I've just read one of the best pieces of writing about the why of applied category theory I ever had the pleasure to read. I resonate so much with it that I want to copy it verbatim here: How can we gain the benefits of standardization, compositionality and generality? There is no one answer, ex[c]ept … Continue reading A complexity-taming thing
I'm in the business of categorical cybernetics. But what is it exactly? Jules Hedges coined the term some years ago (2019), after he had been working on compositional game theory for serveral years already. He moved to Glasgow the following year, and at the same time I moved there to start my PhD. In fact, … Continue reading A personal prospect of categorical cybernetics
Moved to https://matteocapucci.eu/mathematicians-dont-care-about-foundations/ Many people seem to believe mathematicians work in non-constructive, non-structural, battered foundations because they love their Platonic realm and have a kink for AC and LEM. The reality is most mathematicians don't have a clue about foundations, they don't care, and happily work informally for all their lives. Case in point, mathematical … Continue reading Mathematicians don’t care about foundations
In mathematics, proofs are all the rage. I'm currently TAing a course on theory of computation, which is the most math many students have seen in the last four years, and definitely not high school style mathematics (i.e. 'shut up and calculate'). So I've been asked some tips on how to cope with proof writing … Continue reading Tips on learning how to write proofs
I was recently trying to convince Bruno that covectors (in the form of differentials of functions) are the real deal in gradient descent, despite the misleading name and countless pictures showing little arrows pointing downhill.
How can mathematicians be aware of the world they live in
Is most mathematics useless? Yes.
In my previous post, I argued mathematics can be considered as an highly sophisticated, fractal language in which ideas are layered on each other to build very tall mathematical buildings. Rigourous proofs are the strong mortar keeping the tower standing up. All of this was philosphical and suggestive, and stemmed from the evergreen question 'of … Continue reading Math is a language, pt. 2
I always been a lover of 'math for the sake of math' and I found annoying to ask 'but what is this useful for?' when learning about a new concept. It might seem weird, but to a pure mathematician 'apply' sounds like 'spoil'. Applications are a kind of low rank pursue for a mathematician, something … Continue reading Math is a language.
I wrestled with this for some days, but finally I figured it out. Here's a Bash script distilling the lessons I learned. The starting point is obviously Agda (quite cumbersome) documentation. I couldn't manage to run anything installed from apt, therefore I went for the first method. apt-get update # libraries necessary to run Cabal … Continue reading Setting up Agda on Debian
A serendipitous encounter with an intriguing exercise led me to an Eureka! moment, with great beauty involved.
Hey folks, it's been a while! One of my New Year's resolutions is to write more on this blog (at least weekly, says the list), so here I am. My biggest impairment in doing so has been the feeling of incompetence about a lot of the stuff that interests me, hence my good intentions crashed … Continue reading The one integration secret mathematicians don’t want you to know
Category theory is a very fascinating area of mathematics. It's unexpectedly powerful in an incredible width of different contexts, from the purest abstractions to the most concrete applications. I'm far from being an expert in category theory, although I enjoy fiddling with it and looking through the categorical lens at the material of my courses. … Continue reading Perspectives on categories.
Today I stumbled upon an interesting article about a 'paradoxical' appearance of the axiom of choice in a generalization of the known 'hats on prisoners' puzzle. Two Three interesting thing in the linked page: The generalization of the game: multiple colours, infinite prisoners. I also guess ultrafilters appear, in disguise, when talking equivalences on infinite … Continue reading A game with AC, plus the story of a poster.
If you choose not to decide, you still have made a choice. ~ Neil Peart
Thoughts I have and things I note as I learn math
confessions of a relentlessly staggering blunderer in the mindfield
Jade Master's Blog About Categories
A random mathematical blog
"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." - Paul Halmos
Category Theory, Haskell, Concurrency, C++
Miscellaneous maundering
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
Representation theory, geometry and whatever else we decide is worth writing about today.
Derek Wise's blog: Mathematics, Physics, Computing and other fun stuff.
Born to be Wild
General abstract nonsense. 