Beautiful find — congratulations! It's now machine-verified: I formalized the conjecture as stated in the literature (arXiv:2308.02651, Conjecture 1.3) and checked the counterexample in Lean 4 — every routing, path-completeness included, down to three standard axioms.
Discovered by GPT-5.6, verified with Claude. The kernel is the referee.
https://t.co/Ta8DZtgUzg
An 87-year-old conjecture fell this weekend — and the counterexample is now machine-verified. det Jac ≡ −2 and the three-point fiber, formally checked in Lean 4 + mathlib, sorry-free, axioms = [propext, Classical.choice, Quot.sound]. One self-contained file: https://t.co/6el2GAtQcf… #Lean4 #math
hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
Independent formal verification of the counterexample as stated in the preprint: det Jac F ≡ −2 (formal partial derivatives) + the full three-point fiber, over ℚ and ℂ. Lean 4 + mathlib, one self-contained file, sorry-free, axioms = [propext, Classical.choice, Quot.sound]. https://t.co/6el2GAtQcf
Last day at xAI.
xAI's mission is push humanity up the Kardashev tech tree. Grateful to have helped cofound at the start. And enormous thanks to @elonmusk for bringing us together on this incredible journey. So proud of what the xAI team has done and will continue to stay close as a friend of the team. Thank you all for the grind together. The people and camaraderie are the real treasures at this place.
We are heading to an age of 100x productivity with the right tools. Recursive self improvement loops likely go live in the next 12mo. It’s time to recalibrate my gradient on the big picture. 2026 is gonna be insane and likely the busiest (and most consequential) year for the future of our species.
Nice example of the multimodal OCR capabilities of Gemini 2.5 Pro. Just give it dusty old records and ask for JSON!
https://t.co/gTBEXkGLYB
"Which is almost perfect. It has misread a small number of the hard-to-read 8s as 5s. But it is spot-on apart from that. No hallucination.
A revolution is here. I think we will soon be able to rescue historical weather observations data much more efficiently and quickly."
Great to see AI-based weather prediction being rolled out across Africa. This is important because traditional weather forecasts rely much more on ground-based radar, and in Africa, there simply aren't enough to give high quality traditional forecasts.
https://t.co/yonBR65ESU
Today we’re thrilled to announce that real-time and historical AI-based weather forecasts from @Google’s WeatherNext suite of models are now available on Earth Engine and BigQuery. Anyone can access and use these data for research, analysis and operational decision making, which we hope will help accelerate research and development in the weather and climate community.
You can check out the AI-powered forecasts here: https://t.co/Dj1lq1VyZ4
We’re putting our most advanced AI for weather forecasting into more people’s hands. ☁️🌐
Scientists can now access @Google's WeatherNext models as well as real-time & historical data to accelerate research, improve how we respond to disasters, & more →https://t.co/M3TvXO5Q1v
We are incredibly excited to launch the Open Buildings 2.5D Temporal Dataset, open-sourcing annual data about building presence and heights across the Global South from 2016-2023.
An exciting update to our Open Buildings dataset. It now features building presence over time (as well as building height information). It does this by combining high resolution (50cm) but infrequent satellite images and low resolution (1000cm) but frequent (every 5 days). It uses the high resolution imagery as a teacher to predict the higher resolution version from the more frequent lower resolution imagery.
This enables smooth analysis of buildings over time, as you can see in time lapse below of buildings and roads being constructed on the outskirts of Kumasi, Ghana.
Potential uses include:
Government agencies: Gain insights into urban growth patterns to inform planning decisions
Humanitarian organizations: Quickly assess the extent of built-up areas in disaster-stricken regions
Researchers: Track development trends, and study the impact of urbanization on the environment.
Read more on the blog post:
https://t.co/XYaMCOvUdR
Visualize different spots on Earth or count buildings in Earth Engine:
https://t.co/Ccb8CV5h0N
Dataset:
https://t.co/RZogn15KfJ
Kudos to the whole @GoogleResearch team that worked on this! 🎊
Wojciech Sirko, Krishna Sapkota, Juliana T. C. Marcos, Abigail Annkah, Olivia Graham, Emmanuel Asiedu Brempong, Abel Korme, Mohammed Alewi Hassen, Sella Nevo, Tomer Shekel, Abdoulaye Diack, Jason Hickey, and John Quinn.
I'm incredibly proud to share NeuralGCM, our new AI and physics based approach to weather and climate modeling with state-of-the-art accuracy, published today in @Nature:
https://t.co/rtQa0Lq0fT
We just had an amazing visit at the World Food Program (WFP) on the theme of how AI can be used for humanitarian purposes. I was impressed by the scope of work at WFP, and by their drive to have real and immediate impact. Our work at Google Research Africa was well received.
#MachineLearning is playing an increasing role in #WeatherForecasting.
Find out about machine-learning-based progress in improving the initial conditions and the trajectory of physics-based forecasts
➡️https://t.co/6d1b4iiC25
Absolutely biblical skies in Tasmania at 4am this morning. I’m leaving today and knew I could not pass up this opportunity for such a large solar storm. Here’s the image. I actually had to de-saturate the colours. Clouds glowing red. Insane. Shot on Nikon. Rt appreciated
Meet @GreyNearing, a Research Scientist working on flood forecasting at Google Research! Grey & his team produce real-time flood forecasts & alerts in 80+ countries through the Flood Hub to help keep people safe → https://t.co/6GrBUBKWjQ
Learn more → https://t.co/jFXNLM5rib
Their marquee result is Figure 1, which has a shocking punchline: in poorer countries, there's a huge gap in forecast quality, so much so that the median 1-day forecast is only as accurate as a 7-day forecast in richer countries! 3/n
Extremely Dangerous Winds.
The waters from the Big Sur Coast to 60 nautical miles out have been upgraded to Hurricane Force Wind Warnings for winds 35 to 55 kt with gusts up to 80 knots (roughly 92 mph).
#CAwx
We're visiting the Zambia Meteorological Department for the WISER Early Warnings for Southern Africa live testbed, really exciting https://t.co/8OUd5KPUTN
Presenting GraphCast: our state-of-the-art AI model delivering 10-day weather forecasts with unprecedented accuracy in under one minute. 🌦️
It can even help predict the potential paths of cyclones further into the future.
Here's how it works. 🧵 https://t.co/ygughpkdeP