In particular, looking just at mathematics, we find the following names associated with profound innovations made in the first two decades of the last century: Frobenius, Burnside, Poincaré, Hilbert, Minkowski, Hadamard, Cartan, Takagi, Ramanujan, Weyl, Hecke, Noether, Banach.
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Although there is an infinite amount of math to discover, as we progress new math becomes more difficult to discover, because one must first master all of the relevant math that is already known. In that sense, the low hanging fruit has been picked.
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If it were necessary to master all the relevant math that is already known, no progress would ever result. Already in 1900, Hilbert maintained that this was an impossible undertaking.
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There are entirely new fields created in the last 60 years . To name a few: Computer science, geometric group theory, arithmetic geometry, category theory. Those are huge fields that may have earlier origins but are essentially new.
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How many of these were created in the past twenty years?
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My view of current-day mathematics is much more optimistic. So much amazing stuff is going on that the field isn't dominated by a few giants. When you get ten times as many Poincarés, Hilberts, Cartans, and Noethers they don't seem like such a big deal anymore. (1/2)
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So many good new ideas are showing up that it's become much harder to keep up with them all. Voevodsky's homotopy type theory. Lurie's work on (infinity,1)-categories. Witten's work on string theory, M-theory and geometric Langlands (math, not physics). And much more. (2/2)
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I think you're overplaying the "no low-hanging fruit" - though we do plant new trees, we keep climbing the old ones as well, and it gets much harder, but huge breakthroughs do happen - classification of finite simple groups! The geometrization conjecture!
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Fields have been spectacularly rebuilt, sometimes multiple times - algebraic geometry, algebraic topology, logic. And whole new fields - graph theory, numerical methods using computers, category theory...
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Part of this must be that today's "superior" institutional support structures support production of acceptable work, which has indeed increased tremendously in volume, and neglect to support production of revolutionary work, support for which is much different in character.
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I think maths just grows so fast that important innovations will on average have an effect on a smaller proportion of the subject. So a fairer comparison might be between giants of mathematics 100 years ago and giants of some (largish) subdomain of mathematics now.
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One could argue (I'd be interested to know whether people think it would be correct though) that mathematicians like Gauss, Euler and Riemann had an even bigger impact than the ones you list from the early 20th-century.
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