That aside, if you want to make it rational, you can think of leaves in the context of explore-exploit dilema. Probably a wider exploration would allow you to find better things to exploit. Its like the 20% innovation time that some companies offer
Then 20 years go by and you wake up one day with questions that you cannot get out of your mind: why did I start prompting the LLM for? Why did I need these random proofs for? What do i do with my repo with 2billion lines of Lean?
Should I read this as the big labs trying to move maths forward? Or the big labs trying to use professional mathematitians as (cheap?) Labour for validating LLM outputs? On yesterdays "An Alien Mind" post from openAI they openly said that maths is not a priority for them, so I personally know what to think...
We are a student-led initiative. Our sponsors don't pay us and don't have a say in our decisions. All of our funding goes toward our judges and participants.
Hey! Thanks for answering, i appreciate it. Dont get me wrong, this is what you should be doing, understanding what these models are good (and most importantly bad) for. My observation is that this is very very valuable for the labs, and in an ideal world they should be paying you to do this, not just the tokens and "prize" for the winners.
I am also a bit frustrated seeing maths go in the direction of prompt enginnering. I am afraid of a world were a math phd student cannot go one week thinking about a problem without prompting an LLM to give him/her an invented answer. Something is lost along the way.
For me maths is not Lean, or formal systems, or an agent reasoning about formal systems to join literature from different fields. I see the value of it, but i think it will make it way more difficult for students (and profesional mathematitians) to see beyond that. And i see us heading into a reality were those who think like me will in practice remain a minority for quite a few years/decades because the low hanging fruit of LLMs will be to vast to ignore.
Agreed. I think we share the same concerns about LLM use. We just drew different conclusions.
Mathathon's goal is to reshape rather than stop LLM use. Can we set high standards for LLM use? Can we highlight the roles of a mathematician beyond proof generation? Can we redesign our incentives to promote these standards and roles?
I'd love to hear your thoughts on how to improve this event. We're very open to criticisms.
Thanks again for answering! As I told you I think the event is a good idea from your side. I would try to go beyond proof prompting and verification, and discussing the questions that you wrote above is the way to go.
I am mathematitian that is working as a software engineer. I have see first hand what these models are doing to SE. Its not that writting well thought, and compact code is not a good idea anymore, or that it doesnt beat LLM code, but that the people that see the value are a minority. If you write a piece of old school code in an LLM repo, it doesnt really make a difference, because old school code requires a team effort.
In maths the situation is not exactly the same. Probably reading a good piece of well thought math inside a book of LLM assisted proofs will stand out so much for the carefull reader that there will be no question about the value.
However, if the only way to get a position at a university is to print as much papers as possible, then who would risk printing 1 paper instead of 5 for doing old school maths?
So the solution to this is building a culture and community effort around these topics. And for that the topics need to be openly discussed.
Good luck with the organisation! And thanks again for the conversation!
Obviously the latter - this fact is betrayed by how the page lists the S^6 complex structure result, which was released as a 100 page barely readable mess (in fact even this might be too charitable), as still "unverified". Clearly a situation labs would like to avoid for future claimed results.
> Or the big labs trying to use professional mathematitians as (cheap?) Labour for validating LLM outputs?
I am told AGI has been achieved. If so, shouldnt these systems be out and about on their own ? Looking at 1st proof submissions in batch 2 it is clear that fully autonomous AI systems have a long way to go.
AI harnessing human labor with the incentive of 2M in free tokens is the way my skeptic eye sees it, or humans being duped as reverse-centaurs.
It's very clear that the AI still has no motivation beyond its prompts. Humans can mostly outsource their thinking today across a wide variety of topics, but they still need to express their desires.
> I am told AGI has been achieved. If so, shouldnt these systems be out and about on their own
This seems like a strawman. It’s certainly not consensus that AGI has been achieved and I don’t think the people participating in this event feel like there is no value in human input or steering the AI.
Probably many mathematicians want answers to the questions from the page:
> This AI advancement raises the following questions: (a) How much can AI speed up the process from ideation to peer-reviewed publication? (b) What is the role of a mathematician when AI can solve conjectures faster?
and the big AI companies agreed to sponsor them to find out because it is good publicity for the companies.
It looks good at the begining, but at some point it starts saying "half truths", or stating facts/conclusions with confidence as if that was the main reason, but its just half of it (and maybe not the most important half)...
I wanted to read it because I like the topic, but i somehow felt it was folluting my brain. I think i will also start joining the club of AI;dr to protect myself from pollution, even though i may miss some iteresting articles.
Of course it is. Play is a very basal behavior we see in a host of species among their young. Its biological role is to build up musculature and social bonding such that the individual will be strong enough and socialized enough to do what is required to survive among the colony/pack/tribe.
100% agree, and I experienced that behaviour first hand. I got confident, started giving less guidelines, and suddenly two weeks have passed and the LLM put me into a state of horrible code that looks good superficially because I trusted it too much.
Nicely written! I was thinking about this the other day. What is the benefit from your point of view of procesing information full of null pointers? (I know what the benefit of not halting its programming is :P)
De-referencing null pointers is the ultimate tilt but our NNs needed a way to explore just a tiny bit of unmapped memory without halting a.k.a go crazy, surrender to fear etc, probably because planning and anticipating for the next threat/unknown is their main role. It seems that we have devised a clever way of offloading the exact point of no return of our pcregister to handling by fantastical powerful creatures. What if the next crop does not deliver, crash danger alert -> praise a god. What happens when we die -> establish a religion based on afterlife benefits etc.
At the same time and while this jump command is now installed/available it allowed us to explore alternative solutions (medicine, technology etc). Since one can always transfers his main program's control to GOD section, it feels less risky to process methodically information full of unknowns and failures (the context now is "with the help of god we/one can deliver a solution"). This particular section throughout history controlled our lower instincts, maybe even made us more empathetic to other (unknown) humans instead of always perceive them as a threat but ultimately controlled all aspects of life and when misused delivered bloodshed and misery. What a weird section! I think at some point we should become brave enough and refactor/remove it, it served a purpose but now is not required/obsolete.
Think of it as social intelligence if the term “emotional” bothers you.
Solitary intelligence, in the wild, is just a different beast from tracking the exponential complexity of a social system. Everything we see—in biology, psychology and artificial intelligence—indicates that while these functions seem to share resources (you can't be an emotionally-intelligent idiot), they are distinct, with folks (and animals) possessing a lot of one and little of the other being observed, and their handicaps resulting from the lacking part being observeable, too,
If i get your point based on your answers: "intelligence" cannot be divided into categories. If you are intelligent, you can be trained to do whatever skill you want, its just a matter of being taught or exposed to the probelm. So it does not make sense for it to have its own category. So if you train intelligent people to be social, they will be social, its just software.
What i have seen: people can perform outstandingly well on classical intelligence without almost being taught. Think about mathematics or logic. But when you get into social/emotional territory, then it has a bigger correlation with how you were taught or your experienced when you where a small kid (but its not 100% causal). So in that sense its not the same thing.
Now, if you are unconfortable by calling it "intelligence", feel free to call it "skills". For me its the same thing as a football player having spacial awareness of the field. Sure, they have to be trained, but it is some "skill" that some people have an easier time using and improving.
Why not?
I know people who are very good at feeling other people’s emotions but very poor at analyzing them.
In kids you can see it all the time - like a kid started crying because he sees others cry, but if you ask them why they cry - the explanation is always ridiculous.
But even some adults are like that, interpreting your own or even others emotions is both a skill and a talent.
>In kids you can see it all the time - like a kid started crying because he sees others cry, but if you ask them why they cry - the explanation is always ridiculous.
Why can’t it be both? We have dedicated neural circuitry to mirroring others’ emotions, and pheromones that directly signal emotions between individuals.
It just isn't both. Emotional intelligence isn't mirroring others' emotions or smelling their pheromones, it is using the mind to actually understand rationally what is going through someone else's. It's how you can know what an octopus is thinking despite not having the neural circuitry to mirror its emotions or pick up its chemical signatures.
> It's how you can know what an octopus is thinking
You mean, it’s how you can assign anthropomorphised assumptions to the octopus. There’s a world difference between having semi reliable predictive power and actually knowing something.
Yes, exactly how you assign those assumptions to humans despite having no way of actually knowing that they have rich internal lives comparable to your own. It is the ability to simulate a mind foreign to your own and anticipate how it would respond to circumstances.
We don’t have to assume with humans. We can introspect our emotions and discuss them with others. Though we can’t be precise, we can understand and distinguish concepts like shame vs humiliation which appear to be (effectively) universal to the human experience.
That is a world apart from seeing an octopus react to something and assuming that anything resembling emotions are involved at all.
I think your description would be perfect in describing a psychopath - i.e. someone who can rationalize and think about other beings logically, without actually being able to subconsciously empathize.
Not all people like that at all. Some people really do feel emotions of others before being able to rationalize it.
> Some people really do feel emotions of others before being able to rationalize it.
Yeah, they are called empaths. That's empathy. Rationalizing is another process, which can be done faster with high emotional/social intelligence.
> psychopath - i.e. someone who can rationalize and think about other beings logically, without actually being able to subconsciously empathize.
Exactly. Low on empathy but high on intelligence - psychopath. Low on emotional intelligence but high on empathy - empath. Low on both - unfeeling idiot. High on both - a warm kind person.
No, a psychopath is someone who can't empathize. Theory of mind has nothing to do with empathy. The overwhelming majority of people are capable of both, but they are two distinct skills.
Having met many extremely intelligent people who struggle to understand the emotional state and responses of those around them, hell yeah I think it's a distinct category.
Doing math, or telling a joke, or catching a ball, or carrying a tune are all normal human behaviors. People's skills at any of them vary, and we don't refer to those with lower skill levels in that category as mentally deficient or ill.
The only ways that comprehending emotions wouldn't belong in its own category of intelligence would be if everyone were equally capable of deducing the emotional state of others, or that performing such deduction is not something intellectual, or that such deduction is strictly a consequence of existing intellectual categories.
>The only ways that comprehending emotions wouldn't belong in its own category of intelligence would be if everyone were equally capable of deducing the emotional state of others
Not every skill gets a whole category of intelligence.
>that such deduction is strictly a consequence of existing intellectual categories
Someone could be extremely proficient in disciplines that are associated with 'raw' intelligence, and yet utterly fail at theory of mind. Anyone that has been in a college campus probably has seen examples e.g, Classmate might click instantly with real analysis but will routinely perplexed about why their girlfriend is mad, or why they are seen as abrasive.
To be clear, in my experience it wasn't even a case of being on the spectrum or other neurodivergence. They simply had a bad model of other people's thoughts and emotions. Of course this isn't DnD, I've met people a order of magnitude smarter than me in the usual academics and with a deeper understanding of people.
You might not like the terminology, but it's a real thing and can be independent from what we usually call intelligence.
Consider a computer with a cpu and gpu. The CPU is a general purpose computer. It can do literally anything. Including software rendering. But the GPU is purpose designed for graphics so it will be much more efficient at the job. These days the GPU is also a general purpose computer so it could in theory do anythign the CPU does too, but for many things again it will be less efficient.
It's the same with emotional intelligence. The brain has dedicated circuitry for understanding other people. You can reason it through abstractly but it will be less efficient. You can also solve problems about natural science with the emotional reasoning part of the brain. Ever heard the expression "the atom wants a full shell of electrons"? That's empathy.
No, it is more like software. You either grow up around others, socialise and train your intuition or you don't. To believe there is special circuitry really goes deep into the pseudoscience territory.
You are correct that training is necessary, but that isn't the knockout blow you think it is. It goes for many of the specialized tasks (e.g. visual processing, auditory processing, motor skills, spatial awareness) done in the brain. You are born with the potential for these things but they have to be used or they will wilt.
As for where in the brain it happens it does seem to be a little spread out, but the superior temporal sulcus has an important role.
An interesting semi-related story is that taxi drivers in London take a very hard test called The Knowledge requiring them to memorize a huge amount of city layout. Studying for this produces measurable changes in the brain, leading to an enlarged posterior hippocampus. That it consistently leads to changes of the same type across many individuals clearly indicates that the brain is allocating resources to the relevant circuitry when this learning takes place.
There are many other ways to learn about the brains specialized processing such as looking what happens when various parts of the brain get damaged, or by putting people in scanners when they perform certain tasks.
You're the only person here invoking "special circuitry". All intelligence is a mix of both learned and biological factors.
Plus one of the big ways we evaluate the intelligence of other species is trying to see if they have theory of mind, which is intrinsically linked to social intelligence.
Edit: Ah, the person you replied to also invoked special circuitry.
This site is getting invaded by AI bots... how long before its just AI speaking with AI, and just people reading the conversations thinking that its actual people?
To me that graph seems to say that the pure "subconscious" stuff or "ML similar" stuff peaks earlier, but comprehension peaks much later. So you perfect your tools in the brain at around 25, but then it takes another 20 years to really know how to use them correclty.
That aside, if you want to make it rational, you can think of leaves in the context of explore-exploit dilema. Probably a wider exploration would allow you to find better things to exploit. Its like the 20% innovation time that some companies offer
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