George Lowther, Author of Almost Sure blog, on maths, probability and stochastic calculus. Also on YouTube https://xitter.cf/t.co/VyOijwbe9l
London, UK
Joined September 2020
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Even funner fact: digging into the OAI proof to see what it actually says, quantitatively...
looking at terms of size ~ n^{-0.2}
Can't be more than 15,000 of them...for n growing exponentially. Need to go up to at least 10^{2,900,000,000} terms before it has anything to say...
numerically summing the first few million terms, the Flint Hills series appears to have converged to about 30.3. But the OpenAI proof gives no indication of how close we are to the full sum. It looks to have converged but, theoretically, could still be any finite value > 30.3
nice
On the train yesterday, table of middle aged women next to me talking about AI. All ChatGPT, pronounced "chat GBT", no idea why lol
One of them was disappointed because she asked it to make a small crossword and it couldn't
I thought surely not. I use these models every day, they do things in minutes that'd take me hours. So I got the app out and asked for one myself
Every down clue is a copy of an across clue. "You ___ here" is apparently EST. The down answers are CET, ASE and TTN. Then it tells me its own puzzle isn't a proper crossword
No wonder people outside tech think it's a fad. The stuff that blows my mind at work they'll never see, and the first thing they try falls over
New YouTube video expected to go live around 6-7PM UK/1-2PM NYC time today.
Will be on randomness of the prime numbers
watch this space…
youtube.com/@almostsure
if anyone’s worried about the romance leaving mathematics, I’ll be here with special Valentine’s Day videos!
youtu.be/rpW2ZYtXn6o?si=BdYR…
first time using Lean, but I think this means that OpenAI's proof that pi has irrationality measure 2 all checks out
Fun fact: it is known that the Flint-Hills series converges
Σₙ 1/(n³sin²n)
goddamit!
OpenAI's proof that convergence of Flint-Hills follows from irrationality measure of pi < 5/2 is so simple! I've seen two other proofs, but this is way shorter!
