14
votes
Publishing corollaries of previously published results
There is a famous paper where the main result is derived as a simple corollary of a result of another author published 23 years before:
J. Milnor, Eigenvalues of the Laplace operator on certain ...
- 91.8k
12
votes
Noteworthy, but not so famous conjectures resolved recent years
In a preprint recently posted to the arXiv, Jineon Baek claims to have solved the moving sofa problem, which asks for the largest area sofa that can be maneuvered through an L-shaped corridor, like ...
11
votes
Publishing corollaries of previously published results
In general, the rule is that one may (but not necessarily should) publish everything he/she considers worth attracting people's attention to (under the condition that their attention is not there ...
- 61.9k
7
votes
Publishing corollaries of previously published results
IMO, no problem at all. Say, our results on the congruence speed of tetration come from 5+ years of research, and the final formula of the constant congruence speed of tetration invokes a previously ...
- 1,451
7
votes
Why are some heuristics successful?
The Weil conjectures could qualify as a set of heuristics developed into a rigorous proof by Deligne and others:
What was really eye-catching, from the point of view of other
mathematical areas, was ...
6
votes
On the condition of preadditive categories being locally small
I don't completely understand the question, because I don't generally see a problem with locally small ordinary categories. My own experience has generally been that for some esoteric things category ...
- 66.8k
4
votes
Each mathematician has only a few tricks
A trick/technique that I like (and used) a lot is the formal geometry approach (after Gelfand-Kazhdan) for passing from a local to a global result.
Let $X$ be a $d$-dimensional manifold. There is a an ...
4
votes
Accepted
What is the best way to read advanced textbooks in Pure Mathematics (PhD Level)?
If the books have problems sections, the most important thing is to do the problems to the best of your ability -- "tell me, and I forget; show me, and I remember; let me do, and I understand&...
- 3,065
4
votes
Each mathematician has only a few tricks
In all 200+ pages of my category theory notes, there were essentially three tricks I used in proofs:
Prove that two arrows are both the arrow induced by a universal property, so they're the same ...
4
votes
Publishing corollaries of previously published results
To avoid salami-slicing, just keep the size and claims of the new paper appropriately modest. The problematic sense of salami-slicing is when a twenty-page paper appears to claim complete novelty, ...
- 21.3k
4
votes
Noteworthy, but not so famous conjectures resolved recent years
Here is the abstract of Andreas Reinhart, A counterexample to the conjecture of Ankeny, Artin and Chowla, available at https://arxiv.org/html/2410.21864v1
``Let $p$ be a prime number with $p\equiv1\...
3
votes
What is the best way to read advanced textbooks in Pure Mathematics (PhD Level)?
Remembering the ‘core ideas of proofs’ essentially amounts to remembering all the relevant definitions and understanding how they relate to one another; this is essentially the content of any given ...
- 10.1k
3
votes
Accepted
Have Grothendieck's notes in Montpellier already been investigated?
You could keep an eye on the Quaderni del Centro di Studi Grothendieckiani, a biennial refereed journal dedicated to exploring Alexander Grothendieck's mathematical and intellectual legacy. The first ...
- 72
3
votes
Comments and reference-request on books for KK-theory
Here is a very rough outline of the proof of the index theorem using KK-theory:
Define $KK_G(A, B)$, where $G$ is a Lie group and $A$ and $B$ are
[adjectives] C*-algebras, and the Kasparov product ...
- 29.2k
1
vote
Each mathematician has only a few tricks
In my personal field, applied optimal transport for PDEs, we often play the following game, so much so that some of my colleagues and I actually call it Brenier's trick (after Yann Brenier): When ...
1
vote
Every mathematician has only a few tricks
The trivial cohomology box trick
When trying to solve a problem, prove that:
...
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