few would have taken the comparison seriously (seeing it as more of the early-mid-career award that it was). See my article: http://www.ams.org/notices/201501/rnoti-p15.pdf

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