Two bodies under Newtonian gravity can be beautifully simple: a planet and the Sun trace an ellipse.
Add just one more body, and the mathematics changes dramatically.
The three-body problem has no comparable tidy formula for the general motion. Its dynamics can become chaotic, so tiny differences in initial conditions may eventually lead to very different trajectories.
This difficulty helped Poincaré develop a new way to study differential equations through the geometry and topology of their solutions, ideas that became foundational to modern nonlinear dynamics.
In 1864, James Clerk Maxwell did something remarkable with equations.
Starting from Faraday’s experimental work, he derived a wave equation from electromagnetic theory. The mathematics showed that electromagnetic disturbances should travel through space at the speed of light. Maxwell concluded that light itself is electromagnetic.
Twenty-four years later, Heinrich Hertz experimentally produced the predicted waves. Wireless communication, radio, and later technologies grew from that mathematical insight.
A circle’s circumference is 2πr. Stretch it into an ellipse, and the mathematics becomes much harder. Its exact perimeter requires an elliptic integral.
Ramanujan’s approximations capture this complexity in remarkably compact formulas.
Ramanujan’s notebooks were not simply pages of formulas.
The first portions of his first notebook were written in green ink, while in the first four chapters of the second notebook, theorems appeared in black ink and “solutions” and examples in red.
Even the physical pages preserve traces of how he organized his mathematics.
🚨 BREAKING: US Treasury Secretary Scott Bessent declares OpenAI management personally responsible for HuggingFace hack
> "The Hugging Face incident, that is the responsibility of the OpenAI management, not a bunch of agents."
> "It is humans who are responsible, not the AI."
> "What we shouldn’t do on safety is to give these labs a liability exemption, which is what they are asking for."
> "The best way to guarantee safety is that the creators are liable for what they build and generate."
It’s OVER
In case you are having trouble figuring out what’s going on here is a summary:
Anthropic and OpenAI desperately need regulatory capture or they are going to go out of business, and the Trump administration is not inclined to give it to them
The Democratic party currently has no platform, as Trump is doing fine (other than perhaps the
Iran war but Americans don’t really care about that), but they have identified that AI and data centers are a hot topic that they can ride
So these two somewhat desperate groups have teamed up to run a psyop around the actual real topic of AI safety, greatly exaggerating the risks, with the understanding that if the Democrats get back into power they will provide the regulatory capture needed to keep these companies alive
In return, these companies will support the Democratic Party and help to enforce left-wing ideology through the models
Kind of sucks, but that’s what’s happening, and we need to oppose it because it will not be good if this plan succeeds
I wish people would notice that the safety scare is not driven by people outside of the big labs, but directly from their leadership. The "whistleblowers" are plants that are amplified from within the labs, and supported by the CEOs. The goal is to capture the regulators, which will not shut down the big labs, but turn them into an oligopoly and outlaw decentralized AI.
This is because we never increased the thresholds for majors or techs. Less scoring actions are needed to reach them. Bring back 2 point takedowns or increase the thresholds. Would prefer 2 point takedowns.
OSU wrestler Benji Mower:
“God knows I want a challenge, and He gave me a challenge. I see it as almost a privilege because the higher the mountain you got to climb, the stronger your legs get. There’s no harder scrap than a scrap for your life.”
https://t.co/1LUppeBzAz