"Such problems are 'landmarks and lighthouses,' they write, whose deeper purpose is to guide mathematicians toward conceptual understanding and insight. Terence Tao, one of the signers...
has described what’s happening as 'strip-mining' mathematics. Good problems, he argues, are like nonrenewable resources. Some of them — the smaller, easier ones — can help train the next generation of mathematicians. Young researchers try their hand on them, learning what they will need to push the field forward.
If A.I. strips away the big problems and their satellites, it could destroy the entire mathematical ecosystem. Tao has suggested that some questions may even need to be fenced off from automated solvers, as if they were national parks for math problems.... From the outside, mathematicians’ insistence on human understanding looked like guild protection — an attempt to save something for themselves now that machines are starting to beat them at their own game...."
From
"Mathematics Isn’t Just a Game to Let A.I. Solve. History Shows Why. In our field of applied mathematics, the long, human process of trial and error — not just the solutions themselves — is often what has led to progress" (NYT).
83 comments:
Sounds a bit like the "homeless advocacy" industry terrified that government programs to alleviate homelessness might some day work.
The difference between knowing an answer and solving the problem. Anthropogenic intelligence develops through challenging enterprise.
It's their fault for inventing rules of logic. What did they think would happen.
I have some sympathy for their position, but I think it highlights the general uselessness of these mathematical problems. I would disagree with the same stand in the sciences. I have hope that AI can make progress on the leading problems in physics and cosmology.
Oh, Dear. An existential crisis, and the driver of the bus full of mathematicians going over the cliff is an A.I. Agent. Oh, Dear.
Plus, it's overlooking the talent that went into building the machines. SAT solvers etc.
And I *expect* important advances in material sciences from AI, which could be a real boon for humanity.
It's not the destination it's the journey!
"It's not the destination it's the journey!"
It might be the journey for those in the field, but it's the destination for the rest of us.
Preserving the math problems won't work. What are you going to do, put some kids in jail for using AI to solve a protected math problem? Because they will.
It would be like trying not hear who won the game you missed so you can watch it on DVR the next day.
I have a math problem right now that I need the answer to; I'd probably give it to AI if I knew how. But I have to admit it would feel like cheating. And it's very satisfying when you figure out the answer.
It's on the individual: anyone with a really good understanding of certain math problems can easily ask AI. Whether or not it gets the answer is not the issue. It's that these people want barbed wire around certain problems. Anyone can use AI, then copy and paste: look at Rich
Ai is a new method of approaching problems. Advances come from new methods. Would anyone propose going back to the methods of Pythagoras and only allow problems to be solved with straight edge and compass? No, this is a group of young professionals who seem to be afraid that the field they studied for is shifting to something different. It’s like chess masters who are beaten by algorithms and thinking that all they learned was useless.
Well, that is untrue, they created the field, they can expand it in new ways. Attempting to slow progress so you can easily keep up is like tying weights to the fastest runner, useless.
Humans need all the tools they have to make progress, to build starships, to go places and see things. It’s just progress and can’t be stopped to benefit a class who want their profession to become a nature center in a national park.
To these young and excellent mathematicians they will work at solving problems with human brains and will teach students math to develop and expand their minds. If we give up on human math there will be no one who will marvel at the new thjngs that are produced, it’s like all computing, a faster machine that humans make to do tasks.
Dispair and doomerism is what causes problems. These guys have just been trained that if they solve a super problem they will get instant fame and glory, so make fame the product of making better structures to solve harder problems using human and machine methods.
Professional mathematician here. So perhaps a bit of guild-protecting, but on the other hand, I'm near the end of my career, or at least the productive mathematical part of my career.
I have literally never used AI in any of my research. My area is obscure enough that I doubt AI would have much interest any time soon in the research I do. Slightly more broadly, the big unsolved problems in my field (e.g. the Alperin weight conjecture) could maybe be finished by AI, but (best case scenario for AI) it would be pretty transparent that it was putting the finishing touches on a project that humans had been building up for decades (for instance, the McKay conjecture and the Height Zero conjecture were around in my field for decades, and have recently been solved by humans - humans who spent years putting the finishing touches on work that others had spent decades building up).
I'll be the first to admit that all of these problems have zero real-life applications for now or the foreseeable (spelling? - seems like that first "e" shouldn't be there but the squiggly line tells me it needs to be) future. Unless, of course, aliens come to Earth and threaten to blow it up unless we correctly answer whether a block B of a finite group G for which every character has height zero must necessarily have an abelian defect group, in which case we're all set!
A large chunk of math is done without regard to applications. (How large that chunk is relative to "applied" math varies through the decades, a combination of fads and grant funding priorities.) The point is to stretch the human mind, sharpen our intuition, etc.
I look at AI coming up with new important proofs like someone inventing a helicopter to fly to the top of Mount Everest. An impressive achievement, to be sure (I'm assuming it's hard to fly and land up there), but not the one that gets you knighted. Or training a robot to run and win a marathon. Could it be done? Sure. Should it be done? I don't see why.
We don't *need* people to run marathons, any more than we need people to prove the Alperin weight conjecture (although every now and then useful applications pop up in unexpected places in math). But a person watching a marathon on TV might be inspired to train for a 5K to get healthier. A person reading about Edmund Hillary might be inspired to go try a challenging hike. I think we'd all agree these are good for the general well-being. And a person reading about the proof of Fermat's Last Theorem might be inspired to sharpen their analytical skills, learn some math, and that could develop into something useful. Like developing AI, oddly enough.
Perhaps the fields winners could work on making a spell checker that was not a complete useless dumbshit.
"I look at AI coming up with new important proofs like someone inventing a helicopter to fly to the top of Mount Everest."
That one's been done, for what it's worth.
Translation: Don't break our rice bowls!
Wonder how close this is to the reaction to calculators.
I appreciate the point about needing to wrestle with these things. But it seems futile.
My, so many ways to write "AI bad" in alleged feature stories! Trial and error is one of those long-standing traditions in science, not just applied mathematics, that the Institutional Left has abandoned on the road to Wokeville. That's why the FDA can no longer say with a straight face that the vaccines recommended are "safe and effective" because neither has been proven in controlled double-blind trials.
You know the old way. Like learning addition and subtraction before learning multiplication and division, before learning fractions and geometry. I'd lay a bet that "new math" has more responsibility for AI being used to solve equations than abandonment of trial and error.
Think about it this way.
Life is the journey.
Death is the destination.
I used to believe that college was useless because so much of what I had learned in college didn't apply to the jobs I had. None of the jobs I had ever had required me to have a college degree. But eventually I realized that the experience of going to college is a major part of who I had become.
My diploma is totally worthless to me.
The experiences I had in college are priceless to me.
All of the alarmism is from the left. They are terrified unless the corrupt left can take change of it all.
Create a AI: "ministry of truth" with it.
I've been seeing this for the past week or 2 and it seems like complete BS to me. It also seems completely predictable, like writers who refuse to use word processors (in one case, even a typwriter), accountants who refuse to use Excel and salespeople who refuse to use email (there are still a few who want to send faxes)
Seems to me they are just Luddites.
Are they OK with using computers to pursue the math? No? How about calculators? OK, maybe slide rules?
What is the line as to technology that is permissible for mathematicians to use?
Screw 'em. I will use whatever technology helps to get the job done. I do think there is a huge benefit to kids learning to use slide rules and was teaching my 8y/o grandson to use my old Pickett to multiply over the weekend. He already knows grandpa is weird so he was at least polite.
John Henry
John Henry
In other news, horse traders, wainwrights, and makers of buggy whips want those newfangled internal combustion engines outlawed.
John Henry,
I still have not forgotten or forgiven the bastard who purloined my circular slide rule back in 1973.
James, I think, said, SI (let's call it that from now on) would not know how to work on some of these arcane math problems. Don't be so sure. I would be surprised if it didn't. I've been using the paid version ($20) of Claude/Anthropic for 3-4 months now and it is constantly amazing me what it can do.
I'm using a 15 year old version of AccountEdge for bookkeeping. I've been trying to upgrade for years but AE and every other company that does accounting software only sells subscriptions and uses the cloud.
So I asked Claude if it knew any alternatives. It said no, but then asked why not make my own and offered to make a program for me. And in about 15 minutes did.
Very nice looking program that it suggested we call "Simple Books" Fully usable as it was. But there were formatting issues with importing my AE data for 2026 so we spent about an hour getting that right. Then I wanted a couple of changes mainly appearance, that took another 30 minutes.
It does cash flows, POs, Invoices, A/R, A/P, bank reconciliation and a lot more. Evrything I use AE for plus some stuff AE won't do.
Going live today and will run in parallel with AE for the rest of the year.
My first year of college we weren't allowed to use calculators in science courses. Slide rules.
Sophomore year calculators were allowed, and I plunked down a whole lot of money for one.
People will adapt; it is too early to say how. Newton's achievement in the Principia wasn't just 240 propositions and lemmas and 1687 proofs, it was identifying which problems needed to be solved. Language and proofs have changed, the core problems have not.
What a bunch of crybabies.
Fred Drinkwater said...
" John Henry,
I still have not forgotten or forgiven the bastard who purloined my circular slide rule back in 1973."
I used to have a set of 4-5 circular slide rules. 6-8" diameter, High quality printing on heavy plastic. One calculated liquid flow in pipes, another gas flow in pipes, another steam and heat and so on. 2 sided and I never even learned all the functions.
Cost $30-40 in 1980 or so.
I wish I still had them.
I used a circular slide rule when I was learning to fly in the 90s. Sporty's pilot shop still sells them. (I had occasion to look last week)
John Henry
Why climb mountains if you can fly to the top in a helicopter?
Nusic is being changed too. I mentioned last month that I have found several series of light jazz videos, 2-3 hours in length that I like to play while I am working at my desk. Here's one https://youtu.be/aIDH6Fh8JwI?si=8Mah8QQxAqfYokCO
Those are just music, no vocal, no real video.
There is a killer blues tune going around TikTok that constantly pops up. "Don't blame the whiskey, don't blame the jar." I wanted to find out who did it so I could download it and anythng else they might have posted.
It is here: with a nice video of an old country shack with a couple guys playing on the porch and a couple dancing in the yard
And it is pure SI.
John Henry
Forgot the link https://youtu.be/nnqGC0KKkWY?si=TY1uIY0J8YeKGNZI
John Henry
People who want to solve hard math problems will solve hard math problems, or die trying. I know, I'm one of them. But no one is obliged to pay me to do it.
That's the sort of manifesto a mathematician named "Elmer Ludd" might sign. Buggy whip artisans had no use for Henry Ford--and Rockefeller's coal oil refiners had no use for Thomas Edison and electric light. . Progress happens, and some things get bumped along the way.
It seems as though they are seeing their professional field disappear. Very disturbing!
It reminds me of the women who are protesting Sydney Sweeney.
I still have that first calculator (though it no longer works). It's probably in the same drawer as my slide rule, which I'm sure still works fine.
It seems as though they are seeing their professional field disappear
Let's not overlook the political moment: AI is dangerous, we need to control it, vote for us. I was a bit surprised to see Tao among the signers, as he has made use of AI. But he lives in the academic swamp, so perhaps not that surprising. I think I will add this to the list of things Trump can do.
If Mona Charen and Bill Kristol were mathematicians...
We’ll still need mathematicians. Whenever tasks are delegated, the work still needs to be checked by those being held accountable for the action. Do we really want to depend on unchecked math problem solutions brought to you by a computer that can’t get spellcheck right?
SI requires AI capable of discernment and creativity, or out-of-scope intelligence. Matrix requires an AI capable of entertaining abortive ideation.
Do we really want to depend on unchecked math problem solutions
They don't. AI breaks the proof down and writes a Lean file (*.lean). Lean is a proof checker that has a library of formal proofs that can be relied upon in steps of new proofs. It is essentially a reviewer.
If you can do your job with a keyboard or a pencil and paper, or with paintbrushes, welcome to Hell.
In the 20th century, 2.5 million novels were written, now 2.5 million novels are written every year. If your special snowflake is amazing under a microscope, well, good luck anybody finding it in a blizzard.
Who knew that the real terminator was going to be the category killer of many types of high-end jobs.
Slide rules are the best, and I am thinking that they make a comeback after the Butlerian Jihad.
This is what AI told me about the "Butlerian Jihad" when I fact checked my post in Grok.
****
The Butlerian Jihad (also called the Great Revolt) is a foundational event in Frank Herbert’s Dune universe: a galaxy-wide crusade against computers, artificial intelligence, and “thinking machines” that took place more than 10,000 years before the story of Dune.
In Herbert’s original novels it is sketched rather than shown.
The glossary in Dune defines it as the crusade against thinking machines that ran from 201 B.G. to 108 B.G. Its lasting commandment, preserved in the Orange Catholic Bible, is:
“Thou shalt not make a machine in the likeness of a human mind.”
Herbert’s deeper point was not a Terminator-style robot uprising.
A key line in the first novel is:
“Once men turned their thinking over to machines in the hope that this would set them free. But that only permitted other men with machines to enslave them.”
**** - Grok
The younger generations all want to be influencers.
Anyone willing to build a bridge? correctly? using math?
Anyone going to take care of our aging and failing civic infrastructure? electrical/plumbing/water storage.
AI lives in a box. It's not a master race of superior robots with opposable thumbs.
(yet)
enslavement is universal thru-out all time and space.
Gravitational pull. Islam and leftism the new frontier to repeat.
Since math is racist - (according to Teacher's union nazi's and DEI hacks) blame AI! what color are you AI? Did you sneak across the border?
In Dune, the way the problem of doing math without computers was solved was to create a priesthood trained from childhood to do outrageously complex calculations, and they were not allowed to take sides, just shut up and calculate, so to speak.
Anyone willing to build a bridge? correctly? using math?
DEI boss-girls with facial tattoos and purple hair are going to build our bridges now. Half of them will fall down, like the Girl Power bridge in Florida that killed a three or four motorists a few years ago. Yaaaassss, Slay Queen!
***
a priesthood trained from childhood to do outrageously complex calculations
***
"It is by will alone I set my bot in motion..."
@Hassayamper, point f information. Five motorists died, waiting at a red light, plus a construction worker on top of the bridge. The NTSB noted that important safety-related work was going on at the Tmes of collapse without anyone thinking to stop or divert the traffic.
DEI-boss girls.
*shiver*
We are in the post peak math, and I feel fine.
And here I am on safari. I took out “era” after post math, because I thought about a pun error, which just looked like a misspelling. Now no delete.
***
I was a bit surprised to see Tao among the signers, as he has made use of AI. But he lives in the academic swamp, so perhaps not that surprising.
***
Is there any group of people more cowardly and pusillanimous than the grand and glorious Academy? They grovel like worms before their own students whenever any fad or moral panic sweeps through the universities. If the likes of Tao had been at Heidelberg in 1935, they'd be throwing books in the bonfire alongside the Hitler Youth.
Cue will hunting ai is a tool
"Original Mike said...
My first year of college we weren't allowed to use calculators in science courses. Slide rules."
In the 60's it was slide rules all the way through. Plus trig tables of course. The very first calculator I used after college was a desktop Nixie tube machine -- remember those?
Shut up and math
I am sure someone is asking AI to solve Riemann's hypothesis.
And then asking AI to make it look like AI was not involved.
The open letter was prompted in part by the Navier-Stokes result discussed here. That result relied on substantial human input, credible allegations of intellectual property theft by OpenAI, and tens of millions of dollars in computing resources.
Mathematician who struggles with his own productivity issues discovers that AI can be a great research assistant but oddly doesn’t seem to understand how neural networks function. Mathematicians might spend more time on Kaggle problems.
A.I. is like Will Hunting solving that mathematical problem on the M.I.T blackboard?
"Shove that Fields Medal up your fuckin' ass!"
"In the 60's it was slide rules all the way through. Plus trig tables of course. The very first calculator I used after college was a desktop Nixie tube machine -- remember those?"
Trig tables, log tables, sinc tables.
I remember Nixie tubes. Don't think I ever used the calculator you describe.
AI is a tool, like any other tool. We have to learn how to use it. That goes for mathematicians way the heck better than I am.
Even if it doesn't destroy humanity or the planet, AI is going to mess up everyone's "ecosystem." Math is going to be an exception? The sciences recognize that new tools solve problems and create new problems. If mathematicians are brilliant enough, they'll cope with the changes.
I spent a ton of time trying to understand why you can't square the circle and learned a lot that way. There are other math problems in histories of math which you can learn from. I'm not sure how AI is solving problems, how prediction can solve a geometric problem. And I wonder if you can learn from AI solutions in the same way as you learn from human solutions. In other words, trying out a thousand paths in a maze might give a solution but there never was a rational answer. You wouldn't learn from a problem like that. All the same, I agree that there’s something Guildy and exclusive about trying to fence off AI from problems. Much better to solve them in a rational way showing a rational path forward to humans.
meanwhile, the CCP roles on
Why wouldn't solving these problems lead to new problems to solve?
I am reminded of the story about the patent clerk who quit his job in 1905 "because there's nothing more to discover".
This statement by the mathematicians is just retarded. It's like they imagine there's no other problems to solve. Which if true, says a lot about mathematics, and why it needs much less funding.
Once "publish or perish" became the norm in the university, getting Minimal Publishable Units that might have gotten the discipline closer to verifying the Goldbach Conjecture or the Riemann Hypothesis had their value, as did the sort of clarifying that Tom Lehrer satirized in "Lobachevsky," preferably without the plagiarizing!
Number 1 answer at Insta : "If a substantial number of other winners disagree, that could be the beginning of a long division."
James, I'm near the end of my career as a chemical engineer. I was always interested in math, but I was so ill-prepared for it in my high school, that getting through Differential Equations at university was a real slog. Of late, I have been seeing the most amazing short videos illustrating math functions and formulas and it renewed my interest. I decided to get back to work and thought briefly about an online math degree, but then realized that I don't care in the least about credentials and simply want the joy of thinking through the concepts and working through the problems. I had Grok prepare a syllabus and give me a list of textbooks. I ordered them all. I suspect that AI created the simple videos that caught my eye, and I am counting on Grok as a tutor if I get stuck. I don't see how Grok can be worse than the foreign TAs I had decades ago. The texts were surprisingly affordable - I bought them all as books. If you are interested, here is the list and order that Grok gave me:
Stephen Abbott, Understanding Analysis
Sheldon Axler, Linear Algebra Done Right
H. M. Schey, Div, Grad, Curl, and All That
Daniel Fleisch, A Student's Guide to Vectors and Tensors
Michael Spivak, Calculus on Manifolds
Walter Rudin, Principles of Mathematical Analysis
David S. Dummit & Richard M. Foote, Abstract Algebra
Lars Ahlfors, Complex Analysis
James R. Munkres, Topology
Sheldon Ross, A First Course in Probability
John B. Conway, Functions of One Complex Variable I
Gerald B. Folland, Real Analysis
Allen Hatcher, Algebraic Topology
Manfredo P. do Carmo, Differential Geometry of Curves and Surfaces
Rick Durrett, Probability: Theory and Examples
John M. Lee, Introduction to Smooth Manifolds
Kenneth Ireland & Michael Rosen, A Classical Introduction to Modern Number Theory
Lawrence C. Evans, Partial Differential Equations
Thomas W. Hungerford, Algebra
William Fulton & Joe Harris, Representation Theory: A First Course
M. F. Atiyah & I. G. Macdonald, Introduction to Commutative Algebra
Miles Reid, Undergraduate Algebraic Geometry
Joe Harris, Algebraic Geometry: A First Course
Robin Hartshorne, Algebraic Geometry
Herbert B. Enderton, A Mathematical Introduction to Logic
J. H. van Lint & R. M. Wilson, A Course in Combinatorics
Lloyd N. Trefethen & David Bau, III, Numerical Linear Algebra
@Oso Negro
That's a good list, a lot those are standard or classics. An alternative to Hungerford is Lang, different style, perhaps better motivated.
I agree, that seems like a good list - I remember using or at least perusing a lot of those books in my undergrad days. As an algebraist, I certainly recommend Dummit and Foote, and if that grabs you, moving on to Isaacs' Algebra. Of course, little biased since Isaacs was my PhD advisor (in our esteemed blogress' backyard of Van Vleck, in Madison). Rudin is a classic as well - I remember his wife (also a mathematician) occasionally dropping in in Van Vleck - I almost knocked her over running down the stairs once. As for differential equations, well, I'm pleasantly surprised that I've made it this far in my career knowing absolutely nothing about them.
I didn't really understand linear algebra till I got paid once to tutor someone with Axler's book. A great book.
John henry said...
I've been seeing this for the past week or 2 and it seems like complete BS to me.
Exactly. I only ever read the NYT when Althouse or someone else sends me a gift link. As a college math major, I will say that this article is deeply and profoundly stupid. It is hard for me to imagine people actually paying for such trash.
" As a college math major, I will say that this article is deeply and profoundly stupid. I"
Everybody who sees something they actually know about written about in the press says the same thing. But don't worry, you can believe everything else!
"But don't worry, you can believe everything else!"
That's you in spades.
It's not important to them because they Can't solve the problem
I agree, that seems like a good list
I would warn that while some of the texts are undergrad, others are quite advanced. And even if not advanced, if you pick up M. F. Atiyah & I. G. Macdonald, Introduction to Commutative Algebra, you will wonder "Why are we doing this." It is more of a slim summary/reference with exercises than an introduction to the subject.
Oso, if you can get through that book list and complete the problem sets, they ought to give you an honorary degree anyway. A master's degree at least. That goes beyond a bachelor's level.
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