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

# Category: math

# Math is a language.

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.

# Setting up Agda on Debian

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

# You won’t believe what this space is homeomorphic to

A serendipitous encounter with an intriguing exercise led me to an Eureka! moment, with great beauty involved.

# The one integration secret mathematicians don’t want you to know

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

# Perspectives on categories.

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.

# A game with AC, plus the story of a poster.

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.