Most Popular
1500 questions
76
votes
5 answers
Does pointwise convergence imply uniform convergence on a large subset?
Suppose $f_n$ is a sequence of real valued functions on $[0,1]$ which converges pointwise to zero.
Is there an uncountable subset $A$ of $[0,1]$ so that $f_n$ converges uniformly on $A$?
Is there a subset $A$ of $[0,1]$ of cardinality the…
Bill Johnson
- 31,077
76
votes
3 answers
Czelakowski's claimed proof of the Twin Prime Conjecture
It seems like the article "The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I)" by Janusz Czelakowski published in Studia Logica yesterday, claims to have proven that…
Glycerius
- 1,023
76
votes
6 answers
Are there examples of (successful) NSF mathematics proposals available anywhere online?
As anyone who has ever applied to the NSF for a grant knows, such a proposal is a slightly odd piece of writing, not quite like anything else mathematicians are called upon to write. As such, it's a hard thing to learn to do well; of course, the…
Ben Webster
- 43,949
76
votes
4 answers
What are good mathematical models for spider webs?
Sometimes I see spider webs in very complex surroundings, like in the middle of twigs in a tree or in a bush. I keep thinking “if you understand the spider web, you understand the space around it”. What fascinates me, in some sense it gives a…
Claus
- 6,777
76
votes
4 answers
Who first characterized the real numbers as the unique complete ordered field?
Nearly every mathematician nowadays is familiar with the fact that
there is up to isomorphism only one complete ordered field, the
real numbers.
Theorem. Any two complete ordered fields are isomorphic.
Proof.…
Joel David Hamkins
- 224,022
76
votes
31 answers
Atlas-like websites on specific areas of mathematics
In this post, we look for the existing atlas-like websites providing well-presented classifications or database about some specific areas of mathematics. Here are some examples:
GroupNames:…
Sebastien Palcoux
- 25,922
76
votes
10 answers
Least collaborative mathematician
The recent question about the most prolific collaboration interested me. How about this question in the opposite direction, then: can anyone beat, amongst contemporary mathematicians, the example of Christopher Hooley, who has written 91 papers and…
Ben Green
- 4,756
76
votes
13 answers
What computational problems would be good proof-of-work problems for cryptocurrency mining?
What computational mathematics problems that could be used as proof-of-work problems for cryptocurrencies? To make this question easier to answer, I want proof-of-work systems that work in cryptocurrencies that contain many different kinds of…
Joseph Van Name
- 27,791
76
votes
33 answers
Free open-access peer-reviewed math journals
Is there any free (as in free beer, i.e., no publication fees or other fees whatsoever), open-access (free and open access to everyone) and peer-reviewed mathematics journal?
I am interested in a list of journals. I am particularly interested in my…
CAT0
- 177
76
votes
2 answers
Is it known that the ring of periods is not a field?
I have just learned here that we know numbers that are not periods; is it known meanwhile that the ring of periods is not a field? I know that it is conjectured that $1/\pi$ is not a period, but the existence of a period whose inverse is not a…
Franz Lemmermeyer
- 32,176
76
votes
28 answers
Writing papers in pre-LaTeX era?
I wonder how people wrote papers in the pre-LaTeX era? I mean, when typewriters and simple computers were (60th-70th?). Did they indeed put formulas by hand in the already printed articles?
psihodelia
- 565
76
votes
0 answers
2, 3, and 4 (a possible fixed point result ?)
The question below is related to the classical Browder-Goehde-Kirk fixed point theorem.
Let $K$ be the closed unit ball of $\ell^{2}$, and let $T:K\rightarrow K$
be a mapping such that
$$\Vert Tx-Ty\Vert _{\ell^{4}}\leq\Vert x-y\Vert…
Ady
- 4,030
76
votes
6 answers
Which graphs are Cayley graphs?
Every group presentation determines the corresponding Cayley graph, which has a node for each group element, and arrows labeled with the generators to get from one group element to another.
My main question is, suppose that we are given a directed…
Joel David Hamkins
- 224,022
76
votes
6 answers
Math Annotate Platform?
Suppose most mathematical research papers were freely accessible online.
Suppose a well-organized platform existed where responsible users could write comments on any paper (linking to its doi, Arxiv number, or other electronic identifier from…
Ingrid Daubechies
- 1
- 2
- 4
75
votes
4 answers
When is a singular point of a variety ($\mathcal{C}^\infty$-) smooth?
If $X$ is a nonsingular algebraic (or analytic) variety over $\mathbb C$ or $\mathbb R$ then it is certainly $C^\infty$ over the reals.
The converse is false for a silly reason : in the real or complex affine plane with coordinates $x,y$ the…
Georges Elencwajg
- 46,833