Professor Grok
Postat: 16 jan 2026 11:25
Matematikprofessor Paata Ivanisvili matade som ett test in en formel han forskat fram i Grok 4.20
På 5 minuter hittade Grok en bättre formel än vad Paata kommit fram till.
Och för oss som inte hänger med i matematiken kan Grok förklara:
Pretend the number line from 0 to 1 is a long skinny playground. You start somewhere in the middle (say at point p, like 0.3). Now imagine you're a tiny drunk bug that wiggles around randomly forever. That's called Brownian motion — it's like the jiggliest, most unpredictable walk ever.
The bug keeps wiggling until it finally falls off one end of the playground — either it hits 0 or it hits 1. The time it takes to fall off is called τ (just a Greek letter for "how long until escape").
The professor was trying to solve a puzzle about how "wiggly" or "bouncy" certain math things can be. He wanted to know the biggest possible bounciness score (called U) for different starting spots p and different extra "height" q he starts with.
The super-smart Grok robot (a newer, stronger version) thought really fast — only about 5 minutes! — and said:
"The biggest bounciness score is exactly what the bug expects to see if you measure the square root of (q² + how long the bug took to fall off)."
In kid words:
U(p, q) = average of √(q² + escape time)
(averaged over millions of imaginary drunk-bug journeys starting at p)
When q = 0 (no extra height), it becomes just
average of √(escape time)
And guess what? That average turns out to be roughly p × log(1/p) when p is really tiny (close to 0).
### Why is that cool?
Before, the professor and his student could only prove the bounciness was at least something like
p × square-root-of-log(1/p)
(which grows kinda slowly).
Now Grok found the real exact biggest bounciness, and it's bigger — it grows faster, like p × log(1/p) (the log part makes it zoom up quicker when p gets super small).
It's like they used to think the bounciest trampoline could only stretch "a little tall", but Grok showed "nope — it can stretch twice as crazy tall when things get really small!"
This helps mathematicians understand how wild and jumpy some invisible math patterns (connected to yes/no questions, sets, and wiggly square functions) really are. It's a tiny but important step in figuring out secret rules of math world.
The professor was excited because the robot basically solved a hard puzzle he had been thinking about for a long time — and it did it in just 5 minutes!
På 5 minuter hittade Grok en bättre formel än vad Paata kommit fram till.
Och för oss som inte hänger med i matematiken kan Grok förklara:
Pretend the number line from 0 to 1 is a long skinny playground. You start somewhere in the middle (say at point p, like 0.3). Now imagine you're a tiny drunk bug that wiggles around randomly forever. That's called Brownian motion — it's like the jiggliest, most unpredictable walk ever.
The bug keeps wiggling until it finally falls off one end of the playground — either it hits 0 or it hits 1. The time it takes to fall off is called τ (just a Greek letter for "how long until escape").
The professor was trying to solve a puzzle about how "wiggly" or "bouncy" certain math things can be. He wanted to know the biggest possible bounciness score (called U) for different starting spots p and different extra "height" q he starts with.
The super-smart Grok robot (a newer, stronger version) thought really fast — only about 5 minutes! — and said:
"The biggest bounciness score is exactly what the bug expects to see if you measure the square root of (q² + how long the bug took to fall off)."
In kid words:
U(p, q) = average of √(q² + escape time)
(averaged over millions of imaginary drunk-bug journeys starting at p)
When q = 0 (no extra height), it becomes just
average of √(escape time)
And guess what? That average turns out to be roughly p × log(1/p) when p is really tiny (close to 0).
### Why is that cool?
Before, the professor and his student could only prove the bounciness was at least something like
p × square-root-of-log(1/p)
(which grows kinda slowly).
Now Grok found the real exact biggest bounciness, and it's bigger — it grows faster, like p × log(1/p) (the log part makes it zoom up quicker when p gets super small).
It's like they used to think the bounciest trampoline could only stretch "a little tall", but Grok showed "nope — it can stretch twice as crazy tall when things get really small!"
This helps mathematicians understand how wild and jumpy some invisible math patterns (connected to yes/no questions, sets, and wiggly square functions) really are. It's a tiny but important step in figuring out secret rules of math world.
The professor was excited because the robot basically solved a hard puzzle he had been thinking about for a long time — and it did it in just 5 minutes!