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1500 questions
114
votes
30 answers
New grand projects in contemporary math
When I was a graduate student in math (mid-late eighties and early nineties) the arena was dominated by a few grand projects: for instance, Misha Gromov's hyperbolic groups, which spread into many seemingly heterogeneous domains (such as…
Mirco A. Mannucci
- 7,603
113
votes
3 answers
Is St. Petersburg a good place for the 2022 Int. Congress of Mathematicians
There might be just enough time to pick another location, but I am curious what mathematicians think. Will Ukrainian mathematicians be able to attend a conference in Russia if Russia no longer recognizes their passports?
To be clear: I love Russia,…
Ben McKay
- 25,490
113
votes
13 answers
What are the big problems in probability theory?
Most branches of mathematics have big, sexy famous open problems. Number theory has the Riemann hypothesis and the Langlands program, among many others. Geometry had the Poincaré conjecture for a long time, and currently has the classification of…
Simon
- 145
113
votes
10 answers
What are the benefits of writing vector inner products as $\langle u, v\rangle$ as opposed to $u^T v$?
In a lot of computational math, operations research, such as algorithm design for optimization problems and the like, authors like to use $$\langle \cdot, \cdot \rangle$$ as opposed to $$(\cdot)^T (\cdot)$$
Even when the space is clearly Euclidean…
Coco Jambo
- 277
113
votes
15 answers
Top specialized journals
In geometry/topology, there are (at least) three specialized journals that end up publishing a large fraction of the best papers in the subject -- Geometry and Topology, JDG, and GAFA.
What journals play a similar role in other subjects?
Let me be…
Andy Putman
- 43,430
113
votes
2 answers
How would you solve this tantalizing Halmos problem?
$1-ab$ invertible $\implies$ $1-ba$ invertible has a slick power series "proof" as below, where Halmos asks for an explanation of why this tantalizing derivation succeeds. Do you know one?
Geometric series. In a not necessarily commutative ring…
Bill Dubuque
- 4,706
113
votes
1 answer
What happened to Suren Arakelov?
I heard that Professor Suren Arakelov got mental disorder and ceased research. However, a brief search on the Russian wikipedia page showed he was placed in a psychiatric hospital because of political dissent.
Since in Soviet Union days a healthy…
Bombyx mori
- 6,141
113
votes
11 answers
On mathematical arguments against Quantum computing
Quantum computing is a very active and rapidly expanding field of research. Many companies and research institutes are spending a lot on this futuristic and potentially game-changing technology. Some even built toy models for a quantum computer in…
113
votes
25 answers
Examples of math hoaxes/interesting jokes published on April Fool's day?
What are examples of math hoaxes/interesting jokes published on April Fool's day?
For a start P=NP.
Added 2024-04-01 Anything new in 2024?
joro
- 24,174
113
votes
22 answers
What's the "best" proof of quadratic reciprocity?
For my purposes, you may want to interpret "best" as "clearest and easiest to understand for undergrads in a first number theory course," but don't feel too constrained.
Ben Webster
- 43,949
113
votes
54 answers
Which popular games are the most mathematical?
I consider a game to be mathematical if there is interesting mathematics (to a mathematician) involved in
the game's structure,
optimal strategies,
practical strategies,
analysis of the game results/performance.
Which popular games are…
Douglas Zare
- 27,806
112
votes
19 answers
What is the definition of "canonical"?
I just received a referee report criticizing that I would too often use the word "canonical". I have a certain understanding of what "canonical" should stand for, but the report shows me that other people might think differently. So I am asking:
Is…
Konrad Waldorf
- 4,304
111
votes
6 answers
Counterexamples in algebraic topology?
In this thread
Books you would like to read (if somebody would just write them...),
I expressed my desire for a book with the title "(Counter)examples in Algebraic Topology".
My reason for doing so was that while the abstract formalism of algebraic…
Johannes Ebert
- 20,634
111
votes
7 answers
Is the set $ AA+A $ always at least as large as $ A+A $?
Let $A$ be a finite set of real numbers. Is it always the case that $|AA+A| \geq |A+A|$?
My first instinct is that this is obviously true, and there is a one-line proof which I am foolishly overlooking. Can anyone provide one? Of course, any proof…
Oliver Roche-Newton
- 1,478
111
votes
2 answers
Does every non-empty set admit a group structure (in ZF)?
It is easy to see that in ZFC, any non-empty set $S$ admits a group structure: for finite $S$ identify $S$ with a cyclic group, and for infinite $S$, the set of finite subsets of $S$ with the binary operation of symmetric difference forms a group,…
Konrad Swanepoel
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