What is a good definition of a mathematical structure?
May 21, 2020 · I understand a mathematical structure as a subset of the set-theoretic universe in which the real power-sets are well-defined. The formulas determining a mathematical structure are …
Most intricate and most beautiful structures in mathematics
I believe a structure mathematicians are gradually understanding is manifesting itself in various areas of algebra, number theory, analysis, probability theory, theoretical physics, geometry, topology, set …
What are good mathematical models for spider webs?
Sep 13, 2020 · I started to wonder what are good mathematical models for spider webs. Obvious candidates are geometric graphs embedded in surfaces, or rather in space. One could argue that …
mathematical philosophy - Seemingly emergent structures in …
A nice example of seemingly trivial structure that hides highly nontrivial structure is that of a projective space. Such a space consists of "points', "lines", and "planes" with the obvious properties: there is a …
Underlying structure behind the infamous IMO 1988 Problem 6
Dec 30, 2017 · The elementary proof is well known and based on infinite descent using Vieta jumping. What are non-elementary ways of solving it? Which mathematical structure is useful in creating the …
Are there any books/articles that apply abstract coordinate free ...
Apr 14, 2018 · The mathematical structure of thermodynamics by Peter Salamon (pdf) would be an example, but i would like a more abstract natural formulation of application of differential geometry or …
What categorical mathematical structure(s) best describe the space of ...
Is there a standard mathematical structure which well describes the structure of the space of localized measurements which Rovelli has envisioned? I know of Isham's work on topos theory and quantum …
Where does a math person go to learn quantum mechanics?
If you are willing to study some C*-algebras, another suggestion is Strocchi's An Introduction to the Mathematical Structure of Quantum Mechanics. It does not assume any background in physics, but it …
Why do infinite-dimensional vector spaces usually have additional ...
Aug 16, 2023 · But in "real life," we usually start with examples, which come with oodles of structure, and much of our task as mathematicians is to strip away much of that structure in order to clarify …
Examples of unexpected mathematical images - MathOverflow
Aug 12, 2014 · This self-similar structure was first noticed by observing the following drawings of Hasse diagrams. The first one is defined over the integer partitions of $40$ and its self-similarity was …