Yet it is impossible to argue that all these advantages enjoyed today by researchers in the mathematical sciences have led to equally spectacular improvements in the overall quality of their achievements. At best, it may be possible to argue that no steep decline has occurred.
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So what is going on? Why is mathematical practice today not dramatically more successful than a century ago? Why is there no spectacular contemporary flourishing of the art, with entirely new fields opened up by ten times as many Poincarés, Hilberts, Cartans, and Noethers?
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As far as I can recall, most new theories were still motivated out of existing problems, one way or the other. Disclaimer: I’d have to recheck histories of maths by Boyer and Dieudonné, as I’ve read them a while ago. 1/
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In favor of “no low-hanging fruits”, see also the amount of “huge“ proofs that nobody has managed to compress yet to something small (see: 4-color theorem, classification of finite simpler groups).
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