"Mathematics in the Age of AI"
In an age of abundant AI-generated proofs, human understanding may become more valuable than proof generation itself.
This new paper from Terence Tao argues that AI could make solving hard math problems much cheaper and faster, but at the same time, creates a new problem.
If AI can generate thousands of correct proofs, mathematicians can’t possibly read, understand, verify, and teach all of them.
So the scarce resource in mathematics shifts from finding proofs to making sense of them.
The important work becomes deciding which results matter, explaining the key ideas, connecting them to existing theory, and turning them into knowledge other mathematicians can actually use.
https://t.co/otIGL0SQrq
Physicist Successfully Demonstrates the Origin of Time
Giovanni Barontini from the University of Birmingham, UK, has used a cloud of cold atoms to test the origin of time. This is an interesting contribution to the long-standing question of how to define time in a non-circular way (time is what a clock measures and a clock is what measures time). One of the proposed solutions is to define time in quantum physics from the interaction of two different subsystems. This interaction, so the idea, introduces an oscillation that serves as the ‘tick’ of the clock. If that was so, then time would be purely ‘relational’ — an emergent, derived quantity — rather than (as in Einstein’s theory), a fundamental property of the universe.
Barontini used about 24,000 ultracold rubidium atoms in a trap split by a thin light barrier into an observed “bright” part and an unobserved “dark” part. Atoms could move between the two, so the bright part expanded and collapsed in repeated cycles, rather like a toy version of a big bang and big crunch. Barontini then defined an internal “entropic time” from how the entropy of the bright part changed as atoms moved in and out. This internal time ordered the observed events almost as well as laboratory time.
This experiment lends support to the idea that time is not fundamental, but emerges from interactions between parts of a closed system, though one may ask how interactions can change a system if there is not already a time for them to change in, but then maybe that’s just Sabine being grumpy again.
Image: The device, called a ‘trap’, that holds the cloud of cold atoms in place using a combination of lasers and magnetic fields. Credits: Giovanni Barontini/University of Birmingham
The 3rd edition of my book Deep Learning with Python is being printed right now, and will be in bookstores within 2 weeks. You can order it now from Amazon or from Manning.
This time, we're also releasing the whole thing as a 100% free website.
I don't care if it reduces book sales, I think it's the best deep learning intro around, and more people should be able to read it.
In 1950 Claude Shannon showed that brute-force chess is hopeless since there are ~10^120 possible game variations.
He designed the entire blueprint for modern chess engines: minimax search, heuristic evaluation, and move pruning. He did all of this before any computer had ever played a single game of chess.
Learn more here: https://t.co/hwi01a96BU
Found this very interesting monograph (600 pages) available on ArXiv (and Oxford Academic) titled 'The Philosophy and Physics of Duality' by De Haro and Butterfield.
To quote the abstract ''This monograph discusses dualities in physics: what dualities are, their main examples--from quantum mechanics and electrodynamics to statistical mechanics, quantum field theory ...--and the philosophical questions they raise''
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Richard Feynman’s savage takedown of pseudo-science still burns in 2026:
“Social science is an example of a science which is not a science. They follow the forms… but they don’t get any laws. They haven’t found out anything.”
He goes harder:
Experts who “sit at a typewriter and make up” claims — “organic food is better,” “this diet cures everything” — as if it’s settled science, when no rigorous experiments or checks have been done.
Feynman:
“I know what it means to really know something.
How careful you have to be. How easy it is to fool yourself.
I see how they get their information… and I can’t believe that they know.”
The Nobel physicist calls it straight: most of what passes for “expert” opinion is noise dressed up as knowledge.
In an age drowning in TikTok “science,” influencers, and clickbait studies — Feynman’s 1:52 rant feels more relevant than ever.
Who’s the biggest pseudo-expert that grinds your gears right now?
Clip is timeless fire — watch it and feel the clarity.
In 1798, a scientist effectively “weighed” the Earth — without leaving his laboratory.
The English scientist Henry Cavendish designed an incredibly sensitive experiment.
Inside a quiet wooden shed, he hung a horizontal rod from a very thin wire. Two small lead spheres were attached to the ends of the rod.
Nearby, he placed two much larger lead balls.
Because of gravity, the large spheres slightly pulled the smaller ones. The force was extremely tiny — so small that the rod twisted by only a minute fraction of a degree.
Yet that tiny twist held a big secret.
By carefully measuring this small movement, Cavendish determined the strength of the gravitational attraction between objects.
From this, scientists could calculate the mass of the entire Earth.
His estimate was remarkably close.
Cavendish calculated Earth’s mass to be about 6 × 10²⁴ kilograms, while modern measurements give 5.97 × 10²⁴ kilograms.
Sometimes the biggest discoveries come from measuring the smallest forces.
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Palestinians in Gaza and West Bank (Judea and Samaria) constantly attack Israel. Rockets. Suicide bombers. Car rammings. Stone throwing. Stabbings. Shootings. Israel defends itself by neutralizing the attackers, and taking out military capabilities.
Every few years there’s an attempt to come to a deal for land for peace, a pathway to two states. The Palestinians refuse to recognize Israel’s right to exist, turn down the deal, and attack again.
Rinse. Wash. Repeat.
Are the areas where the Palestinians live under Israeli control? Fucking right they are. When you have people constantly attacking your citizens, you do what you can to stop it and mitigate that risk.
Is that ever going to change? Not as long as Hamas is in power and the Palestinians continue to attack.
Does Israel want to wipe out the people of Gaza? Surprisingly, no. Because I don’t know of any other nation in the world that would put up with what Israel has put up with and not wipe out the people that constantly attack them.
Have some far-right Israelis made comments about wiping out Gaza? Sure. That doesn’t make it Israeli policy.
There is zero intent by Israel to wipe out the Palestinians. There is zero desire by Israel for the war that the Palestinians started. There is zero genocide.
We can go back and forth all day long about chicken and egg and cause and effect but it’s really simple. In 1947 both Jews and Arabs were living the the area known as the British Mandate of Palestine. There was a plan for both sides to have a state. The Jews said “yes” and Israel was recognized. The Arabs said “no” and attacked.
Ever since then the Arabs have been attacking. Every time Israel tries to make peace, they are attacked. They left Gaza in a hope that would bring peace, and it backfired.
Yes, people in Gaza are dying in the war.
And yes, they are dying because of a genocide.
But not because of a genocide being carried out against them.
Because of a genocide their leaders are trying to carry out against Israel.
If the Palestinians want peace, they need to help get rid of Hamas and other extremists. Once that happens, there’s a chance.
Because when it comes to the chicken and egg, the one who strikes first, has always been the Muslims. And then the world blames the Jews for responding.