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      Questions tagged [soft-question]

      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. In other words, questions that can be answered without making computations or applying theorems and axioms.

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      4
      votes
      0answers
      69 views

      Survey article model theory research

      I've taken a graduate course in model theory and I like it so much that I can imagine doing research in this area. Are there survey articles or review papers on the current research topics in model ...
      27
      votes
      13answers
      3k views

      Unconventional examples of mathematical modelling

      Disclaimer. The is admittedly a soft question. If it does not meet the criteria for being an acceptable MO question, I apologize in advance. I'll soon be teaching a (basic) course on mathematical ...
      8
      votes
      1answer
      844 views

      Who invented Monoid?

      I was trying to find (and failed) the original author of either the concept of Monoid (set with binary associative operation and identity) the name (which sounds french ? and also Dioid (for what ...
      37
      votes
      3answers
      4k views

      On math looking obvious in retrospect [closed]

      Admittedly, a soft-question. I, being a very young researcher (PhD student) have personally faced the following situation many times: You delve into a problem desperately. No progress for a very long ...
      3
      votes
      3answers
      906 views
      +50

      Reference request: any 20th century German critiques of Bourbaki?

      Vladimir Arnold is known, among other things, for offering a scathing critique of Bourbaki: The Arnold – Serre debate Recently I've been reading some Nietzsche, and he chides some Germans in the ...
      -1
      votes
      0answers
      182 views

      The meaning of “geometric intuition” II [closed]

      I am trying to think of geometry in a pedagogical context and in particular, to what extent "geometric intuition" is a built-in part of our brain (and to what extent is it earned through experience). ...
      4
      votes
      1answer
      113 views

      Graphs with Hermitian Unitary Edge Weights

      Very recently, Hao Huang proved the Sensitivity Conjecture, which had been open for 30 years or so. Huang's proof is surprisingly short and easy. Here is Huang's preprint, a discussion on Scott ...
      20
      votes
      2answers
      763 views

      Why would one number theorems, propositions and lemmas separately?

      When it comes to numbering results in a mathematical publication, I'm aware of two methods: Joint numbering: Thm. 1, Prop. 2, Thm. 3, Lem. 4, etc. Separate numbering: Thm. 1, Prop. 1, Thm. 2, Lem. 1,...
      4
      votes
      2answers
      291 views

      Texts on moduli of elliptic curves

      I want to study FLT (Fermat's Last Theorem), and now I'm studying moduli of elliptic curves. I've heard that Deligne-Rapoport, Katz-Mazur, Mazur's "Modular curves...", and Katz's "p-adic..." are very ...
      0
      votes
      2answers
      209 views

      Naming convention: Adjective for linear operators that are endomorphisms

      If a matrix has the same number of rows and columns, we call it a square matrix. The analogous concept for linear operators would be operators with the same domain and range, i.e., endomorphisms. Is ...
      -4
      votes
      1answer
      164 views

      Are there major research areas in math? Or is it a lot of individual efforts? [closed]

      In physics, for example, dark matter is a major research area now. And there are specific parts of that trending. Is there anything similar in math? Is there something the majority of mathematicians ...
      2
      votes
      0answers
      279 views

      Is there such a field as applied $\infty$-category theory?

      It seems that applied category theory has exploded in popularity in recent years. My question is simple: had there been any work using $\infty$-category theory in applications? Edit: By ...
      34
      votes
      26answers
      4k views

      Examples of simultaneous independent breakthroughs

      I'm looking for examples where, after a long time with little progress, a simultaneous mathematical discovery, solution, or breakthrough was made independently by at least two different people/groups. ...
      1
      vote
      0answers
      139 views

      What imaginations of Lebesgue spaces or other Banach spaces do people intuitively share?

      At several occasions I heared people discussing about the ?colors“ of Lebesgue spaces $L^p$: $L^2$ is red, $L^1$ is white, $L^\infty$ is black, and the other $L^p$ are blue or violett. Of course this ...
      14
      votes
      1answer
      378 views

      Legendary extra parameters to simplify a counting problem

      I am reading Proofs and Confirmations, the history behind the alternating sign matrix conjecture, regarding counting $n \times n$ alternating sign matrices. In the introduction, it is written that ...

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