Linked Questions

1 vote
0 answers
193 views

What are some great examples of wordsmanship in published literature? [duplicate]

David L. Goodstein begins his book on statistical mechanics, ''States of Matter'', with the following introduction: "Ludwig Boltzmann, who spent much of his life studying statistical mechanics, ...
Klangen's user avatar
  • 1,962
185 votes
127 answers
65k views

Most memorable titles

Given the vast number of new papers / preprints that hit the internet everyday, one factor that may help papers stand out for a broader, though possibly more casual, audience is their title. This view ...
197 votes
94 answers
107k views

Famous mathematical quotes [closed]

Some famous quotes often give interesting insights into the vision of mathematics that certain mathematicians have. Which ones are you particularly fond of? Standard community wiki rules apply: one ...
92 votes
74 answers
27k views

Pseudonyms of famous mathematicians

Many mathematicians know that Lewis Carroll was quite a good mathematician, who wrote about logic (paradoxes) and determinants. He found an expansion formula, which bears his real name (Charles ...
87 votes
33 answers
24k views

Parodies of abstruse mathematical writing

Perhaps under the influence of a recent question on perverse sheaves, in conjunction with the impending $\pi$-day (3/14/15 at 9:26:53), I recalled a long-ago parody of abstruse mathematical language ...
44 votes
6 answers
4k views

Explaining the main ideas of proof before giving details

I'll be the first to admit that this is a risky question to try to get away with on math overflow, but I'm going to give it a shot anyway. Roughly speaking, the question is this: Is it good to try to ...
25 votes
3 answers
7k views

In model theory, does compactness easily imply completeness?

Recall the two following fundamental theorems of mathematical logic: Completeness Theorem: A theory T is syntactically consistent -- i.e., for no statement P can the statement "P and (not P)" be ...
Pete L. Clark's user avatar
15 votes
4 answers
3k views

Chevalley–Shephard–Todd theorem

The wikipedia article claims that the theorem "was first proved by G. C. Shephard and J. A. Todd (1954) who gave a case-by-case proof. Claude Chevalley (1955) soon afterwards gave a uniform proof". I ...
Roman Fedorov's user avatar
3 votes
2 answers
3k views

What is the smallest cardinal number of a set that requires the axiom of choice to prove that it exists and is non-empty?

Let C(x) be a formula belonging to the language of ZFC in which the variable "x" and no other variable occurs free. Suppose that (a sentence of this language equivalent to) the following statement, is ...
Garabed Gulbenkian's user avatar
7 votes
2 answers
2k views

Variant of Fermat's last theorem

By Fermat's last theorem, the equation $u^3+v^3=w^3$ has no solutions in positive integers $u,v,w$. Now consider the following variant : call $\rho(x)$ the distance between $x$ and the nearest integer,...
Ewan Delanoy's user avatar
  • 3,595
8 votes
1 answer
208 views

Can the defining rep of $E_7$ split over a finite subgroup while the adjoint remains simple?

Does the (simply connected compact) Lie group $E_7$ contain a finite subgroup $G \subset E_7$ such that the $56$-dimensional irrep of $E_7$ splits over $G$ as $28 \oplus \overline{28}$, but the $133$-...
Theo Johnson-Freyd's user avatar
12 votes
0 answers
435 views

History of use of "=" symbol to mean "is canonically isomorphic to"

Let $A$ be a commutative ring, and let $f$ and $g$ denote elements of $A$ such that the prime ideals of $A$ containing $f$ are precisely the prime ideals containing $g$ (a not completely trivial ...
Kevin Buzzard's user avatar
2 votes
1 answer
323 views

Special Lagrangians and fat

I am unable to find the MO comments about the first use of the phrase "fat slags" in an article. On page 26 of this we find "these correspond to thickenings of the corresponding special Lagrangian (...