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.
Anthropic pays $750,000+ a year for engineers who can build LLM architectures from scratch. Stanford taught the entire thing in 1 hour lecture & released it for free.
Bookmark & watch this today before someone takes it down.
Theorem of the Day (December 17, 2025) : The Catalan–Euler–Segner Bijection
Source : Theorem of the Day / Robin Whitty
pdf : https://t.co/3ocb4gvm7B
notes : https://t.co/Qw69BGfoDA
#mathematics#maths#math#theorem
“ The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars. We are made of star stuff. ”
— Carl Sagan
"Some days I wake up and think: did we really solve Go with a learning-based approach or was it all just a dream?"
—Lex Fridman
Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “lexfridman” (May 3, 2020).
Learning where to look, learning what to see.
Work on Continuous Thought Machines continues to be exciting! As a teaser, take a look at our approach to "Foveated Active Vision". Check it out 👇
(details in the thread)
https://t.co/vUttjVWP8a
Neural networks are game-changers in data science, uncovering complex patterns and insights that traditional methods can’t. If you're in this field, understanding them is a must.
To help you dive into this topic, I’ve created a comprehensive tutorial that explains how to build and train a neural network in Python using TensorFlow, Keras, and Scikit-Learn.
Check out the tutorial: https://t.co/3MBTqBfAIY
I’ve also started a series of posts on related topics across my social media channels. Here are a few examples:
- Convolutional Neural Networks: https://t.co/dDzH19Jrdd
- Reinforcement Learning: https://t.co/IBAqRd9kfd
- Activation Functions: https://t.co/VgRBz8KORk
Make sure to follow my social media accounts so you don’t miss any new posts.
#datascience #neuralnetwork #deeplearning
New paper in Imaging Neuroscience by Antoine Klauser, Ovidiu C. Andronesi, et al:
ECCENTRIC: A fast and unrestrained approach for high-resolution in vivo metabolic imaging at ultra-high field MR
https://t.co/zLbdQnwTjk
Integrating brainstem and cortical functional architectures | https://t.co/hmGC40nJq2
led by @JustineYHansen in @NatureNeuro
400 cortical regions + 58 brainstem nuclei. Lesgo 🤘🕶️⤵️