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Results tagged with big-list
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user 6107
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
13
votes
Examples of simultaneous independent breakthroughs
A very recent example appears to be the simultaneous discovery of functorial (and "easy") resolution of singularities in characteristic 0 by McQuillan-Marzo (arXiv:1906.06745) respectively Abramovich- …
4
votes
Short papers for undergraduate course on reading scholarly math
Might László Lovász' resolution of the Kneser conjecture qualify?
Lovász, L. Kneser's conjecture, chromatic number, and homotopy. J. Combin. Theory Ser. A 25 (1978) 319–324.
Link
The statement …
20
votes
Interesting applications (in pure mathematics) of first-year calculus
Following on from the Galois theory example of Johannes, one straightforward way to produce an explicit polynomial with non-soluble Galois group over ${\mathbb Q}$ is to use an irreducible quintic wit …
- 3,202
26
votes
Algebraic geometry examples
One of my favourite sets of examples, stolen from Miles Reid, is the determination of rings $R=\oplus_m H^0(X, mD)$ for ample divisors $D$ on projective varieties $X$. A nice sequence, where a lot of …
3
votes
Do you read the masters?
Bolyai: Appendix, the first account of non-Euclidean geometry by one of its inventors. If nothing else, the beauty, clarity and brevity of exposition alone make this a must-read.
10
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Papers that debunk common myths in the history of mathematics
David Fowler's book "The Mathematics Of Plato's Academy: A New Reconstruction" sets out to deconstruct the myth that "the early Pythagoreans based their mathematics on commensurable magnitudes, but th …