I think when thinking about progress as a society, people need to internalize better that we all without exception are on this world for the first time.

We may have collectively filled libraries full of books, and created yottabytes of digital data, but in the end to create something novel somebody has to read and understand all of this stuff. Obviously this is not possible. Read one book per day from birth to death and you still only get to consume like 80*365=29200 books in the best case, from the millions upon millions of books that have been written.

So these "few tricks" are the accumulation of a lifetime of mathematical training, the culmination of the slice of knowledge that the respective mathematician immersed themselves into. To discover new math and become famous you need both the talent and skill to apply your knowledge in novel ways, but also be lucky that you picked a field of math that has novel things with interesting applications to discover plus you picked up the right tools and right mental model that allows you to discover these things.

This does not go for math only, but also for pretty much all other non-trivial fields. There is a reason why history repeats.

And it's actually a compelling argument why AI is still a big deal even though it's at its core a parrot. It's a parrot yes, but compared to a human, it actually was able to ingest the entirety of human knowledge.

> Yes, current LLMs likely still lack some major aspects of intelligence.

Indeed, and so do current humans! And just like LLMs, humans are bad at keeping this fact in view.

On a more serious note, we're going to have a hard time until we can psychologically decouple the concepts of intelligence and consciousness. Like, an existentially hard time.

Luckily for us, whole fortunes can be made by filling in the blanks between what we know and what we realize.

People keep saying this, but the only ways I know of for formalizing this statement, appear to be probably false?

I don’t know what this claim is supposed to mean.

If it isn’t supposed to have a precise technical meaning, why is it using the word “interpolate”?

And homo sapiens, glancing at a system that gets better and better at solving problems, tries to deny it and comes up with the broken-clock analogy.

Those are just analog. If it's a broken digital clock, then all bets are off.

They are bad at math. But they are good at writing code and as an optimization some providers have it secretly write code to answer the problem, run it and give you the answer without telling you what it did in the middle part.

What tier are you using? I have run lots of problems and am very impressed, but I find stupid errors a lot more frequently than that, e.g., arithmetic errors buried in a derivation or a bad definition, say 1/15 times. I would love to get zero failures out of thousands of (what sounds like college-level math) posed problems.

calc, stat etc from a text book is something they would naturally be good at but I don't think book based computations thats in the training set and its extrapolations is what is at question here.

They are not great at playing chess as well - computational as well as analytic.

I only have rudimentary understanding of calculus, trigonometry, Google Sheets, and astronomy, but I was able to construct an accurate spreadsheet for astrometry calculations by using Grok and Gemini (both free, no subscription, just my personal account) to surface the formulas for measuring the distance between 2-3 points on the celestial sphere. The LLMs assisted me in also writing functions to convert DMS/HMS coordinates to decimal, and work in radians as well.

I found and fixed bugs I wrote into the formulas and spreadsheets, and the LLMs were not my sole reference, but once the LLM mentioned the names of concepts and functions, I used Wikipedia for the general gist of things, and I appreciated the LLMs' relevant explanations that connected these disciplines together.

I did this on March 14, 2026

>I rely on them constantly for maths (linear algebra, multivariable calc, stat)

That's one way to waste a ton of tuition money to just have a clanker do your learning for you.

Unless you're teaching it, in which case I hope your salary is cut by whatever percentage your clanker reduces your workload.

It's 80 minutes, not 80 hours.

How long do you figure it’d take to solve the problem yourself?