Whatever doesnt count as maths is just not maths. Its just carrying out instructions to get some "gain".
Other people usually care only about "gain", its their only motivation. Non "gain" results are just happy accidents.
And "gain" (once you have your survival covered) is just an invented abstraction with 0 real meaning. But people try to convince themselfs that it has meaning.
This goes back to the classic story for "kids" about the emperor that has no clothes.
Into eh concept of the mathematics discussion, I wouldn't care to hire a plumber that could work through theoretical plumbing designs that have nothing to do with my house.
Having a plumber that can better solve problems during their work fixing a system is obviously a good thing. That simply isn't what is being discussed here, most mathematics research being raised are theoretical math that has no immediate practical use. That doesn't mean it shouldn't be worked on, but it isn't the same as solving a real world problem we have today.
I dont get this. What is the difference if you replace "AI" by "Tao"? And people still were doing math.
I get HN is a Software site. But all math posts are invaded by people that think Math=Software. Probably based on the way they were taught maths when they were young.
Why would a theoretical physicist spend 30 years developing a theory that could be made false by a new experiment with a new technology? Was Newton gravitation worth if einstein was going to come later?
We are heading directly into a world where people forget about what values, philosophy, poetry, math, physics, or any other "non economically valuable" things are. And we all know what happened any other times in history when that happened.
Thanks for telling it better than I could have! But if you could expand on your last sentence, what instances in history are you referring to? Dot com boom? Great depression?
I was thinking more about dictatorships that block the entry of outside knowledge into the population for example, because its not useful to their goals (which is a particular shape of what economic value is for them). But you dont have to go that far away, you can just see the difference between democratic cultures that value at different levels those fields. In the end "economic value" is less objective than what it seams.
The main issue here is that people that are able to "Strong disagree" is shrinking with every model release, because it requires skills. So it will get more difficult to get funding.
You may say "hey, before AI people payed for math salaries even though they didnt understand the math or the economic outcome". But the issue is there are now "mathematitians" trying to convince not to fund.
In this new reality, you will get "mathematitians" trying to convince that only AI maths matter. And on the other side someone speaking about "understanding", "taste", "community". And the people deciding to fund dont have the skills to differentiate. So they will fund the AI boosters with a higher probability.
Thats how the job of professional mathematitian dissapears. By being replaced by something that on the surface looks similar, but its just an ugly copy.
I guess this AI wave will divide the population more between people that think that only economic value exists, and people that dont.
Thats one of the timeless human debates.
We are now living in the perfect combo of low morality and general human automation. So i expect the next few decades dominated by people who think (and have a "proof") that doing something without an expected economic gain is useless.
Can we please stop reducing human activity to "taste", conferences, talks, "understanding"? I think this is a very unproductive trap.
There is a world where we get to the edge of AI capabilities, and we build on top of that. As humans have always done with every new technology.
There is another more pessimistic view where LLMs just replace every human capability, and our economic overlords dont need us for anything and we just eat the small pieces of bread that are left.
This comes down to the fact of:
is human existence/intelligence just the simbolic representations we make in our brain? Or are they just a tool?
I tend to think of Godels incompleteness theorem as a proof that on the limit LLMs are useless. The real question for me is at what point approaching this limit becomes an issue, and if it has any practical consequences.
I know that is the whole point. But i may dream of being as tall as a house, but it does not matter how hard i dream, it wont happen.
In my experience, every new model release allows me to go further, although every time i see every time the limitations, and i identify where i add value. And this value gets bigger every time.
But on the other hand, every model release reduces the amount of people that are able to value this "added value", because it requires more skills.
So we have the paradox that the added value i can bring on top gets bigger and bigger, but the perception of the economic value for the majority of the population gets smaller.
In contrast to what these philosophical pieces tend to convey, the main crisis in mathematics is a labour one.
Mathematitians exchanged proofs for employment. That was the currency. Now they cannot use that currency anymore, so the question is how does someone know if they should hire an unknow person or not?
Philosophicaly who cares if you like more theory building or theorem proving? You dont need to convince anyone. The only solution is to be curious and follow your interests and naturally humanity will redefine what the new mathematics feels like.
You cannot convince anyone about it, its not something rational.
Where does the money come from? Who controls it? Convincing the funders of mathematics that they should still fund it, but for different reasons, seems pretty urgent. Studying theoretical mathematics is a prestigious activity, and these philosophical arguments are a high-status way of coming up with new justifications with somewhat different goals.
It comes from AI boosters like XTX markets or the Simons Foundation.
No convincing is needed. The part of mathematicians that are elite and online are already bought and put up various websites that allow tolerated dissent but are really dog and pony shows for AI.
The offline part perhaps works on real math like Wiles and Perelman did.
This is very untrue. Academic mathematicians do more than just proofs. They teach, they conduct research, etc. There are almost no privately employed mathematicians who spend their time doing proofs. And academia has a substantially lower pay grade than things someone good at math can do, like quant or big tech. Academic mathematics and these specific kind of proofs have never held tons of value in our society economically. They have always been more culturally and academically relevant as a symbol of our frontier knowledge, than they have been financially lucrative. I doubt many math departments would even consider paying for the kind of token spend that might have gone into the proofs for some of those "big name" problems
Proof assistants like Lean are there to catch any errors. Now, can you just feed the error logs back to the AI and let it iteratively fix any mistakes? I don't know, I haven't used those things in two decades.
Laymen understand very little about the how the world works at the most fundamental level even with all the resources in the world.
For example there’s enough information available to know what you’re describing but the people with the IQ, time, access, ability - basically asymptote to zero for anything more complicated than cleaning a house.
> To take on this responsibility, we may need to broaden our view of what a mathematician can contribute. I have in mind something like a “deployable intellectual reserve”: communities of mathematically sophisticated people that humanity can call upon to help understand consequential AI-enabled breakthroughs.
> Our ability to understand difficult and unfamiliar ideas may become one of the most important contributions we can offer to society. We should be willing to bring that skill to problems far beyond our usual research interests. [3] Doing so asks us to expand our sense of our vocation.
Am I reading this wrong, or is he talking about what (mathematitian) Data Scientists have been doing for years? So he is basically saying that former Data Scientist that have turned into prompt/software engineers should go back to being data scientists.
In any case, people should stop trying to fit AI in the previous status quo. What we need is curious people, that is what we have always needed.
A few centuries ago there were no "mathematitians", there were mathematitians/philosophers/artists/physicists all in one person. So its not like "mathematitias" is something that has existed for millenia.
We need curious and ethical people.
Maybe AI brings back the age of a well rounded scientist/philosopher. I know this sounds counter intuitive because the article is saying that we cannot keep up with the AI.
I believe he’s advocating for mathematicians to understand the novel concepts introduced with each breakthrough rather than individuals understanding data stemming from empirical observations.
Im at a point where i think the way to steer the situation we are in is to steer the machine from the inside, not quit and leave the people with the opposite mindset keep all the economic resources.
I doubt a movement of the people from the outside will work this time when all of the capital is in the other peoples hands. We need at least some of it held by someone with the opposite view to make the movement credible. And I dont think VC and IPO dynamics are compatible with this.
If you are already thinking of quiting, you can organize and internal movement and use the power of your labor to steer things. One person quitting is nothing for the company. The risk of big group quitting at the same time on the other hand... The labor is the only thing the company cares about. So we cannot wait until we are all replaceable by AI and we lose that leverage.
Clearly the details matter in this making such a decision, and not everyone has the same capabilities to "steer the ship" from within or out. You don't know if there are concerned people within acting, but see most obviously concerned people leaving to act (or at least refuse to act).
Good point! I was speaking from my experience (at non tech companies, thats true). What i have seen is that there is an internal self selection of people that "refuse to play the game". My point is that that could have been a fair choice before, but the stakes in this new AI situation are at a point where they seem too high for that to be a good choice.
But nothing would make me more happy than knowing that there are concerned people acting internally.
Other people usually care only about "gain", its their only motivation. Non "gain" results are just happy accidents.
And "gain" (once you have your survival covered) is just an invented abstraction with 0 real meaning. But people try to convince themselfs that it has meaning.
This goes back to the classic story for "kids" about the emperor that has no clothes.
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