"Magari gli uomini obbedissero alla spinta del loro interesse! Obbediscono invece al potere magico dei fantasmi della loro vanità, della loro fantasia, del loro stupore davanti alla novità e ad altre ancor meno nobili forze interiori." (Prezzolini)

I'd like to hand out to you an invitation to logics and metamathematics, via this set of lecture notes by Warren Goldfarb, from Harvard University. Axioms, rules of inferences, Godel, primitive recursion, computability and more is covered Link in the comments

Demis Hassabis and John Jumper, the 2024 Nobel Prize laureates in chemistry, have developed an AI model to solve a 50-year-old problem: predicting proteins’ complex structures. In 2020, Hassabis and Jumper presented an AI model called AlphaFold2. With its help, they have been

In the 1960s, Stanislaw Ulam, while doodling during a boring presentation, discovered a surprising pattern when he arranged numbers in a spiral and highlighted the primes. This spiral revealed a striking pattern and structure in the distribution of prime numbers. 📷visualizing

"One sign that you're suited for some kind of work is when you like even the parts that other people find tedious or frightening." (P. Graham)

There is a fascinating connection between infinity and fractals, which are geometric shapes that have self-similarity at different scales. For example, the Mandelbrot set is a fractal that is defined by a simple formula, but it has an infinitely complex boundary that contains

Updated: Poster on distances with underlying geometries 1/2

FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI epochai.org/frontiermath/t…

The Draghi Plan in 30 Slides linkedin.com/posts/aonetti_…

It’s shocking how much we know about how learning happens, all the way down to the mechanics of what’s going on in the brain. And it’s not just how learning happens, but also, what we can do to improve learning. There are plenty of learning-enhancing practice strategies that

There have been several remarkable developments in combinatorics, my field of mathematics. A few weeks ago I gave a talk to a general mathematical audience in which I described six breakthroughs from the last five years. youtube.com/watch?v=726OMr…

A ‘Wikipedia for cells’: researchers get an updated look at the Human Cell Atlas, and it’s remarkable nature.com/articles/d4158…

... any *knot* in the Menger sponge: you can deform any knot without the string having to pass through itself so that it ends up as a subset of the Menger sponge. quantamagazine.org/teen-mathemati… arxiv.org/abs/2409.03639

Teen Mathematicians Tie Knots Through a Mind-Blowing Fractal quantamagazine.org/teen-mathemati… via Quanta Magazine

The Moore's Law Update NOTE: this is a semi-log graph, so a straight line is an exponential; each y-axis tick is 100x. This graph covers a 1,000,000,000,000,000,000,000x improvement in computation/$. Pause to let that sink in. Humanity’s capacity to compute has compounded for

Machines of Loving Grace - How AI Could Transform the World for the Better darioamodei.com/machines-of-lo… Dario Amodei

Jacques Hadamard wrote this long essay 'The Psychology of Invention in the Mathematical Field', which is an exploration of how do mathematicians invent new ideas, taking creative experiences of some of the great thinkers of his time get the pdf 🔗👇

Terry Tao's article "Machine Assisted Proof" is out in the Notices of the AMS: ams.org/journals/notic…

This visualization shows the occurrence of earthquakes on Earth between July 2017 and July 2018, but differently from other charts, this ones shows them with their depth. [🎞️ nicolaraluk]

Epoch AI - ML Trends dashboard offers curated key numbers, visualizations, and insights that showcase the significant growth and impact of artificial intelligence.epoch.ai/trends