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1500 questions
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11 answers

Standard model of particle physics for mathematicians

If a mathematician who doesn't know much about the physicist's jargon and conventions had the curiosity to learn how the so called Standard Model (of particle physics, including SUSY) works, where should (s)he have a look to? References (if they…
Qfwfq
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47
votes
23 answers

Good programs for drawing (weighted directed) graphs

Does anyone know of a good program for drawing directed weighted graphs?
dan
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47
votes
4 answers

Volumes of n-balls: what is so special about n=5?

I am reposting this question from math.stackexchange where it has not yet generated an answer I had been looking for. The volume of an $n$-dimensional ball of radius $R$ is given by the classical…
Andrey Rekalo
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47
votes
3 answers

Clearing misconceptions: Defining "is a model of ZFC" in ZFC

There is often a lot of confusion surrounding the differences between relativizing individual formulas to models and the expression of "is a model of" through coding the satisfaction relation with Gödel operations. I think part of this can be…
Jason
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47
votes
9 answers

What examples of distributions should I keep in mind?

I'm learning a bit about the theory of distributions. What examples of distributions will help me develop good intuition? Definitions: Let $U$ be an open subset of $\mathbb{R}^n$. Write $C_c^\infty(U)$ for the complex vector space of infinitely…
Tom Leinster
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47
votes
10 answers

What is the most "concrete-feeling" equivalent formulation of the Continuum Hypothesis that you can think of?

There are many equivalent formulations of the Continuum Hypothesis, but I think the most standard one is that there is no infinite cardinality lying strictly between the cardinality of the natural numbers and the cardinality of the real…
Julian Newman
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47
votes
3 answers

A metric characterization of the real line

Is the following metric characterization of the real line true (and known)? A nonempty complete metric space $(X,d)$ is isometric to the real line if and only if for every $c\in X$ and positive real number $r$ there exist two points $a,b\in X$ such…
Taras Banakh
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47
votes
2 answers

Well known theorems that have not been proved

I believe that there are numerous challenging theorems in mathematics for which only a sketch of a proof exists. To meet the standards of rigor, a complete proof of these theorems has yet to be established. Here is an example of a theorem that as…
Piotr Hajlasz
  • 27,279
47
votes
10 answers

Rings in which every non-unit is a zero divisor

Is there a special name for the class of (commutative) rings in which every non-unit is a zero divisor? The main example is $\mathbf{Z}/(n)$. Are there other natural or interesting examples?
lhf
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47
votes
35 answers

Ingenuity in mathematics

[This is just the kind of vague community-wiki question that I would almost certainly turn my nose up at if it were asked by someone else, so I apologise in advance, but these sorts of questions do come up on MO with some regularity now so I thought…
Kevin Buzzard
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47
votes
6 answers

Algebraic Attacks on the Odd Perfect Number Problem

The odd perfect number problem likely needs no introduction. Recent progress (where by recent I mean roughly the last two centuries) seems to have focused on providing restrictions on an odd perfect number which are increasingly difficult for it to…
Cam McLeman
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47
votes
6 answers

Are hypergeometric series not taught often at universities nowadays, and if so, why?

Recently, I've become more and more interested in hypergeometric series. One of the things that struck me was how it provides a unified framework for many simpler functions. For instance, we have $$ \log(1+x) = x\ {_2F_1}\left(1,1;2;-x\right) ;$$ $$…
Max Muller
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47
votes
1 answer

Lecture notes by Thurston on tiling

I am looking for a copy of the following W. Thurston, Groups, tilings, and finite state automata, AMS Colloquium Lecture Notes. I see that a lot of papers in the tiling literature refer to it but I doubt it was ever published. May be some notes are…
Vagabond
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47
votes
8 answers

Ron L. Graham’s lesser known significant contributions

Ron L. Graham is sadly no longer with us. He was very prolific and his work spanned many areas of mathematics including graph theory, computational geometry, Ramsey theory, and quasi-randomness. His long association with Paul Erdős is of course very…
kodlu
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5 answers

How and when do I learn so much mathematics?

I am about to (hopefully!) begin my PhD (in Europe) and I have a question: how did you learn so much mathematics? Allow me to explain. I am training to be a number theorist and I have only some read Davenport's Multiplicative Number Theory and parts…
sudolearn
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