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How was he viewed. I am interested in what the mathematical community thought of his philosophy of mathematics. What Hilbert thought of him etc. etc.?

  • He had some influence on the philosophy of math debate, but no influence whatever on the development of math research itself. – Mauro ALLEGRANZA Dec 24 '17 at 8:43
  • See Claire Ortiz Hill's On Husserl's Mathematical Apprenticeship and Philosophy of Mathematics. He anticipated some elements of Hilbert's programme of foundations, including consistency, completeness and conservative extensions ("transition through the imaginary"), but opposed "excessive symbolism" and advocated, contra Hilbert, that formalisms must develop formal ontologies to become mathematics. He was actively engaged with Göttingen mathematicians in 1890-s and 1900-s and later had profound philosophical influence on Weyl and Gödel. – Conifold Dec 27 '17 at 20:59
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Surprisingly little appears to have been written on the purely mathematical reception of Husserl's ideas, so one might surmise that he has not received much official acknowledgement. Richard Tieszen has written numerous papers on Husserl and maths but they are mostly philosophical. There is a 72-page article in French on arxiv "Husserl, Cantor & Hilbert: La Grande Crise des Fondements Mathematiques du XIXeme Siecle". A popuar story about Husserl and Hilbert is told by Pierre Cassou-Noguès (available at diff. places).

In a nutshell: Husserl in his Philosophy of Arithmetic was critical of Frege who in turn wrote a negative and influent review. Husserl definitely turned from maths and set theory towards philosophy but he still knew most of the important figures in the maths world and exchanged many letters with them. Cantor is said to have congratulated him for his Habilitationschrift.

Between 1901 and 1913 he was at Gottingen, the department of philosophy housing there the mathematics faculty, that is Hilbert and Klein. Hilbert has had many discussion with Husserl but does not appear to have said anything notable (either good or bad). However many thought Husserl close to Brouwer who was not well seen by mathematicians. The exception is Hermann Weyl who for a few years has been very enthousiastic about both.

From a contemporary standpoint, the most impressive acknowledgement of Husserl's ideas is due to Godel who studied them and wrote about them but did not publish anything (see Tieszen for an extensive tratment).

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There were three reviews in mathematical journals of Husserl's Philosophy of Arithmetic:

  • Carl Theodor Michaëlis, in Jahrbuch über die Fortschritte der Mathematik XXIII/1 (1891), 58–9.
  • Heinrich Schotten, in Zeitschrift für Mathematik und Physik (Historisch- literarische Abtheilung) 38 (1893), 88–90.
  • Friedrich Pietzker, in Zeitschrift für mathematischen und naturwissenschaftli- chen Unterricht XXVI (1895), 512–17.

Pietzker's is the most detailed one. Translations of the reviews are available here: https://philpapers.org/rec/IERHPO-2 (pdf available on request).

There are several monographs and (collections of) articles on Husserl, Phenomenology, and Mathematics, i.a. Stefania Centrone, Essays on Husserl’s Logic and Philosophy of Mathematics (Springer 2017), Mirja Hartimo, Guillermo Rosado Haddock. Husserl's contributions are much more in the foundations and philosophy of mathematics than in technical matters, i.e. the relation of mathematics to logic, set-theory/theory of manifolds, epistemology, etc. which was (likely) of more interest to philosophers than mathematicians. Husserl's views in the Logical Investigations remarked explicitly on the "division of labor" among philosophers and mathematicians (Prolegomena, §71).

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