Monthly Archives: July 2017

Compressing and summarizing. Part 1.

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

Posted in Uncategorized | Leave a comment

Compressing and summarizing. Part 0.

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

Posted in compressing and summarizing, expository, Olds | Leave a comment

Vignettes. Part 8.

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

Posted in Category Theory, expository, logic, Mathematics, Olds, Vignettes. | Leave a comment

Vignettes. Part 7.

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

Posted in expository, kind-of-a-cycle, Mathematics, Vignettes. | Tagged | Leave a comment

Mathematical Aphorisms. Part 2.

One should intentionally take an intensional view on the things one cares about.

Posted in Category Theory, expository, felicities, logic, mathematical aphorisms, Uncategorized | Leave a comment

Vignettes. Part 6.

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

Posted in Category Theory, expository, logic, Olds, Vignettes. | Leave a comment

Vignettes. Part 5.

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

Posted in expository, Higher trees, Mathematics, Olds, Research | Leave a comment