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Besides the Peano axioms which perhaps brought him fame but which are considered a refinement of similar previous axioms Peano seems to have done relatively little original work. Does the rest of his work compare favourably to the totality of the works of the other great mathematicians of the same era? It seems to me that whether this can be answered objectively enough or not may be determined by his "significance distance" from the great mathematicians of that era.

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Actually, Peano did much more original work than that. Among other things, he

  • gave the modern definition of vector spaces and linear maps;
  • defined the first space-filling curve;
  • stated and proved the Peano existence theorem (on the existence of solutions to certain initial value problems); and
  • developed the logical notation that would be later used by Bertrand Russell and Alfred North Whitehead to write Principia Mathematica.

So, although he was not on the same level as Henri Poincaré (who was four years older than he) or as David Hilbert (who was four years younger), he was a very gifted mathematician, whose work was important and concerned several distinct areas of mathematics.

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  • $\begingroup$ But are his achievements comparable to the mathematical contributions of other great mathematicians of the era(lets say to the top 40 mathematicians)? $\endgroup$ – GEP Sep 23 '20 at 14:39
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    $\begingroup$ That's very subjective. I think so, but the answer would be negative if you were asking about the ten greatest ones. $\endgroup$ – José Carlos Santos Sep 23 '20 at 15:00
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See also

The forgotten mathematical legacy of Peano Volume 537 / 2019 Szymon Dolecki, Gabriele H. Greco Dissertationes Mathematicae 537 (2019), 1-77 MDOI: 10.4064/dm769-4-2018 Published online: 28 February 2019 (free download)

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