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Results tagged with soft-question
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user 120914
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
12
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Why is the Dyck language/Dyck paths named after von Dyck?
The Dyck language is defined as the language of balanced parenthesis expressions on the alphabet consisting of the symbols $($ and $)$. For example, $()$ and $()(()())$ are both elements of the Dyck l …
2
votes
Progress on a problem list
Q3: For group theory, you will probably not find many more comprehensive surveys like this than the Kourovka Notebook; this has been active since 1965, and is regularly updated with new problems, whic …
7
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Examples of long running and consecutively numbered international meetings
There’s the AAA (Arbeitstagung Allgemeine Algebra), Workshop on General Algebra, which has been running for over 50 years (since 1971). It takes place all around Central Europe several times a year, e …
7
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What is an important mathematical question?
As Gil Kalai mentions in his answer that he "will not try to define depth", here's a possible complement to his answer. John Stillwell has an excellent lecture on this question and its history, availa …
3
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Results with short, advanced proofs or long, elementary proofs
I think a good example is the 1955/1958 Adian-Rabin theorem. This says that "given a finite presentation of a group, one can deduce almost nothing about the properties of the group". For example, the …
17
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Noteworthy, but not so famous conjectures resolved recent years
The Hall-Paige conjecture, first posed in 1955 by Marshall Hall and L. J. Paige, is the following:
A finite group $G$ has a complete mapping if and only if its Sylow $2$-subgroups are not cyclic. …
16
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Theorems with many distinct proofs
The Nielsen-Schreier theorem from combinatorial group theory ought to qualify, as it is one of the most fundamental theorems of this area. It was originally proved in a restricted form by J. Nielsen i …
8
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Examples of unexpected mathematical images
In the Jones monoid, a monoid associated to the Temperley-Lieb algebra, the idempotents were discovered (see Organic Semigroup Theory for an overview) to exhibit fern-like qualities when the Green's $ …
10
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Which great mathematicians had great political commitments?
How about a very recent political appointment? Eric Lander co-chaired Obama's "Council of Advisors on Science and Technology", and was very recently appointed to President Biden's director of the Offi …
4
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PhD dissertations that solve an established open problem
I suppose my own thesis fulfils this. Let $M$ be a monoid generated by a finite set $A$ and defined by a single defining relation $w=1$. The language of all words $v \in A^\ast$ representing the ident …
17
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Decision problems for which it is unknown whether they are decidable
The word problem for a finitely presented group $G = \langle A \mid R \rangle $ and the associated canonical homomorphism $\pi : F_A \to G$, asks: given an element $w \in F_A$, do we have $\pi(w) = 1$ …
11
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Atlas-like websites on specific areas of mathematics
The Blocks of Finite Groups wiki, which aims to classify the Morita equivalence classes of blocks with a given defect group. This is in part to understand Donovan's Conjecture better.
34
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What are examples of (collections of) papers which "close" a field?
This is not, perhaps, a very large area, nor a complete "ending", but it was an interesting development in early semigroup theory that I think bears writing down.
Some background, first. A semigroup $ …
10
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Appearance of proof relevance in "ordinary mathematics?"
Proof mining (which even has a short Wikipedia article!), and area in large part developed by Kohlenbach, is mentioned briefly in the comments, and I thought it deserves a bigger mention. Roughly spea …