Disclaimer: this a blog-post consciously written in the style adumbrated in Compressing and summarizing. Part 0. For the original, see Historia Mathematica Volume 6, Issue 3, August 1979, Pages 294-304. For brevity, the source is referenced by loc. cit., and … Continue reading
Some are of the opinion that blogs add noise to the internet and make good information harder to find. There certainly is something to this view, but I think by and large blogs are to the good, when done well. … Continue reading
The following is an illustration of a very widely known, yet not widely-enough-known basic connection between things. Explanations will not be given. They can easily be found, given internet access. This connection gives a structure and systematic explanation for some … Continue reading
Did you know that mathematicians have beautifully imaginative ways to conceive of lines as cycles? For example, for many, is just a string of symbols. Yet, e.g. for mathematicians working in homological algebra this is kind-of-a-cycle in the sense that … Continue reading
One should intentionally take an intensional view on the things one cares about.
If one cares for categories, one should intentionally take an intensional view on them: axioms matter. In particular, associativity is an axiom. But it is excusable that one sometimes forgets that associativity is axiomatic: so many categories are concretizable (and then, … Continue reading
Arguably the simplest non-trivial example of an unlabelled simple undirected graph which is not reconstructible from its vertex-deleted subgraphs is the -regular tree, illustrated in parts by Needfull to say: that you only see five neighbors at each vertex is … Continue reading