I got very serious recently about using formal languages in mathematics, and I am trying (like I did once with Magma) to internalize how they function and how I can think in them naturally and basically keep up with a formal proof like I can grasp the flow of regular mathematical text in my field. Obviously, due to the popularity, structure of the type theory, and expressive power (+Mathlib), I decided to explore in depth Lean and one other language which I've built with agents for Peano arithmetic. So far, the main obstacle I can see is that the architecture of many tactics makes it super unfriendly to follow the proof. This is one of those gaps + strange syntax in Lean which still makes me very confused when I try to read such a text. I don't have such problems with Magma, where the ideas are encoded in a much more natural way. This is probably one of those directions in which I want to develop: how to make formal languages which are easy to follow, have a particular deduction style, or are simply expressive enough to make the argument look very compact, yet understandable. In hindsight, I can see that these were some of the problems which Georg Cantor had when he tried to formalize the mathematical work of the day. I had a look at Anthropic's formalization of FLT and... there is so much work :) I can definitely sympathize with Kevin Buzzard that his quest is different. We can appreciate some proof artifact, but the composition of the code, high-level engineering, and difficult choices about how things should be formalized to make them work better (filters for limits...) are equally important, or sometimes even more important than a particular proof artifact itself. Overall, mathematics is an art of exploring new avenues, and Lean and other formalized languages give us so much space for beautiful discoveries, new engineering, and can simply help us organize human knowledge better. So yes, learn formalization as something entirely new, a higher, deeper insight into thoughts. You won't be disappointed, maybe only with how badly AI is still doing this autonomously. We should keep improving this too. Going back to work on elliptic curves in Lean :)

AI labs will pay you to learn from your agent's mistakes. AI products generate large volumes of user-agent interaction data. Magma turns that into training datasets and enables companies to earn recurring revenue from it.

I got into @ycombinator I'm 18, solo founder, and 3 years ago was studying 10th grade at a random city in Iran (Qazvin, love it). In Iran, I had to build my own VPN to access UK curriculum material, then got myself into a boarding school in Oxford, paid the tuition by selling my AI thing, and then got a full-ride to study AI at Rice University. After I got in the US I did some more things that led to Magma. I don't have much to say for advice as I'm unlearning a lot recently. However, as an observation, the laws of physics seem to be flexible enough that you can simply do things; anything in fact. Human brain just evolutionarily underestimates that flexibility. PS: Repost and I'll send you the full application that got me in.

MAGA Republicans cut TRILLIONS from healthcare in the Big Ugly Bill and STILL refuse to pass ACA Tax Credits in the Senate. The bully-in-chief now wants to kick even more Americans off their healthcare. VOTE THEM OUT to check this cruelty, corruption and chaos. #BlueWaveIn40Days#

Maga candidate Bo French’s campaign turned into a national political controversy after his racist social media posts triggered an argument within the Republican Party that is seeping into the bigger race for one of Texas’s US Senate seats.