Gavin Zhao @[email protected]

Normalize these things as normal everyday fashion accessories
https://twitter.com/ctctyo_H/status/1802174373320876312

I need to set up cameras

#ScientificAmerican recently reprinted an interview I had a few months ago on the future of proof assistants and #AI in #math: https://www.scientificamerican.com/article/ai-will-become-mathematicians-co-pilot/ . In it, I made the following assertion:

"I think in the future, instead of typing up our proofs, we would explain them to some #GPT. And the GPT will try to formalize it in #Lean as you go along. If everything checks out, the GPT will [essentially] say, “Here’s your paper in #LaTeXmath; here’s your Lean proof. If you like, I can press this button and submit it to a journal for you.” It could be a wonderful assistant in the future."

This statement seems to have received a mixed reception, in particular it has been interpreted as an assertion that mathematicians would be become lazier and sloppier with writing proofs. I think the best way to illustrate what I mean by this assertion is by a worked example, which is already within the capability of current technology. At https://terrytao.wordpress.com/2016/10/18/a-problem-involving-power-series/ I have a moderately tricky problem in complex analysis. In https://chatgpt.com/share/63c5774a-d58a-47c2-9149-362b05e268b4 , I explained this problem and its solution to #ChatGPT in an interactive fashion, and after the proof was explained, GPT was able to provide a LaTeX file of the solution, which one can find at https://terrytao.wordpress.com/wp-content/uploads/2024/06/laplace.pdf . GPT performed quite well in my opinion, fleshing out my sketched argument into quite a coherent and reasonably rigorous full proof. This is not 100% of what I envisioned in the article - in particular the rigorous Lean translation in order to guarantee correctness is missing, which I think is an essential requirement before this workflow can be used for research quality publications - but hopefully will illustrate what I had in mind with the quote.

No rational person would do this

First full day running @buddiesofbudgie #Budgie Desktop on top of a Wayland compositor. Even in it's still very heavily WIP form.

Panel exclusion zone now implemented and thanks to some rubber ducking / help from @EbonJaeger , figured out what was wrong with my Budgie PopoverRedux.

Old Budgie.Popover code is gone, all the popovers are using the new implementation which are basically just Gtk.Popover. It'll be renamed back to Budgie.Popover once I do cleanup of PopoverManager and maybe refactor some more code.

Screenshot shows the bluetooth applet... well now being shown, as well as VS Code not being allowed to be maximized under the panel.

Biggest usability thing next for me will be making Raven not 100% full screen and the panel to always be set to the primary monitor rather than whichever monitor is in focus.

In math research papers (particularly the "good" ones) one often observes a negative correlation between the conceptual difficulty of a component of an argument, and its technical difficulty: the parts that are conceptually routine or straightforward may take many pages of technical computation, whereas the parts that are conceptually interesting (and novel) are actually relatively brief, once all the more routine auxiliary steps (e.g., treatment of various lower order error terms) are stripped away.

I theorize that this is an instance of Berkson's paradox. I found the enclosed graphic from https://brilliant.org/wiki/berksons-paradox to be a good illustration of this paradox. In this (oversimplified) example, a negative correlation is seen between SAT scores and GPA in students admitted to a typical university, even though a positive correlation exists in the broader population, because students with too low of a combined SAT and GPA will get rejected from the university, whilst students with too high a score would typically go to a more prestigious school.

Similarly, mathematicians tend to write their best papers where the combined conceptual and technical difficulty of the steps of the argument is close to the upper bound of what they can handle. So steps that are both conceptually and technically easy don't occupy much space in the paper, whereas steps that are both conceptually and technically hard would not have been discovered by the mathematician in the first place. This creates the aforementioned negative correlation.

Often the key to reading a lengthy paper is to first filter out all the technically complicated steps and identify the (often much shorter) conceptual core.

I hope this email finds you well, and taking better care of yourself.

At last, some information from Google that students can really use!