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Results tagged with soft-question
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user 450
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
80
votes
Examples of conjectures that were widely believed to be true but later proved false
In 1908 Steinitz and Tietze formulated the Hauptvermutung ("principal conjecture"), according to which, given two triangulations of a simplicial complex, there exists a triangulation which is a common …
10
votes
Notable math from those without math PhDs
Buffon(Georges-Louis Leclerc, Comte de Buffon; 1707 – 1788) is a towering figure in biology.
As a mathematical hobbyist he invented geometric probability theory.
His method of calculating $\pi$ by th …
26
votes
What makes a theorem *a* "nullstellensatz."
What I find intriguing is that the Nullstellensatz is underappreciated in the sense that many people appeal to a variation of it without saying (or realizing) they do.
For example, Hadamard's lemma …
44
votes
Theorems that are 'obvious' but hard to prove
That $\mathbb R^n$ has topological dimension $n$. In a similar vein that affine space $\mathbb A^n_k$ over a field $k$ has Zariski dimension $n$.
30
votes
Accepted
The influence of string theory on mathematics for philosophers.
Dear Jeff, string theory has had a colossal influence on the renewal of enumerative geometry, a two century old branch of algebraic geometry inextricably linked to intersection theory.
Here is a telli …
3
votes
Individual mathematical objects whose study amounts to a (sub)discipline?
$SL_2\mathbb R$ and its evil universal covering.
23
votes
Serre's FAC versus Hartshorne as an introduction to sheaves in algebraic geometry
Dear J, here is a little technical warning which might be relevant to your question.
If you open Hartshorne and read the definition of "coherent" (Chapter II, §5, page 111) you might get the impress …
53
votes
Pseudonyms of famous mathematicians
Rainich=Rabinowitsch (of trick fame : cf. Nullstellensatz).
Here is an anecdote related by Bruce P. Palka, Editor of American Mathematical Monthly
in Vol.111 (2004) of that journal (page460).
Rai …
170
votes
Most memorable titles
The flattering lie You Could Have Invented Spectral Sequences by Timothy Y. Chow.
7
votes
Alternating forms as skew-symmetric tensors: some inconsistency?
Dear Paul, first of all let me congratulate you for the extremely clear formulation of your interesting question (which is not silly at all, contrary to what you say): +1.
The source of your trouble …
- 47.5k
6
votes
Accepted
Why did the word "exterior" get chosen for the idea of "exterior derivative"?
I) The term exterior multiplication ("äussere Multiplication") is due to Grassmann, who introduced the term in his book (written in 1844)
Die Wissenschaft der extensiven Grösse oder die Ausdehnungsl …
- 47.5k
88
votes
Widely accepted mathematical results that were later shown to be wrong?
In 1882 Kronecker proved that every algebraic subset in $\mathbb P^n$ can be cut out by $n+1$ polynomial equations.
In 1891 Vahlen asserted that the result was best possible by exhibiting
a curve in …
2
votes
Accepted
The origin of the satisfy-verify mixup
Dear Harry, in Serre's collected papers, vol.1, page 183 [or Annals of Math.58(1953) page 270]
you'll find (line -5)
"Soit $\mathcal C$ une classe vérifiant (II_A)..."
and many such examples on the …
15
votes
Consolidation: Aftermathematics of fads
In the seventies and eighties of the preceding century, existence and classification of vector bundles on projective space $\mathbb P^n$ were all the rage, with contributions from such luminaries as A …
17
votes
Accepted
Motives versus Motifs
Dear Donu, here are Grothendieck's own words:
"Contrary to what occurs in ordinary
topology, one finds oneself confronting
a disconcerting abundance of different
cohomological theories. One has the
d …