public research notebook
Joined July 2023
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perry retweeted
I never understood what people mean by “making computing more human” It’s all human. We invented all of it. It’s all as human as it can possibly be
perry retweeted
The experience of being human: on the day it becomes abundantly clear that all open problems in mathematical theory and physics will be solved in ~2 years tops, 98% of the people paying attention to the situation will be too fixated on the human drama about who should get credit to notice that the world changed under their feet in a permanent and quite astonishing way. I feel a strange mix of pride, annoyance, affection, and fear for us all.
perry retweeted
As AI generates more and more proofs, one useful thing we could do on social media is this: instead of saying, “Look, AI solved the 100-year-old Mumbo Jumbo Conjecture,” explicitly state the question and then state the final answer AI produced.
That way, even people outside the field can at least learn what the question was and what the new result says.
perry retweeted
Kind of wild how "importance" works on mathematics: subfields are siloed so deeply that you just have to use proxies like word of mouth
Like surely experts know better about what's *relatively* important in a subfield, but we also use that to measure *absolute* importance..
perry retweeted
okay so. when a mathematician proves a random conjecture you are supposed to politely clap. this is because it would be rude and embarrass the mathematician to point out that most conjectures are not that important or meaningful
when an LLM proves a random conjecture mathematicians are caught in a funny position where they want to say "these are not very important or meaningful conjectures and having magic proofs or counterexamples come out of nowhere is not particularly interesting or useful to anybody, except possibly the person who proposed the conjecture and some of their colleagues" but saying that puts them in an awkward position - why didn't they say that when humans were doing it? was nearly all mathematics actually pointless this whole time and mathematicians were just politely avoiding ever pointing this out so they could all still have jobs?
if the best defense you can come up with of mathematics as a human endeavor is, effectively, "it's really fun for us to come up with these baroque puzzles and then solve them, don't screw this up for us," you are completely abdicating your responsibility as a public endeavor that taxpayers fund. i have occasionally argued that pure mathematics lost the plot decades ago and gave up on having any kind of meaningful relationship to the rest of the human quest to understand reality. this was a slow-burning tragedy, and mathematicians have been able to hide this state of affairs from everybody else because nobody else knows enough mathematics to critique what mathematicians are doing
i saw a famous professor point out a few years ago that the machine learning that underpins AI is powered by 18th or maybe 19th century mathematics, you don't need much more than multivariable calculus, linear algebra, a bit of probability. he said this as if it was a dunk on ML and AI; imo it's a much bigger dunk on mathematics. you're telling me the most important scientific revolution of our lifetimes doesn't involve any of the math that mathematicians have been working on over the last century or two? you see how that's worse, right?
(tbc i'm not saying that stuff is all useless, you need a bunch of stuff from the first half of the 20th century to do physics, e.g. functional analysis, lie theory, representation theory all feed into the standard model. after 1950 or so things get more dicey)
if mathematicians still want to have jobs they are going to have to do a better job than they have for the last few decades convincing the public they do something that actually matters, and figuring out what that actually is or should be. this is an opportunity for the field to do some very serious soul-searching, as serious or more serious than the foundational crisis from a century ago. this kind of whining is absolutely not going to cut it
I am so tired of seeing these posts.
I am so tired of seeing my beloved field of study be the testing lab for a technology that is disrupting everyday life at such a high pace.
Mathematics were always about the beauty of seeing the ideas of a person unfolded in an extremely precise language so we can all look into a mathematician's mind and see their purest form of ideas, their understanding of a problem, their style, their way of communicating to other fellow researchers through mathematical results... this often transcends the common language humans use to communicate with each other and it is incredibly exciting to bump into shared ideas another person had thousands of kilometers away several years ago without even knowing them.
I am extremely unexcited about AI-breakthroughs in Mathematics in the same way I am extremely unexcited about a picture created by AI or an AI-generated video, not to speak about AI-generated text. Mathematics requires soul and intention. Mathematics need not be useful by definition, Mathematics are pure art that need hard work and effort to understand. The high you get when a year of work gets condensed in a one-page result is incomparable to anything else and, certainly, a machine is not apt to relate to humans in such a humane way.
I am not interested in the truth of the results. I am interested in how was the mind behind a result able to connect those dots. I am interested in the diversity human thoughts bring to Mathematics. I am not interested in a bunch of servers running probabilities to return a Theorem, even if true: that lacks the objective of Mathematics as I see them.
perry retweeted
Poor Yitang Zhang. He spent years working in fast food after his PhD, and was homeless at one point, until his famous breakthrough with the twin prime conjecture. It's clear that his advisor Moh absolutely resented him (for whatever reason) and did everything possible to sabotage his career.
Sadly these stories are common in academia, and often lack a happy ending. It takes a generational hater to shit on a former student 2 decades later when they found success.
In this game, it's an open secret that unscrupulous advisors may deliberately set certain students up for failure by assigning impossible problems that are expected to go nowhere. We can only speculate but: Moh was one of the main contributors to the reputation of the Jacobian Conjecture as a notoriously difficult problem that defeated the best mathematicians; a problem believed to be well above the capabilities of a grad student. Tbh the layers to this messy backstory makes the LLM counterexample even more crazy.
perry retweeted
There's a point Vogel is making here that I largely agree with and can elaborate on another time, but let me add some nuance.
Greek philosophy, going all the way back to Thales, placed a very heavy emphasis on mathematics, especially geometry. I don't think this emphasis would have been nearly so strong if it was not a very generative source of inspiration.
It's very easy for an intuitive understanding of the world to obscure strange corner cases. If you're forced to prove something rigorously, these corner cases may add a lot of additional difficulty but once addressed can draw out truths that your intuition would never have seen.
The past two centuries of mathematics has involved the development of new techniques that have solved problems that the ancients struggled to, but also have strange implications that I don't think we've fully grappled with. Incompleteness, logical independence, the Principle of Explosion, Complexity Theory, etc. The applied forms of these things have heavily shaped the physics, engineering, and computing that enabled the modern world. The philosophical implications seem only shallowly explored.
Infinity was a taboo for thousands of years, as the church considered a number beyond all others to be an affront to God; in short, God cannot create something greater than Himself. In the late 1800s, we found that infinity didn't quite work the way we thought. In a series of letters, Cantor debated Pope Leo XIII and other theologians over the theological implications of transcendental infinities, won the debate by showing that the church had ignored a very strange possibility for the nature of infinity, but then no one seems to have bothered to consider much about what this may actually mean on the theological side.
I'm hopeful that as we make mathematics more legible to interactive computers via things like theorem provers, a lot of this obscure mathematics may become far easier for people to learn, and more thinkers can look to rigorous logic to find strange possibilities that their intuition has missed.
perry retweeted
Yes. Software engineers will all go away. There will be a new profession of people whose only job is to tell the machines what they should do in a manner that’s efficient and precise.
perry retweeted
I have a guest essay in @nytimes today about autonomous vehicle safety. I wrote it because I’m tired of seeing children die. Done right, we can eliminate car crashes as a leading cause of death in the United States
@Waymo recently released data covering nearly 100 million driverless miles. I spent weeks analyzing it because the results seemed too good to be true. 91% fewer serious-injury crashes. 92% less pedestrians hit. 96% fewer injury crashes at intersections. The list goes on.
39,000 Americans died in crashes last year. More than homicide, plane crashes, and natural disasters combined. The #2 killer of children and young adults. The #1 cause of spinal cord injury. We’ve accepted this as the price of mobility.
We don’t have to.
In medicine, when a treatment shows this level of benefit, we stop the trial early. Continuing to give patients the placebo becomes unethical. When an intervention works this clearly, you change what you do.
In driving, we’re all the control group.
Cities like DC and Boston are blocking deployment. And cities are not the only forces mobilizing to slow this progress.
It’s time we stop treating this like a tech moonshot and start treating it like a public health intervention that will save lives.
Link to article below.
👀 this video of Waymo cars evading crashes with people and vehicles. I especially note the ones that require it having a 360° view.
My sincere thanks to Alex Ellerbeck and @acsifferlin for their wisdom and sure hand in editing this piece.
perry retweeted
The I Ching (1000 BCE) used 6-layer binary networks for sequence prediction tasks. Yarrow stalk dropout prevented overfitting to cosmic patterns. Interesting how Western AI history consistently overlooks these Eastern foundations
perry retweeted
Mathematics is yours. You deserve it. No one owns it. It is yours to learn or not if you choose
perry retweeted
Calling Bay Area math enthusiasts interested in weekly sessions doing rigorous foundational mathematics the modern way - with computer-verified proofs in Lean.
(An experiment in rigorous math education outside traditional academia)
course info - docs.google.com/document/d/1…
interest collection form - docs.google.com/forms/d/e/1F…
