
UX Engineer @Microsoft | creator of those easing functions | building next-gen Responsive Easing tools
Brooklyn, NY
Joined October 2008
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Robert Penner retweeted
I think it's becoming rather clear that ALL of mathematics will become possible to formalize rather soon. There are deep implications:
1. Mathematics becomes super interactive. Formalizations make it easy to browse, recombine, and build mathematical proofs from components.
2. Each new idea and paper can be checked much faster. The deep part is meaning and explanation. Validation is almost automatic.
3. Optimization and identification of new proofs can be done partially via agents, and humans can contribute much faster with great new ideas. Proofs from the Book are possible at scale.
4. Scientists and people at large can finally use mathematical artifacts as black boxes with trust and confidence. We can commoditize mathematical theorems.
I think the mathematical enterprise also becomes very gamified. We can clearly see each unproven statement as a concrete goal, identify existing tools and directions, and focus quickly on what's missing. And everyone can contribute, with agents or through understanding.
Soon, new languages and new theories will also develop, but the structure will keep growing steadily, with no mistakes and on fundamentally solid foundations. Hilbert's dream is becoming a reality.
One important caveat: mathematics is by no means trivial now! It's just becoming extremely well-structured and laser-focused. I think the jump in capacity, quality, and scale will be massive. I also hope that our understanding of the big picture will remain solid, because there will be a lot to grasp.
HBO's @LastWeekTonight has a long track record of citing social science findings without the appropriate context, massaging them to support whatever point @iamjohnoliver is trying to make.
John Oliver Warned Against Cherry-Picked Studies
Then he cherry-picked his own.
Robert Penner retweeted
I wanted to share something I built over the last few weeks: isometric.nyc is a massive isometric pixel art map of NYC, built with nano banana and coding agents.
I didn't write a single line of code.
Robert Penner retweeted
I've read this 3 times and feel like I'm losing my mind.
Tao is comparing an AI math proof to an AI cancer cure, which is insane enough by itself.
But the point of the comparison is that just like you would obviously rather die from cancer than accept an AI cure a human doesn't understand, we should reject AI proofs that mathematicians don't understand.
The mathematicians have truly lost their minds.
Robert Penner retweeted
Terry Tao: "Problem-solving alone is now actively harmful to mathematics."
I would like to politely disagree, and encourage everyone to continue solving math problems.
teorth.github.io/tao-web/sli…
Robert Penner retweeted
Most of the recent math results were not reached by a swarm, the way Navier–Stokes was. I think that part got lost in the excitement around the release. OpenAI's unnamed internal model, which I'm going to call Aeon, reached most of them in one shot, from a single prompt, with no interruptions. This model did not even exist before the end of August, and it is still training. Notice how the returns are not dropping off? That chart is from a month ago. It is a log scale. What does Aeon look like now?
On average, each result used three hours of thinking. Aeon was given 4000 problems to work on by OpenAI. How many more have been solved in the last three days? That number is not zero.
It's like hearing notes in a song that is slowly rising. I don't think Pacing the Frontier was just about Hugging Face or hacking. They've seen how close we are to closing the loop, and as the hour draws near, their resolve begins to quaver. The last piece was model creativity, and I think that threshold was crossed internally by Anthropic and OpenAI in September. You see it in Opus 5.5, which gets it from Fable 5.5. You see it in the math results from Aeon.
All that was needed to start the event was the ability for models to think of novel ways to improve themselves. That was the last piece. This is directly analogous to the ability to think of strange, alien ways to solve math problems: solutions so inhuman that they are difficult to express in existing human terms, so the proof winds up incomprehensible. I think these same kinds of alien solutions are now being applied to model improvements internally. That's what all this recent consternation is really about. They see the invisible frontier. And they see what is about to happen.
Robert Penner retweeted
I suggest that the right attitude to take toward the OpenAI math release is to imagine we have discovered a notebook full of results from a deceased mathematician. Our job it to make sense of the notebook.
Robert Penner retweeted
One little trick to make your codebase more readable:
* Install cccc github.com/moznion/cccc
* Configure it with max-cognitize and max-cyclomatic 40
* In AGENTS.md, instruct to validate that cccc passes
* Have one agent in ultracode refactor everything until cccc passes
🤩
Robert Penner retweeted
Systematically deriving efficient programs from specifications with formally verified step-by-step transformations was a beautiful idea from the 80s from Richard Bird Lambert Meertens. With the advent of AI coding agents and AI theorem provers its time has finally come. I think this can form the basis of AI coding agents that generate correct by construction code accompanied by the working out that explains its derivation to a human (or another agent). The linked article reproduces one of Richard Bird’s classic examples in Lean 4, along with proofs and performance results.
satnam6502.github.io/bird-me…
Robert Penner retweeted
1000% this
If you're "one-shotting" animations with Opus 5.5, the default output is slop (impressive slop but still):
- Pacing & animations are way too fast
- Too many effects (less is more!)
- No cohesion (movement in all directions)
- No focal point (where to draw attention?)
- Generic easing applied everywhere
- No consistent choreography
- Motion without meaning
Good animation explains something. Default animation is just meaningless eye candy.
Robert Penner retweeted
“The life you seek is hidden inside the discipline you avoid.”
- Epictetus
Despite being born into slavery, Epictetus rose to become one of history’s most influential Stoic philosophers. He believed that genuine freedom does not come from having an easier life, but from developing the ability to master yourself.
His teachings emphasized a challenging yet powerful principle: while you cannot determine everything that happens around you, you can choose your reactions, guide your decisions, and remain persistent when confronted with adversity.
“The life you seek is hidden inside the discipline you avoid.”
Although this quotation has no verified connection to Epictetus, its message reflects a central theme of Stoic philosophy. The future you desire may depend on confronting the responsibilities you repeatedly put off, whether that means exercising when you lack motivation, completing difficult tasks, or finally making the uncomfortable choices you have been avoiding.
Robert Penner retweeted
Just got this incredible news from UCLA Math Circle.
Two high school students, Aayush Bathija and Prince Rohatgi, working with postdoc Daniel Soskin through the UCLA Math Circle, have solved a problem that Fields Medalist June Huh had previously worked on without solving.
The paper was heavily AI-assisted.
Whatever your view on AI in mathematics, enabling high school students to push the frontier of mathematical research is something worth celebrating.
arxiv.org/abs/2609.05341



























