Now we just need this as a service. Another LLM that would encourage your agent like a cheerleader and provide emotional support and reassurance if necessary
As Tao points out, merely suggesting new open questions isn't really sufficient. Part of what gives these problems their fame is their notoriety, their difficulty, the fact that many prodigious mathematicians have spent an evening or week or month or several years studying it.
It wouldn't be as interesting if it had just been solved by the fifth random mathematician who considered it
Notably, gardening a new field of study in math is somewhat nontrivial. You have to introduce the field, illustrate some relevance or connections, and then - and this is key - not solve all of the low-hanging fruit yourself! Because you need somebody else to become an expert in that particular field.
The analog in programming is: if a large company merely open sources a product that's decent but not great and in a language nobody wants to maintain, but they don't commit to maintaining it themselves.
Suddenly there's a bit of a vacuum because in order to provide something of value, you either need to:
1. Implement something more complete than was initially open sourced
2. Or maintain something in a horrendous language while incrementally improving it and keeping it relevant
3. Or rewrite it into a tolerable and maintainable modern language.
What the large company has done is create a vacuum in the tool space where you now require extreme motivation to get someone else to step in.
Note that in this scenario, in 2026, it's actually not such a big deal. I think several recent models could happily translate it into a more maintainable language themselves or happily maintain it in the original crufty one. And so the question is: which parts of this analogy are true in math, too?
Yes, these things are definitely being conflated and there's a fourth conflated thing I think Tao is particular getting at:
(4) Mathematics, the community which is a living system that decides what is interesting, constructs shared frameworks, transfers ideas between domains, develops taste, teaches new mathematicians, and continually emphasizes what counts as important mathematics, especially in it's overall value to humanity.
This is the level in which theory building, simplification, integration and applications are built on. Contributing meaningfully here requires much more than generating solutions - it requires direction and restraint.
Tao seems to be saying that this direction and restraint is the scarce resource that drives mathematical progress, not problem-solving ability. And AI is not only insufficient at it, but results generated by AI are destroying human ability to excercise this resource.
This seems similar to another problem AI sucks at - drafting legal agreements. Despite being great at evaluating, interpreting, and comparing legal agreements it fails amazingly at drafting them. This is because what you don't say/do is vastly more important than what you do say/do.
And AI is great saying and doing things, it's the selection based on implied values that it struggles with.
You pick your axioms and you see what must be true. With math and logic, we can reason about any possible universe even though we live in only one of them.
Let’s say I’ve already worked on something, so the KV cache is already there. If I use /clear, I’ll have to do that work again.
And yes, the KV cache will remain available for one hour, but who knows when this claude api will recover? We might forget about it, and when we come back after an hour—boom - we’ll be charged for cold writes.
Yep, AFAIK. I have a statusline that tells me how far I'm into the cache lifetime. I tend to have dense prompts and carefully read its outputs, so by the time this outage occurred when I was ~50m into it. Cue frantically spamming "esc esc up enter", and 10m later it's dead Jim.
Well no, by the same logic it would be quaverquaverquaverquavic.
A hemidemisemiquaver, while a little scary for the performer, at least makes immediate perfect sense. Unlike that stupid "sixty-fourth note" rubbish. Music is art, not fractions!
awesome! keep going
great work! keep going
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