The math-philosophy tag has no wiki summary.

**28**

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### Categorical foundations without set theory

Can there be a foundations of mathematics using only category theory, i.e. no set theory? More precisely, the definition of a category is a class/set of objects and a class/set of arrows, satisfying ...

**1**

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**4**answers

471 views

### Does the Golden Ratio Apply to Timing as Well? [closed]

I've seen the golden section applied to art, but does it apply to sound/timing as well? Just curious.

**13**

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**2**answers

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### synthetic differential geometry and other alternative theories

There are models of differential geometry in which the intermediate value theorem is not true but every function is smooth. In fact I have a book sitting on my desk called "Models for Smooth ...

**4**

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**4**answers

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### Badiou and Mathematics [closed]

Does anyone have an opinion on Alain Badiou's use of set theory? Is there anything interesting mathematically there? Also could anyone shed any light on the comment in the Wikipedia article link text ...

**3**

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**2**answers

476 views

### Broken Symmetry

I have a tangled web of ideas about natural transformations, vector spaces, equivalence classes, local coordinates, etc. in my head that I'm trying to unravel. So here are some of the questions I ...

**17**

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**8**answers

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### The Importance of ZF

It seems as though many consider ZF to be the foundational set of axioms for all of mathematics (or at least, a crucial part of the foundations); when a theorem is found to be independent of ZF, it's ...

**8**

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**2**answers

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### Math History Question about the exponential function

While tutoring a student recently, I have come across the situation of explain logarithms by first introducing functions of the form $$f(x)= a^x$$ where $a \ge 0,x\in \mathbb{R}$. My student then ...

**9**

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**3**answers

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### Is formal proof (formalized mathematics) interesting to practicing mathematicians? To educators? [closed]

Formalizing mathematical proofs so that they can be checked for correctness and manipulated by computer is a recurrent proposal, most notably stated in the QED manifesto (1994). The December 2008 ...

**6**

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**2**answers

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### How platonistic is your attitude towards mathematics? [closed]

A discussion in the n-category cafe
about Manin's 'emotional Platonism' made me wonder how such a perception of mathematics is distributed among mathematicians and how that influences attitudes ...

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**2**answers

456 views

**13**

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**7**answers

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### Is no proof based on “tertium non datur” sufficient any more after Gödel?

There are many proofs based on a "tertium non datur"-approach (e.g. prove that there exist two irrational numbers a and b such that a^b is rational).
But according to Gödel's First Incompleteness ...

**53**

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### Why do Groups and Abelian Groups feel so different?

Groups are naturally "the symmetries of an object". To me, the group axioms are just a way of codifying what the symmetries of an object can be so we can study it abstractly.
However, this heuristic ...