Comment by randcraw
4 days ago
I think Thompson has no understanding of endeavors like pure math or the theoretical sciences. In the words of Einstein, "I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know his thoughts; the rest [is] just details."
I think mathematicians aren't bemoaning their lost sunk costs. They're now aware that they may never again have the joy of being the first to pull up the edge of the tarp of ignorance and see the raw truth beneath _for the first time_. Their voyages of discovery, which give life meaning, may never leave dry dock again.
It is strange, because in a sense, when you start learning math, you never explore, you are being taught. Now mathematicians were able to exercise curiosity. That is going to change. Back to the ranks of eternal learners if you will. The fun was in the research. Now I think it will leave the door open toward more Applied math. What can people do with all the discoveries. The curiosity will be there. I think it is better that way. It will also put a cap on abstractions that overlaps. In essence, AI is less likely to create new theories, coin new terminology, etc. But it is better suited to recognize emerging patterns. That will probably simplify mathematics. Unless the domain of abstraction is infinite and with each new abstraction comes its own results but I doubt it. Who knows though...
> The story of human discovery and the triumph of the human spirit will soon be excised from this discipline. The Dinitz-Garg-Goemans counterexample was the most egregious demonstration. It revealed that the process of prompting novel proofs will be as auraless as ordering doordash. Watch as magic and mystery evaporate. Watch as the sun sets on our heroic age. Is there not something evil in the act of blocking all future generations of mathematicians from the experience of discovery? Forget about accuracy or even attribution. Something fundamental to the experience of mathematics is being taken.
> You are a helpless onlooker. Before you a channel through which humans have accessed the ineffable and sacred for thousands of years is being sealed for eternity.
https://kirwinhampshire.substack.com/p/the-dark-night-of-mat...
As someone with friends in the mathematics community, they've expressed similar sentiments.
I have to wonder if this is the equivalent of teleporting back in time and finding Marco Polo or any of those early explorers who traveled for the love of the game (and fame and money), and opening up Google Maps on your phone and showing them the zoomed out world. And showing them any island or village they could name.
my analogy is that it is like an explorer being handed access to satellite imagery. and then being told that your experience will still be valuable in telling the satellite where to point and interpreting the photos. folks who got joy from traversing unknown terrain might find it distressing to become an image analyst.
This is absurd and silly. Discovery doesn't go away because more new things are being discovered. This position only makes sense if you make an arbitrary cut point where some instances "don't count". If you were to go back to scientists or mathematicians several hundred years ago and tell them that one day science would be done by tens of millions of full time researchers around the globe, often working in teams, some of them might also bemoan the loss of the "hero scientist" as any commoner could now participate. But science and math have only benefited from this, and this has increased, not decreased, the beauty and wonder in these fields.
It is not the same because the act of problem solving for discovery is now to be done exclusively by machines, as humans are no longer remotely competitive.
If you read the linked article, the author goes into more detail about how doing mathematics also has been an act of communication with past and present human mathematicians. This is very much true when math and science are done by millions of human researchers, but not so when it is done by massive swarms of agents at a couple labs.
I am sure science and math will benefit in the sense of solving more problems than ever before. But you are not really understanding the agony of the humans caught in the change.
> they may never again have the joy of being the first to pull up the edge of the tarp of ignorance and see the raw truth beneath _for the first time_
Until we can demonstrate AI consciousness, “seeing the raw truth” will be a human activity. Even now, verifying and understanding these AI proofs is a massive endeavor. Coming up with an intuitive (to humans) distillation of the finding remains an open challenging demanding expertise.
i think to certain types of people (who are probably more likely to be mathematicians), the "self" discovery aspect of it is important, they don't want to read about a new proof for a problem they were grappling with, they want to come about it through their own thoughts.
LLMs are not feeding us things, we are asking it and getting answers. This dialectic I think is super powerful and it still requires the human to ask questions and continue expanding intellectual curiosity to go down the rabbit hole and discover. LLMs are just an incredible rubber duck but the discovery is still there.
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> Until we can demonstrate AI consciousness, “seeing the raw truth” will be a human activity.
I don't think this matters a bit. We individually can't demonstrate "consciousness" in other humans, it's not even a word with a definition. What we can do is miss the feeling of discovering something on one's own rather than having it explained to you over and over again until you understand it.
I mean, dead mathematicians are definitely not "conscious," but their books keep you from discovering things that you may have discovered yourself if left to your own devices.
The joy that was mentioned is the joy of knowing a bit of gossip that no one else knows, of being the first explainer. Interpretation is just being able to pass gossip on; a decidedly lesser joy. And there's no reason that AI shouldn't be able to explain findings in an intuitive way - LLMs at least purely operate based on human intuition as written in human communications and then captured in matrices.
If these proofs are good (doubtful, imo) and can be reduced (intuitively distilled, sorry), there's no reason that an LLM shouldn't be able to do that.
That's such a nice way to put it! I recently stumbled into "The Last First- Winter K2"[1] and saw the same spirit along with a similar misguided effort to win without the will, nor capacity to do it — e.g. influencers taking a stab at K2 is like prompting your way to results.
1: https://en.wikipedia.org/wiki/The_Last_First:_Winter_K2
Why is not like changing to a different type of vessel for the voyage? Unless and until it is all AI in closed system, could direct machines where to look etc.
Climbing a mountain is different from flying a helicopter to the top
True, but then the moonlanding wasn't possible on foot.
Only the journey is different.
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> They're now aware that they may never again have the joy of being the first to pull up the edge of the tarp of ignorance...
Not "never again", it would be extremely difficult but science and math are also built on random, trial and error, and intuitions that could not arise from AI.
That's the issue - trial and error. A human can try a couple ideas in a day, but realistically, there are not that many sane ideas.
Computer can iterate without frustration on a completely random garbage. Once in a while it stumbles upon a gem. Even if it's one in 10000, that's still hundreds of good ideas in a day (provided enough GPUs).
Your comment assumes math and science are some kind of closed systems that can mechanistically pursue any endeavour but reality (whatever it is (e.g. the universe)) is much more complex than that, and there are realities that are outside of those systems. Not saying that humans can see all those realities though.
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I'll say it again: AI is capable of answering the questions put to it but AI is not yet capable of knowing which questions are worth asking. Mathematicians have no cause to weep, they will be fine.
Most of these questions Mathematicians posed to each other have no practical application, and probably will never have a practical application. (ex: the solution to the Navier Stokes question doesn't change anything at all.)
In many ways, the teleporting machine that teleports to the solution is against the point of the questions. No one wants the solution to be "Run $10,000,000 worth of tokens to cover all possible Lean formulations of the problem".
I think for Mathematicians, I'd say that the human level formulation is still possible and with a new perspective. We as a society (and outside of Mathematics) need to also understand that this AI teleport to the answer thing has less value than we all expected. The value is in the journey.
The open question is if people will still want to take the journey if the teleport machine exists. Or if the existence of the teleport machine halts exploration.
> "Or if the existence of the teleport machine halts exploration."
You're overlooking that the teleport machine costs lots of money to use. The AI providers are not going to waste money by teleporting randomly around.
Someone is going to have to find a new destination that is worth spending the money to teleport to (or walk by themselves) and that someone is mathematicians.
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