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Results tagged with big-list
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user 1459
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.
32
votes
Situations where “naturally occurring” mathematical objects behave very differently from “ty...
Thanks to Boris Tsirelson, we know that not all infinite-dimensional Banach spaces contain either $c_0$ or $\ell_p$ for some $p\in [1,\infty)$. But all known counterexamples are constructed in a parti …
21
votes
Are there any good websites for hosting discussions of mathematical papers?
Time to mention the Selected Papers Network: https://selectedpapers.net
EDIT:
I hope that Tim does not mind me editing this to add extra links:
Introductory discussion by John Baez: http://johncar …
13
votes
Believing the Conjectures
I initially wrote this as a comment, but it got too long and it sort of contains an example, so here goes. Reflection seems false in a number of contexts, since there are many properties that can't be …
8
votes
Casual tours around proofs
Timothy Chow's article on forcing (called A Beginner's Guide to Forcing) is one of the best of this general type.
http://www-math.mit.edu/~tchow/forcing.pdf
15
votes
Examples of theorems misapplied to non-mathematical contexts
This is a wonderful and fascinating still life by Juan Sanchez Cotán: https://www.khanacademy.org/humanities/monarchy-enlightenment/baroque-art1/spain/a/juan-sanchez-de-cotn-quince-melon-and-cucumber
…
8
votes
What are some slogans that express mathematical tricks?
Pick a random example.
If you add lots of small and reasonably independent things together then the result will be highly concentrated about its mean.
2
votes
Video lectures of mathematics courses available online for free
Eight recent lectures by Emmanuel Candes on compressed sensing are linked to from here: http://www.newton.ac.uk/programmes/INI/iniw04p.html
More generally, the Newton Institute has been making a larg …
117
votes
Books you would like to read (if somebody would just write them…)
I don't know for certain that this doesn't exist, so I'm in a no-lose situation: if this is a rubbish answer then it means that a book that I want to exist does exist. Many mathematicians of a pure be …
49
votes
Theorems that are 'obvious' but hard to prove
There are a number of facts in multivariable calculus that are obvious but hard to prove. For instance, the change-of-variables formula in a multiple integral is very easy to justify heuristically by …
131
votes
Theorems that are 'obvious' but hard to prove
If $I_1,I_2,\dots$ are intervals of real numbers with lengths that sum to less than 1, then their union cannot be all of $[0,1]$. It is quite common for people to think this statement is more obvious …
41
votes
Examples of undergraduate mathematics separation from what mathematicians should know
One category of mathematical result that belongs to 1 is statements that you need to know are true and that have complicated proofs. Obviously some such proofs are worth knowing because they will help …
15
votes
Problems where we can't make a canonical choice, solved by looking at all choices at once
Another thought is the path-integral formulation of quantum mechanics, where one integrates over all possible histories of a system, with appropriate weights.
14
votes
Problems where we can't make a canonical choice, solved by looking at all choices at once
I don't know whether you would count this, but the proof of the existence of quotient groups seems to fit your description. Some people define the product of the cosets $gH$ and $g'H$ to be the coset …
24
votes
Proofs of the uncountability of the reals
Although I very much take Timothy Chow's point, and don't have a way of constructing anything like a model where Cantor's diagonal argument is blocked (I'm not sure what the diagonal argument is in th …
- 29k
9
votes
What are examples of mathematical concepts named after the wrong people? (Stigler's law)
In honour of the recently departed Benoit Mandelbrot, perhaps it is appropriate to offer up the example of the Mandelbrot set, the first pictures of which were drawn in 1978 by Robert Brooks and Peter …