Hegel and mathematicians

Question

I'm new to the study of philosophy, feeling around slowly, finding my way. Am I misinterpreting, or did Hegel have contempt for mathematicians?

Answer 1

Hegel considered mathematics as a subordinate science. Philosophy, as far as it shall be science, cannot borrow its methods from such a subordinate science as mathematics is.

Die Philosophie, indem sie Wissenschaft seyn soll, kann, wie ich anderwärts erinnert habe, hierzu ihre Methode nicht von einer untergeordneten Wissenschaft, wie die Mathematik ist, borgen, so wenig als es bei kategorischen Versicherungen innerer Anschauung bewenden lassen, oder sich des Raisonnements aus Gründen der äußern Reflexion bedienen. (Georg Wilhelm Friedrich Hegel: Wissenschaft der Logik - Kapitel 2)

EDIT

From Hegel: Phänomenologie des Geistes, Vorrede, his contempt of mathematics should become crystal-clear:

Im mathematischen Erkennen ist die Einsicht ein für die Sache äußerliches Tun; es folgt daraus, daß die wahre Sache dadurch verändert wird. Das Mittel, Konstruktion und Beweis, enthält daher wohl wahre Sätze; aber ebensosehr muß gesagt werden, daß der Inhalt falsch ist. ... Die Evidenz dieses mangelhaften Erkennens, auf welche die Mathematik stolz ist und womit sie sich auch gegen die Philosophie brüstet, beruht allein auf der Armut ihres Zwecks und der Mangelhaftigkeit ihres Stoffs und ist darum von einer Art, die die Philosophie verschmähen muß. ... Das Wirkliche ist nicht ein Räumliches, wie es in der Mathematik betrachtet wird; mit solcher Unwirklichkeit, als die Dinge der Mathematik sind, gibt sich weder das konkrete sinnliche Anschauen noch die Philosophie ab. ... Eine Kritik jener Beweise würde ebenso merkwürdig als belehrend sein, um die Mathematik teils von diesem falschen Putze zu reinigen

Its contents is wrong, insufficent rekognition, poorness of its purpose and insufficiency of its stuff, ...

Answer 2

You are misinterpreting. As far as Hegel's biography goes, Hegel's relatives record mathematics was one of his favorites subjects, and as a theology student he would take long "sick leaves" to basically go home and study math and physics (and botany). He would have known more mathematics than essentially any other philosopher of his era.

There are a number of complications that make the naive answers others are rattling off unsuitable. One issue is what, in modern mathematics, Hegel would have called "mathematische Erkennen". Obviously Lawvere considers everything in modern category theory to correspond to the contents of the Wissenschaft Logik; so in that sense the core of what Hegel considered "philosophy" is currently taught in nearly every serious math department, but in nearly no philosophy department.

Most of modern number theory and topology would also, I believe, fall outside what Hegel is describing as "mathematics"; for the simple reason that they attempt to come up with a completely conceptual understanding of what numbers are from scratch (via Peano or similar) without assuming, at the beginning, an abstract system of numbers that behave like "everyday" quantities without referring to any specific count or measure. I suppose some touchy mathematicians might read things Hegel says about "math" and accuse him of failing to see what mathematicians were capable of - but Hegel wasn't denying you could come up with these pure foundations for mathematics (that's what was in the Wissenschaft Logik!), he was just sketching out a disciplinary division of labor between philosophy, abstract tools like mathematics and predicate logic, and the natural sciences that assumed his readers had some idea how the material was divided between philosophy, physics, and math in 1807.

Now, I have interpreted your question as one about the field of mathematics. If we are talking about people,

(a) There were some German philosophers who were floundering after they realized that it wasn't really easy to reduce Kant's philosophy to a deductive argument. Many of Hegel's cutting remarks about the difference between philosophy and syllogism/arithmetic/geometry are aimed at them, and yes Hegel had contempt for them. (They were not "mathematicians", however.)

(b) There was a tradition in German mathematics (still very much alive in the 1920s) that held that proofs were secondary to pure mathematical insight, that you can just visually see that, say, the Pythagorean theorem is true. In a sense Hegel respects that vision of mathematics (in that he sees geometrical intuition as genuinely powerful, within its proper domain) but he also was quite dismissive of the idea that these mathematical ideas couldn't have or didn't need any logical foundations. Here too his dismissiveness was mainly aimed at other philosophers (Schelling) who tried to make parallel claims about other fields, but some actual mathematicians definitely took it as an attack on their purely intuitive conception of math as well.