KD

American physicist Edward Witten explains why it wasn’t until Einstein's work that we fully understand the reason behind the inverse square law, and why it's specifically a square rather than some arbitrary decimal 1 / distance² vs. 1 / distance¹·⁷⁴⁸²²⋅⋅⋅

Evidence of exceptional ability and asking how they solved hard problems down to the brass tacks level is what matters. Those who actually deserve credit know the details of the solution, because it was so hard it got seared into their brain. The phonies and posers who falsely claim credit will flounder at the second or third level of detail.

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

TFW when you have 100 pages written of an unfinished Little Book of Mathematics.

The World of the Indo Greeks I have long been fascinated by Gandharan art and the way it fuses Greco-Roman techniques with Indic subjects. But its origins are far more fascinating than most people realise...

🚨 The Indian government is set to block US-based prediction market platforms, Polymarket and Kalshi.

slightly disrespectful question: is there anything in game theory math that leads to insight that you couldn't get just by thinking about the situation properly?

Of course. The same establishment that cannot get a tehsildar to issue a clean land title in under nine months has now decided it understands prediction markets better than the people using them, and has arrived at the only conclusion sattvic boomer ministers and risk-averse babus ever reach when confronted with anything they have not personally pre-approved: ban kar do, satta hai saar, aunty-nashnul saar, kuch toh chal raha hai saar. A prediction market is not a casino. It is the most efficient information aggregation mechanism humans have built. Thousands of people putting real money on whether RBI will cut rates, who actually wins Uttar Pradesh, whether the Iran-Israel conflict escalates, produces a real-time probability calibrated by skin in the game. Polls lie because lying is free. Analysts drift because being wrong has no cost. A market with money on the line filters signal from noise faster than any think tank, any sarkari forecasting cell, any godi anchor shouting from a Noida studio. Polymarket called the 2024 US election outcome days before mainstream pollsters caught up because the participants had money on the line and the model had no incentive to flatter anyone. Polymarket also correctly predicted that BJP had the edge in West Bengal weeks before the results were declared. This is why serious governments and central banks quietly watch them. They generate cleaner reads on inflation expectations, geopolitical risk, and policy probability than most official surveys. Businesses use them to hedge regulatory exposure. Journalists use them to fact-check their own narratives. Researchers use them to calibrate models. Citizens use them to see what informed money actually thinks instead of what TV studios want them to think. None of this is gambling in any economically meaningful sense. It is information generation, and the only reason a state would want to suppress that particular kind of information is that the resulting prices would inevitably reveal things the state prefers unsaid. This is what bishwaguru looks like in operation. Not ease of doing business, not ease of living, not viksit anything. License raj 2.0 dressed up in gazette notifications, a state willing to order ISP-level blocks for any small exercise of financial or informational freedom it did not personally license, tax, and supervise. The crypto founders are already in Dubai and Singapore. The prediction market users will route through VPNs. The signal will find a price somewhere, because that is what markets always do, except now that intelligence is no longer visible to Indian regulators, Indian researchers, or Indian citizens. We have chosen to make ourselves deaf and blind, but "proud nationalists" will call it an exercise of flexing digital sovereignty.

Following up on the suggestion from Will Sawin, here is an illustration of the new configurations that disprove Erdos' unit distance conjecture (made with the help of ChatGPT 5.5 Thinking).

bro it isn’t generally intelligent bro its only read every book and paper ever written and just making connections between them bro. its only thinking for twenty hours bro it’s just brute force thinking bro. its only solving erdos problems bro it could never be an accountant bro

Central planning hot take: it’s not a computational problem—at least not in the conventional sense. It’s a recursion problem. People will act in accordance with conditions, so the computation has to account for reactions to its own computations, which makes a feedback loop.

Good lord. Half-ish of the cloud backlog at Microsoft, Oracle, Google and Amazon is OpenAI and Anthropic????