git commit -m "<scoped message>" -- path/to/file1 path/to/file2 skips git add and commits just specific already tracked files. Use git restore --staged :/ && git add "path/to/file1" "path/to/file2" && git commit -m "<scoped message>" -- path/to/file1 path/to/file2 for untracked files (which have to be added first). Now you can trust agents to use git (agent file).If something takes longer than I anticipated, I just hit escape and ask “what’s the status” to get a status update
Tab in Codex to queue next prompt. Can use for related featuresMy current approach is usually that I start a discussion with codex, I paste in some websites, some ideas, ask it to read code, and we flesh out a new feature together. If it’s something tricky, I ask it to write everything into a spec, give that to GPT-5-Pro for review (via chatgpt.com) to see if it has better ideas (surprisingly often, this greatly improves my plan!) and then paste back what I think is useful into the main context to update the file.
Ask the model to write tests after each feature/fix is done. Use the same context. This will lead to far better tests, and likely uncover a bug in your implementation.
My Agent file is currently ~800 lines long and feels like a collection of organizational scar tissue. I didn’t write it, codex did, and anytime sth happens I ask it to make a concise note in there.
China has more engineers both in absolute terms and per capita. America has far more lawyers. This imbalance extends to STEM PhDs. China produces more in absolute numbers, though not yet relative to population. But it is clearly heading in that direction.
If we normalize by population and limit to graduates from top-200 universities
America produces 4.7 times more STEM PhDs per capita than the best universities in China.
I think it is fair to treat university rank as crucial when it comes to research, since talent, funding, and lab resources are highly concentrated at a few institutions (not always correlated with rankings).Note, for education, this is much less true. Most universities teach roughly the same material. The main differences are peer group, credential value, and access to opportunity — none of which are the education itself.
Additionally, America brain drains the other nations
We retain 77% of international STEM PhD graduates in the long term.
However, there are still two questions at hand:
After enough internalization, enough transformation, enough generalization, enough use, and enough connection, the mathematical community eventually decides that the central concepts in the original theorem, now perhaps greatly changed, have an ultimate stability. If the various proofs feel right and the results are examined from enough angles, then the truth of the theorem is eventually considered to be established. The theorem is thought to be true in the classical sense—that is, in the sense that it could be demonstrated by formal, deductive logic, although for almost all theorems no such deduction ever took place or ever will.
Mathematicians use simplicity as the first test for a proof
It must go through social processing to gain validity. And complex deductions can be harder to validate because of their length and minutia. If a proof cannot be read, its truth does not function as knowledge. A verifier would be the gold standard, but for sufficiently complex systems, such verifiers do not exist in practice.
Since the requirement for a program is informal and the program is formal, there must be a transition, and the transition itself must necessarily be informal.
Moreover, the specification itself evolves through the labor of implementation. Coding shapes the spec just as much as the spec shapes the code.
“Babysitting for a sleeping child for one hour does not scale up to raising a family of ten—the problems are essentially, fundamentally different.”
This echos a common insight (Mythical Man Month, etc.) that processes scale non-linearly.