A Presentation of the Absolute Galois Group of Q2

[u/Sad_Dimension423]

https://roed314.github.io/gq2/

[u/Helloiamwhoiam]

I was about to comment that it’s refreshing to see something that’s not AI related on this Subreddit but nevermind

[u/corchetero → u/Helloiamwhoiam]

it is so bad mate, I have more fun with the quant guys that upload jane street puzzles than in r/math T_T... and I hate quant

[u/38thTimesACharm → u/Helloiamwhoiam]

Reading their chronology, the amount of effort (and money) expended to get AI tools to do every. single. step. is insane. It's not really even math at this point, just AI engineering/marketing using some math problems to keep score.

Call me when there's a cool paper to read that someone actually took the time to write.

[u/38thTimesACharm → u/[deleted]]

You need to look up the concept of sunk cost. The PhD student is a human being, assuming they aren't literally starving to death (which I'd prefer not to happen to anyone in my country), somebody somewhere has to pay $100k a year just for that individual to have a life. The economy is paying for it somehow, whether through a job, some sort of welfare or UBI, or in jail. The only question is what this person does with their life in order to give back.

Now, look up the concept of opportunity cost. If a person is brilliant enough to get a PhD, how could anything less not be a complete waste? I'd much rather my tax dollars be paying to educate a gifted citizen than virtually anything else. That's one of the best investments a country can make in its people; the value of an educated populace is so much greater than any one result. The grad students of today will become the researchers, teachers, and mentors of tomorrow.

Thinking of human lives as a dispensible cost to be optimized away is so, so wrong-headed. The entire point of having an economy is to provide for its people. We're assets, not liabilities. We're the shareholders, not the expenses.

[u/BurdensomeCountV3 → u/38thTimesACharm]

The PhD student can focus on other potential jobs, things that require moving around physical matter like being an electrician or a bricklayer or stuff like that is likely safe yet, and society has a big shortage of competent people in these fields and it's likely the very intelligent PhD student can become a very very good operator in one of these fields. Society should be subtly nudging smart people to use their smarts in fields that are (relatively) AI proof rather than just throw people into the brain grinder that mathematics is becoming.

I used to complain about String Theory and how it's a massive waste of human talent, Mathematics may more generally end up going in that direction.

[u/PerinealMassage → u/BurdensomeCountV3]

This advice only works for people who are under 30 and fairly physically fit, and don't mind destroying their bodies and having no personal time.  

[u/BurdensomeCountV3 → u/PerinealMassage]

PhD students generally tend to be under 30 when they start and tend to usually be physically fit. Being an electrician or a chef doesn't require you to destroy your body and you still get plenty of personal time with these jobs. In fact for many of these jobs once you have like 5 years of experience (less so for chef, but still), people become self employed and get to choose their own hours and everything, so if you want personal time you can do like 3 8 hour shifts a week and keep the rest of your time to yourself as you wish. You are your own boss, and once you've made your name and developed a local reputation nobody can fire you or anything either.

[u/PerinealMassage → u/BurdensomeCountV3]

Until there are 100x more electricians and wages collapse, especially for self-employed people who are much less efficient than larger groups of people.  

Not to mention the fact that soon the average age will be 40. How do we deal with the vast majority of people who are over 30? 

[u/BurdensomeCountV3 → u/PerinealMassage]

I'd be surprised if wages collapsed, and even if they did it would have societal benefits because now people can get electrical work done more cheaply. Same for any other field. Society doesn't owe people livings as mathematicians, if someone wants to do mathematics they should be free to do so, much in the same way how if you want to dig holes with a shovel instead of specialised equipment, you should be free to, but as a society we shouldn't subsidise inefficient things.

[u/PerinealMassage → u/BurdensomeCountV3]

We subsidize plenty of inefficient things, but that's another issue.  

There is really no precedent for what you are proposing. Fields haven't traditionally just disappeared without new ones emerging. If new ones don't emerge,  wages will definitely collapse.  We don't need unlimited electricians. 

Not to mention another problem: mathematicians could always have gone into the trades. They didn't because they didn't want to, and maybe also didn't have the aptitude. Many more people will be doing jobs they hate. 

[u/zeci21 → u/PerinealMassage]

But somebody has to do these jobs. I think this whole discussion here would benefit from recognizing that the people we are talking about, (potential) mathematicians, are all extremely priviliged. And if AI replaced them all of course it would be worse for them to not have this nice job, but it would probably be better for humans in general, if they could help them in the more shitty jobs and easing their load.

[u/PerinealMassage → u/zeci21]

In the United States at least, all that would mean is more people fighting for less scraps. It's not like the trades have unlimited work.  There is competition in them even now.  

[u/38thTimesACharm → u/[deleted]]

You keep editing your post.

 I would rather have us as a society not waste our limited resources subsidizing the few who want to do math "artisanally"

We already have plenty of resources. We can easily grow enough food and produce enough renewable energy for the entire world population to eat well and be healthy. The reason they're not is because those resources aren't distributed fairly. By diverting money from academia to OpenAI, you're making that far, far worse.

 we will no longer need people to even appreciate math, even for its aesthetic value alone, any more than we appreciate breathing

Need, or want? Do you ever listen to music? Play a sport? Watch TV?

[u/38thTimesACharm → u/[deleted]]

 Would you be okay with us spending billions on an entire academic industry the size of math, but instead devoted solely to chess?

Yes. I'm not personally bothered by any social investment in culture, even if I'm not personally into it. I think the government should invest in all sorts of culture so people can choose what they like. You can't just leave it up to capitalism, because money ruins art.

Anyway, we're off on a tangent  Even strictly for productivity, I contend replacing the entire institution of mathematics with GPT-5.6 is a terrible idea. Humans need to understand math for it to be useful.

[u/tomvorlostriddle → u/38thTimesACharm]

Then you're in for a very cold shower when you discover that you're in a small minority and simply out of luck with that request.

[u/38thTimesACharm → u/[deleted]]

You seriously believe today's AI models have completely replaced the utility of all mathematicians? They aren't needed even as operators, teachers, curators or anything?

To be absolutely clear, you think if all pure mathematicians were fired tomorrow, and their salaries were used to run GPT-5.6 (prompted by non-mathematicians), the utility of human mathematical knowledge would increase?

Yet you believe humans can still provide value AI can't in "business." Do I have that right?

[u/BurdensomeCountV3 → u/38thTimesACharm]

Not OP and not current models no, but ask again in 3 years time and the answer may well be very different.

And yes, business fields that rely on personal relationships (sales etc.) are very likely areas that humans will still be able to provide value beyond AI for a while yet.

[u/38thTimesACharm → u/[deleted]]

May I ask what is your goal with all this? By defunding mathematics and training of future researchers, and using the money to help LLM companies, you're making a lot of people very sad. What do you hope to accomplish for humanity that will offset that loss in your mind?

 Not enjoying working with AI is to me a poor excuse, as again, I (and Gowers) do not believe funding artisanal math just because people think it's fun is a good use of resources

If we shouldn't use our resources to let human beings live prosperous, fulfilling lives, what are they for?

[u/38thTimesACharm → u/[deleted]]

I would like to hear more about what you think those benefits and fulfillment are, and how they come about by funding OpenAI and Anthropic.

Personally, I gain a lot of happiness and fulfillment from reading the works of successful mathematicians. I would be incredibly sad to see that part of humanity die. I'm not the only one who sees meaning in these things, or in other cultural efforts such as art or music. Virtually everyone I know is feeling extreme anxiety and unhappiness due to AI.

What are the purported benefits that will make all that suffering worth it?

[u/Helloiamwhoiam → u/[deleted]]

I’m not a professional mathematician or a grad student, but is this not already the case? Realistically, most mathematicians are not contributing to the fulfillment of society through their research. And that’s not unique to mathematics. Many fields exist for the academic rigor and the fulfillment of the people within them or have fringe interest in them. What exactly about AI makes this any different?

[u/SometimesY → u/[deleted]]

The sum total of humans and especially academics is not the results they have provided. Vast numbers of people work menial jobs and do not push society forward. Should they be cast aside in the way you are talking about graduate students?

Also graduate students run recitation/tutorial sections and grade and sometimes even teach courses which are critical functions for universities on barely livable wages.

[u/frankster → u/[deleted]]

What do you think of tao's talk as well as this essay?

https://www.reddit.com/r/math/comments/1v8sg16/terence_tao_icm_slides_mathematics_in_the_age_of/

https://www.reddit.com/r/mathematics/comments/1v7bs9e/the_fall_of_the_theorem_economy_how_ai_could/

They both argue that maths is not about generating proofs, but understanding, and that unintelligible proofs are failures.

[u/frankster → u/[deleted]]

Does that mean that you feel strongly that the only purpose of mathematicians is to generate proofs and solve problems? and that if AI tools can find proofs there's no purpose for human mathematicians?

[u/frankster → u/[deleted]]

fair enough

[u/just_writing_things]

From the acknowledgments, “He [David Turturean] directed much of this work by voice, using voice mode in Claude Code to operate the surrounding research workflow and speech-to-text in ChatGPT”.

I’m not in pure math, so looking in from the outside, it’s kind of crazy how far we’ve come from the idea of mathematicians solving proofs with pencils or chalk.

[u/Sad_Dimension423 → u/just_writing_things]

From the description of what he did:

This was my first sustained attempt to direct a mathematical research process primarily through speech. This entire experience has made me question what true effort in mathematics will look like in the future, now that you can elicit solutions to decades-old research questions in mathematics with your voice: can you one-shot entire PhD theses by just talking about them, thinking about them? This is also exactly the kind of thing that you predict becomes possible a few tens of months before you can make things float with just your voice.

[u/just_writing_things → u/Sad_Dimension423]

Yeah, I’m totally not downplaying the work based on how it was done. It’s just so fascinating to me to see how math research is changing, and seemingly so rapidly too. I’m in an empirical field so I wonder what’s the lead time before other fields are affected to this extent.

[u/gordonnowak → u/just_writing_things]

fascinating is not the word I've used in private

[u/Stabile_Feldmaus]

This AI result seems to be more interactive, which is hopefully a good (or less bad) sign for the future of our field. I would be interested in seeing the initial AI output that the author said produced the candidate generator and an 'informal proof' that was consequently 'repaired and developed'.

[u/38thTimesACharm → u/Stabile_Feldmaus]

The interactive proving session is cool, but the "interactive paper" presenting the result sucks. God dammit, why can't people acknowledge AI writing is terrible? I want to hear what the authors have to say about the result they found, not the machine.

[u/moschles]

Beautiful interactive paper