Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.
Mathematics in the age of AI
211–220 of 292 posts
Re: Mathematics in the age of AI
#212Re: Mathematics in the age of AI
#213Earlier quoted context omitted.
Math that humans don't understand but nonetheless allows AI systems to develop breakthroughs in various fields of science, technology, physics, engineering, medicine, etc., would have great value to humanity even if it doesn't help humans understand abstract truth at all. Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it, it initially seemed useless, the…
But at that point you have full AGI and its not just today's models. Today's models still need humans to understand things since it builds upon human knowledge. When you have full AGI of course you no longer need humans to understand math. > Imagine if humans couldn't understand multivariable calculus, but we had access to an AI system that developed it Developing multivariable calculus requires much more than just s…
The idea of AI stepping from a graph theory/combinatorics innovation to some new and useful algorithm isn't crazy.
Re: Mathematics in the age of AI
#214Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.
Re: Mathematics in the age of AI
#215Tao's Rule of Thumb (which applies very well to software): > My own suggested rule of thumb: if the authors cannot convincingly demonstrate that they are able to give a clear, expert-level talk on their results, one that is correct and properly attributed, then the result should not be published. A proof that no human can properly explain should be viewed as incomplete, even if it has been formally verified.
I believe this rule of thumb will come to fail. The combination of superhuman mathematical reasoning and synthesis in upcoming AI models plus the rapid build-out of scalable formal verification infrastructure means this exponential in math is going to take off quite explosively, and we've barely seen anything yet. Mathematics is going to decisively move beyond human ability fairly soon (within our lifetimes, if not m…
Re: Mathematics in the age of AI
#216Terence Tao's quote about AI's math proofs is relatable outside of pure math: "the writing very often dwells at length on trivialities while passing briefly through — or even actively obscuring — the most interesting and novel portions of the argument."
Re: Mathematics in the age of AI
#217Earlier quoted context omitted.
The essay On Proof and Progress in Mathematics by a Field's medalist is worth reading: https://arxiv.org/abs/math/9404236 He wrote it in 1994. He writes about how he almost "destroyed" a subdiscipline in mathematics by becoming so good at it that he outclassed everyone. PhD students were advised to stay away from the whole field. When he discovered this, he realized his error was that he was focusing on producing res…
I don't understand why people are so fixated on the minds doing the mathematics being made out of meat. It seems obvious that soon, minds made of meat aren't going to be able to keep up. Useful thought, rather than hobbyist thought, seems destined to be the exclusive domain of silicon.
Re: Mathematics in the age of AI
#218Re: Mathematics in the age of AI
#219Earlier quoted context omitted.
> The problem with that rule of thumb is that unless there's some status/reward for completing the result, it won't happen. He says it shouldn't be able to published if they can't explain it. Publishing it is the reward.
The thing is, the cost of creating these results, and the expertise needed, is being greatly reduced. So it's possible for people who wouldn't actually care about the results to spoil them by just putting out a formalized proof (for example, to Tao's Palomar site). These people wouldn't care about the prestige; they aren't on a career track where that would matter.
Edit: I just saw Tao actually mentions the above essay in his paper.
Re: Mathematics in the age of AI
#220Earlier quoted context omitted.
Says more about your own effort to learn math than Tao's ability.
You should definitely inform the wikipedia editors as well https://en.wikipedia.org/wiki/Terence_Tao#Recognition . (I don't know why you're so butthurt BTW - neigher of your ad-hominem comments actually outline your concern)
It's mostly memorization and recall and a single proof about primes he is well known for. It's akin to being well versed in Star Wars canon.
If Tao can be replaced by a model he isn't that smart just hyper-optimized in a narrow scope. As a scientist such evidence has to be a part of the assessment; it's not hard; find gaps in a syntax system and generate meaningful syntax to close the gaps. It's an idea printed in information theory books almost a century old.
He's well versed in existing content but has broken no interesting new ground. Where is his calculus or linear algebra. That to me is the real bar; definition of truly never before seen axioms and proof of them.
Lewis Hamilton is a great car driver but he didn't invent the internal combustion engine or racing; he's just a butt in a seat.
Butt hurt; because I don't easily accept awards handed out by innumerates who, not being mathematicians themselves, cannot possibly have an informed opinion on the quality of his work.
Many a mathematician and physicist out there have claimed there's no telling how much of this is verified; there are endless papers out there that constrain what we can actually know via scientific inquiry. Everyone in research just pretends they know it all because hey it's a living made not working in the mines.
But my bad for discussing and debating this all with experts over the years and not just accepting the populist take. If going with popular thing is the expectation Christianity is way more popular around the globe; lets just bin this science thing.
Good for Tao for achieving celebrity in a world of willfully ignorant people; convincing people too ignorant to challenge him to just give him awards sure means those awards are meritorious.
I simply don't carry water for and deify individuals when everything is clearly due to a mesh web of human labor across the globe.