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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.
170
votes
Most memorable titles
The flattering lie You Could Have Invented Spectral Sequences by Timothy Y. Chow.
159
votes
What are some examples of colorful language in serious mathematics papers?
Andre Weil (Oeuvres, vol. 2, page 558) purporting to be R.Lipschitz writing from Hades:
"Unfortunately, it appears that there is now in your world a race of
vampires, called referees, who clamp down m …
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 …
85
votes
6
answers
50k
views
How many mathematicians are there?
Although we are not so numerous as other respected professionals, like for example lawyers, I wonder if we could come up with a reasonable estimate of our population.
Needless to say, the question m …
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 …
64
votes
Too old for advanced mathematics?
Dear bitrex: your enthusiasm is heart-warming!
I have had students much older than you and they have always been a joy to teach: their maturity more than compensated for their potential knowledge-gap …
- 47.5k
62
votes
How has "what every mathematician should know" changed?
Many, many things have changed in the last 60 years. A mathematician of the fifties (in Europe) was required to know descriptive geometry, rational mechanics, maybe some astronomy, and a lot of physi …
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 …
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 $n$.
38
votes
Accepted
Justifying a theory by a seemingly unrelated example
[In front of a blackboard, in an office at Real College]
Skeptic: And why should I care about holomorphic functions?
Holomorphic enthusiast:$\;$ Can you compute $\quad$ $\sum_{n={-\infty}}^{\infty …
34
votes
Theorems for nothing (and the proofs for free)
Wedderburn's theorem: "Every finite division ring is a field."
This is really astonishing if you think of quaternions: nothing analogous in the finite case.
Then of course the classification of finit …
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 …
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 …
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 …
17
votes
Which mathematicians have influenced you the most?
Otto Forster.
He is the most brilliant expositor I have ever met. I cherish the notes I took a long time ago of courses he gave in Italy and France, in perfect Italian and French.
He wrote a wonderful …