Tag: mathematics
OpenAI published its proof. Navier–Stokes is not settled yet.
The Lean code makes OpenAI’s claim inspectable. Machine checking, expert review, prize recognition, and provenance remain separate.
Shut Up and Prove
My first love was the foundations of mathematics. Or maybe the second love; the first was quantum mechanics. But my first love where I had any kind of technical purchase on the domain of inquiry was the foundations of mathematics. In fact, I think I read a proof of Gödel’s theorem and tried to understand it, and perhaps even rework it, before I was truly fluent in much older kinds of mathematics, like the differential calculus.
why is it not like chess
why mourn math. we'll always have that one truth the system will miss
Claude did not solve the Riemann hypothesis
Anthropic published a 67.25% lower bound, a paper, a Lean artifact, and process transcripts. The theorem is substantial, but it is not progress toward 100%.
Vectors
How vectors represent data and make similarity search possible
Math Academy, update 6: I completed Multivariable Calculus
I finished the Math Academy course in multivariable calculus. Next stop: probability and statistics.
A famous math conjecture failed in one formula
A short AI-assisted counterexample can be checked exactly. The result is clear; Claude Fable's role in finding it is not.
The best Algebraic Structure
It's categories.
Video Games that Secretly Teach Mathematics
A love letter to the mathematics hiding inside video games, and a protest against the expression 'I'm just not a math person'. From parallel universes in Super Mario 64 to the technical exegetes mapping Animal Crossing, The Sims 2, Pokémon, and Paper Mario. Then Balatro and the IEEE 754 double-precision ceiling, tetration, Knuth's up-arrows, Conway chained arrows, Graham's number, TREE(3). A history of notation catching up to the infinite.
The Lion’s Claw
If the em dash is the AI’s 'Lion's Claw,' then our messy, unpolished flaws are the only fingerprints we have left to prove we aren’t bots.
Math Academy, update 5: I completed Calculus II
I finish up my Math Academy education in single-variable calculus, and look forward to multivariable calculus.
A year of Math Academy
I started my Math Academy one year ago. What have I learned?
Math Academy, update 4: I completed Calculus I
I continue my Math Academy journey by trying to fill in holes in my knowledge of calculus
Math Academy, update 3: I completed Linear Algebra
I report on my Math Academy progress as I complete my fourth class and finally know what an eigenvector is
Math Academy, update 2: I completed Mathematics for Machine Learning
I report on my Math Academy progress as I complete my third class
Learning how to teleport quantum states with PhysicsGraph
PhysicsGraph proposes to do for physics what Math Academy is doing for mathematics
Math Academy, update 1: I completed Mathematical Foundations III
I report on my Math Academy progress as I complete my second class
Math Academy, part 11: Final thoughts
I pronounce my final verdict on Math Academy
Math Academy, part 10: Customer feedback (pedagogical)
I express my opinions on the pedagogical aspects of Math Academy.
Math Academy, part 9: Customer feedback (non-pedagogic)
I express my opinions on the non-pedagogical aspects of Math Academy.
Math Academy, part 8: Follow-up questions
I summarize answers to various questions about the Math Academy system.
Math Academy, part 7: Technology brief
I look what the technical underpinnings of the Math Academy system.
Math Academy, part 6: Customer responsibilities
I look what Math Academy students and anyone responsible for them needs to provide in the way of coaching.
Math Academy, part 5: Product features
I look at the technical feautures of the Math Academy system as touted by its creators.
Math Academy, part 4: Addressing objections
I look at various objections Math Academy prospects might have, and how they can supposedly be addressed.
Math Academy, part 3: The sales pitch
I try to figure out what Math Academy is selling and why anyone should buy it.
Math Academy, part 2: A skeptical prospect
I start my exploration of Math Academy with a jaundiced view of its prospects.
Math Academy, part 1: My eigenvector embarassment
I start a series of posts on Math Academy and its system for learning mathematics.
Logarithms are just orders of magnitude with a glow up, part 2
I continue to try to explain logarithms to myself.
Logarithms are just orders of magnitude with a glow up, part 1
I try to explain to myself how logarithms work.
Math + The Mechanics
The story of the Curta Calculator, a stylish portable mechanical calculator that doesn’t use electricity and has a surprisingly dramatic origin story.
Real magic is hard and also unsatisfying
There is real magic in the world, but the difficulty of it leads people to turn to fake magic instead.
The Magic of Fractal Snowflakes
The winter ❄️ has finally come. I have been wishing for snow for a long time. Coming from a warm country such as Portugal, snow is not the most common thing to see. In fact, I only saw snow in Portugal once when I was a kid when I went to Serra da Estrela, the highest mountain in continental Portugal.
Plotting A Takeover
The Texas Instruments graphing calculator, the long-neglected computing platform required by many high school math students, finally gets some competition.
A Game Boy For Math
Educators had a love-hate relationship with graphing calculators when they launched, but students loved them because they were great for games.
Pi Day '15
Today, 14th march, is the Pi Day 2015. See this small video which talks a little bit about Pi.
Que Postura Ter Perante a Matemática
Algumas dicas para o estudo de Matemática, uma das disciplinas em que os estudantes têm mais problemas. Prepara-te para os exames continuamente.