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Results tagged with big-list
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user 3106
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.
6
votes
Favourite scholarly books?
Éléments de mathématique by Nicolas Bourbaki.
13
votes
Mathematical research papers in general science journals
MathSciNet is another obvious resource. I just tried this myself and found that typing "Science" in the "Journal" search box does not have the desired effect; instead, I had to go to the Journals tab …
1
vote
Older editions of which books were better than the new ones?
This kind of thing is very subjective, but in my opinion the third edition of Computability and Logic by Boolos and Jeffrey is better than the fourth, at least from the point of view of someone intere …
3
votes
Real number happens to be an integer
See Making Transcendence Transparent: An Intuitive Approach to Classical Transcendental Number Theory by Burger and Tubbs. It is only a slight exaggeration to say that the entire book is devoted to s …
3
votes
Favourite scholarly books?
Abramowitz and Stegun's Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, and its successor, the NIST Handbook of Mathematical Functions.
16
votes
Papers in which the questions were more interesting than the results
The importance of Subhash Khot's paper on the Unique Games Conjecture derives primarily from the significance of the conjecture that he introduced, which has stimulated an enormous amount of research …
5
votes
Papers in which the questions were more interesting than the results
The $n!$ conjecture is perhaps another near-miss. It was posed 25 years ago by Garsia and Haiman, and the ideas in the paper are interesting and non-trivial, but the conjecture itself was probably th …
10
votes
Which mathematical definitions should be formalised in Lean?
This might be slightly controversial, but I think that one thing that would be valuable to formalize in Lean is the definition of a set.
Working mathematicians are used to formalizing things in terms …
2
votes
Lesser known examples of perseverance with a successful ending
I'm not sure if you're insisting on examples in which a mathematician (or group of mathematicians) works single-mindedly on a single problem for many years and finally conquers the problem. If so, th …
18
votes
List of long open, elementary problems which are computational in nature
Finding the set of forbidden minors for the class of toroidal graphs (finite graphs that can be embedded in the torus with no crossings). By the Robertson–Seymour theorem, this set is finite, but it …
18
votes
Examples of statements that provably can't be proved using a promising looking method
The statement, though unfortunately maybe not the proof, of Wilkie's solution to Tarski's high-school algebra problem, is certainly accessible to freshmen.
7
votes
Unnecessary uses of the Continuum Hypothesis
A Dowker space is a normal Hausdorff space whose product with
the closed unit interval $I$ is not normal. In 1971, Mary Ellen Rudin constructed the first ZFC Dowker space, which had cardinality $\alep …
26
votes
Examples of famous 'workhorse' theorems
As others have noted, this sort of thing is commonplace in analysis. The best results often flow directly from the strongest available estimates, and the strongest estimates are often complicated and …
1
vote
Favourite scholarly books?
The Encyclopaedia of Mathematics.
25
votes
Fields of mathematics that were dormant for a long time until someone revitalized them
This might not be exactly what you're asking for but I think it's close: Manjul Bhargava's generalizations of Gauss's composition law to higher composition laws. While Gauss's composition law did not …