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**49**

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**5**answers

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### Changing field of study post-PhD

I am doing my PhD in algebraic graph theory, for not much more reason than that was what was available. However, I love deep structure and theory in mathematics, and I do not particularly want to be ...

**55**

votes

**6**answers

7k views

### Still Difficult After All These Years

I think we all secretly hope that in the long run mathematics becomes easier, in that with advances of perspective, today's difficult results will seem easier to future mathematicians. If I were ...

**32**

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**9**answers

4k views

### Dimensional Analysis in Mathematics

Is there a sensible and useful definition of units in mathematics? In other words, is there a theory of dimensional analysis for mathematics?
In physics, an extremely useful tool is the Buckingham Pi ...

**46**

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**6**answers

5k views

### Does a referee have to check carefully the proof ?

I have always checked very carefully the papers I was refereeing when I wanted to suggest "accept". Actually I spend almost as much time checking the maths of a paper I referee than checking the maths ...

**90**

votes

**94**answers

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### What would you want to see at the Museum of Mathematics?

EDIT (30 Nov 2012): MoMath is opening in a couple of weeks, so this seems like it might be a good time for any last-minute additions to this question before I vote to close my own question as "no ...

**114**

votes

**16**answers

15k views

### When should a supervisor be a co-author?

What are people's views on this? To be specific: suppose a PhD student has produced a piece of original mathematical research. Suppose that student's supervisor suggested the problem, and gave a few ...

**42**

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**19**answers

6k views

### Are there proofs that you feel you did not “understand” for a long time?

Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed my question was ...

**34**

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**33**answers

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### Structures that turn out to exhibit a symmetry even though their definition doesn't

Sometimes (often?) a structure depending on several parameters turns out to be symmetric w.r.t. interchanging two of the parameters, even though the definition gives a priori no clue of that symmetry. ...

**32**

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**6**answers

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### Negative impact of wrong or non-rigorous proofs

The recent talks of Voevodsky (for example, http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf), which describe subtle errors in proofs by him as well as others, as well ...

**13**

votes

**16**answers

2k views

### Individual mathematical objects whose study amounts to a (sub)discipline? [closed]

Certain mathematical objects have a theory so rich that their study
alone arguably constitutes a distinct (sub)discipline. My own list
would begin with
1) the absolute Galois group of the rationals;
...

**21**

votes

**2**answers

1k views

### What might extraterrestrial mathematics look like? [closed]

In an extensive anthropological joint research project concerning the necessities in the development of life and civilisation my group is concerned with mathematics. This forum seems to be extremely ...

**18**

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**3**answers

991 views

### Results that are easy to prove with a computer, but hard to prove by hand [closed]

Consider the assertion:
There is no completely multiplicative function $f:\mathbb{N}\rightarrow \{\pm 1\}$ with $\left|\sum_{n\leq x}f(n)\right|\leq 2$ for all $x\geq 0$.
One can write a very short ...

**12**

votes

**0**answers

350 views

### Which limit to take as a key applied math decision

The Borel-Kolmogorov paradox refers to situations where non-uniqueness in the notion of conditioning on a set of measure zero leads to apparent contradictions. As a formal matter, one requires ...

**2**

votes

**4**answers

1k views

### When did you “meet Polya”? [closed]

I guess most of us didn't meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess that most of us have met one of his writings (or alike) on problem solving, and ...

**-6**

votes

**3**answers

748 views

### Where is the belly button of the Universe? [closed]

It's fine and nice and wonderful when a part of learning mathematics is chaotic, ad hoc, spontaneous, social, ...
However it would be perhaps of fundamental value to know a very central point of ...

**6**

votes

**1**answer

473 views

### Sources of Theorem drafts by the original author

When I look at first time to a theorem and I try to understand it or when I try to memorise a useful theorem I always have difficulties (I am not the only one. For example: I read a question: I always ...

**2**

votes

**5**answers

978 views

### Circumference of convex shapes

Here is a puzzle I found in "Mitteilungen der DMV" (roughly "Letters of the German Society of Mathematicians") issue 19/2011. It was posed by Alfred Schreiber in "Wie man Hasen fangt" (How to catch ...