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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.
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 …
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 …
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 …
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 …
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
5
votes
Most helpful heuristic?
Dear harrison,
in complex geometry there is Oka's principle.
It says that on a stein manifold, if there is no obstruction to a continuous construction there will be no obstruction to a holomorphic c …
13
votes
Is there an existing name for "piecewise vector multiplication"
If $k$ is a field, the vector space $k^n$ endowed with the componentwise multiplication is called a diagonal algebra ( and so are isomorphic algebras). The terminology is due to Bourbaki and is justif …
- 47.5k
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 …
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
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 …
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 …
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 …
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 …
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
3
votes
Individual mathematical objects whose study amounts to a (sub)discipline?
$SL_2\mathbb R$ and its evil universal covering.