A video on an actual formalization task from my Polynomial Freiman Ruzsa (PFR) project, which is sufficiently tricky (and sufficiently far from existing training data of current models) that one still has to largely formalize these proofs by "hand":
I think the most tricky thing people run into is how should you put together your data structures? I mean for your code you can mostly do the same things as you can in other languages. I mean that's not entirely true but the big thing is really the data structures.
I expect AI to increase productivity of top mathematicians much more than that of top writers, because formalization is a kind of translation task, it doesn't require much judgement, and as long as it compiles noone needs to read the result.
the reason that I think this is kind of tricky is quite subtle. And it's the fact that anytime you use an LLM to assign a reward, those LLMs are giant things with billions of parameters and they're gameable.
the current situation in Iran shows that even if an "IAEA for AI" is necessary for some purposes, it won't be sufficient for resolving the tricky geopolitical issues raised by AI.
So right now I estimate that the time and effort taken to formalize it, proof is about 10 times the amount taken to write it out. So it's doable, but it's annoying.
"It’s honest in how it covers topics like navigating tricky power dynamics with CEOs, surviving 'peer panic,' dealing with competition within leadership teams, and in its overall breadth and depth."
While we love GraphQL for many use cases, implementing a secure and performant GraphQL API can be tricky and there is a definite cost to requiring it during early prototyping of your app.
As the title suggests, this offers a highly pictorial introduction to complex analysis. I would not use this as the only text to learn about complex analysis, but Needham does a marvelous job of conveying the beauty of the subject, with numerous helpful intuitions for otherwise famously tricky ideas.
On the other hand, by avoiding foundations, projects also avoid the question of how to formalize their governance, thus risking a “tyranny of structurelessness” that might range from projects living inside a company forever, to disorganized chaos that negatively impacts project velocity.
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