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So I was reading a History of Mathematics by Katz, and noticed that the first definition of a field came from Weber, who had previously done extensive joint work with Dedekind. His definition was used in German Textbooks for 30 years.

It has been explained to me that Dedekind's approach to mathematics was "bottom-up" which essentially means that from concrete realizations we build up by examination of properties to broader definitions (such as field).

My question is simply did Weber share this approach in his mathematics? Or was he more of a formalist.

PS: This is my last question. Cheers.

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  • $\begingroup$ See Heinrich Martin Georg Friedrich Weber: he worked mainly on algebra, collaborated with Dedekind and his courses were attended by the young Hilbert. Algebra was at that time onf of the main fields of abstract math and thus we can assert that he was an "abstractionsit" like Dedekind, but as far as I know we have no Weber's works on foundational issues. $\endgroup$ Mar 1 at 15:04

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