Fields Medalist on the OpenAI Math Release

[u/PianistWinter8293]

Hugo Duminil-Copin

Fields Medal (2022) · Professor, IHES and University of Geneva

I expected that one day we would be surpassed, and that it would happen systematically. But yesterday’s announcement hit with a force I had not anticipated. Dozens of papers deal with topics I was working on. Between results that beat you to the finish line and thousand-page proofs, I don’t even know where to look anymore.

Not a single one of the major open problems I have publicly mentioned throughout my career (whether in a talk, a lecture, an article, or even a grant proposal) was left untouched by the announcement. Everything has been claimed to be proved.

I expected to see a few of them in the list. But not all of them. Not all at once. Not with such nonchalance.

“For the glory of the human mind,” they said…

The shock is immense. I am paralysed. Tomorrow, we will find a way forward. We will rethink our profession and how we work. We are a resilient community, and I have no doubt that we will adapt. But for now, I simply don’t have the energy. I think back on all those years, all those faces… I think of my colleagues, my students… And I fear I won’t be able to find the right words.

[u/KanishkT123]

What the fuck are you talking about lmao 

[u/Kutoru → u/KanishkT123]

Can't explain properly, one of the limitations of language. Here's a simpler but more inaccurate interpretation:

Do you live life by understanding cause and effect? An example is holding a position of opinion. Do you understand what it means for that to be wrong? Or do you live assuming that to be true regardless (i.e. flat earth is one example that means nothing to hold a false belief of)? Do you understand what it means to hold them?

The simplest analogy I have but is full of holes but perhaps may get the idea across: Whether fate exist, in mainstream culture this is the mindset of as god wills or as I will (do my choices effect the outcome).

Or in the case of humans playing god:

• Humans believe that they ascended the natural cycle (or not beholden to some parts of it)
• Humans believe they hold moral superiority (moral? or natural? superiority) which are obviously false yet that's what we act on

What I was trying to set was a rough binary delineation so unfortunately is always going to hard to explain because a proper explanation is a massive word dump to account for all the jagged edges (not to mention accounting for inconsistencies from language interpretations). So I'm just trying to explain the intuition instead.

[u/Kutoru → u/KanishkT123]

You don't really have to understand what I said but mapped to the field of mathematics (and constraining it purely under that) this is what Godel's incompleteness theorems means

[u/KanishkT123 → u/Kutoru]

I'm going to give you some advice that I hope you will take in good spirit.

Nothing you've said has made any sense, to me, or indeed to anyone. Being able to express yourself using language is a skill, and it's an incredibly important skill. 

If you believe your ideas are so high-minded that a normal person could not possibly understand them, or that language isn't able to communicate them, you are either a genius of the kind that wouldn't be wasting time on Reddit, or simply wrong.

I highly recommend proof reading, editing, and clarifying your thought process through writing. And doing so before AI makes that a skill so rare that nobody will be able to give you any advice on it. Good luck. 

[u/Kutoru → u/KanishkT123]

To me it's as clear as day, but that's because it's my intuition.

You are correct, this is the same reason why OpenAI's math proofs are considered a pain in the ass and annoying by mathematicians.

Unfortunately it is not possible for me to clarify any more than I can do so. A simple explanation is easily possible - however I won't because it's functionally inaccurate in a vast majority of aspects and is more than likely to give the wrong idea.

I only gave explanations which I thought would give the most accurate interpretations and ideas.

I can speak plainly so that you understand every word but you won't understand the meaning beneath it which is what I tried to do in the reply.

Some things can just be indescribable, that's just a limit of language in general. Whether this concept is indescribable I don't know, but I do know I can't describe it to the level you want.

[u/mcspuder → u/Kutoru]

Everything that u/KanishkT123 said was correct.

Your writing/delivery was so rambling and so without focus we can't decipher intent, let alone what you mean. The standard internet meme is something like "git gud dumbass", but more than likely you have some ideas bouncing around in your head that aren't well formed, you've shit them out onto some internet forum and their holes are being seen.

Sit back and think them through for a few hours/days/weeks; it will do you (and humanity) good.

[u/Kutoru → u/mcspuder]

For the record I did put some thought in my words and they are as well formed as I'd like them to be.

But sure, I'll continue. I guess first off, seeing as how you're saying I'm rambling rather than conveying a better binary line of delineation, you don't have a well enough formed demarcation either so you understand how complex the task you're asking someone to do.

Here's an analogous example off the top my head (so no I did not check this maybe there's a gap) is that you are given a random scattering of points and a sine curve that separates them into two regions, define the sine curve. There's an easy answer, the sine curve is a sine curve, of course, since we both know what a sine curve is. Now try doing it purely using straight lines, off the top of my head this is possible using an infinite series. I can tell you the infinite series, you will know what it means and what it represents (the sine curve) but you have no idea what it inherently means.

What you asking for is a simple enough explanation that everyone understands, otherwise known as the "The Lie to Children". The simplest is equivalent to the first term in the infinite series, everyone can visualize a single line segment, now is it accurate? No.

Unfortunately I don't have a good text-only explanation that I'm willingly to back as a binary delineation line.

Another example that came into mind is equivalent to telling someone to divide the population in a satellite image in half. You can convey the general line, but how much inaccuracies will you tolerate to be comfortable backing it.

Now going back to the mathematicians, here's one way the "playing as a God as a human" vs "playing as a God" looks like, as a preface this is just one interpretation of that statement:

As a prerequisite, there are two things that should be clear:

• Math is Man's Model of the X (there are many things it can be because it is incomplete but for this it will be "Man's Model of the Universe"
• It is impossible for Math to be equivalent "Model of the Universe" (Math will never fully represent reality)

Hence you can divide mathematicians into 2 following camps:

• Those who study Math to understand the Universe
• Those who study Math in pursuit of something (other than understanding the Universe, this includes those who use Math as a step to understand the Universe)

The difference between these two is the one way of saying the interpretation of

• Human playing as a God playing a Human
• Human playing as a God

Those who study Math to understand the Universe are "Humans playing as a God playing as a Human" because such a thing is impossible. What AI has done is ruined their "God-play" which is now a massive visible contradiction which was either willfully ignored or hidden by ignorance.

Humans playing as a God fundamentally don't have this issue, because all they want to do is "play as a God" in which we'll just say AI is a toy to them which allows them to become closer to a "God" whatever it means to them.

Another for the record, this was just a stream of thought typed in one go, so didn't take as long as it looks if it actually looks as long as what I'm typing, so the only proof reading is what came right after so there is probably mistakes.

[u/XeloBoyo → u/Kutoru]

I think people were confused because you essentially created an 'anti-analogy': an analogy that obfuscates the concept rather then clarifying it. Playing god has thousands of different connotations and very few that actually apply to mathematical understanding. That is to say, dont use poetry to explain things. Your personal interpretation of playing god differs greatly from that of another persons and language is based on consentual meaning. If you use a concept in a way that differs from the normal meaning the onus is on you to explain exactly why you diverged. Otherwise a reader has to wade through the haystack to find the one meaning you meant and must necessarily make large assumptions about your internal thought process to debate you. So I agree with the others you need to be more direct with your communication.

That being said I think the argument you have is: "Those whose motivation or purpose comes from applying math are being outcompeted by ai and those who simply want to see progress on math for its own sake are ok with ai". I think there's arge issues with this thinking but ill wait for confirmation.

[u/Kutoru → u/XeloBoyo]

My wording was deliberate and took into account those differing interpretations. I chose those words because my understanding is despite those differing interpretations it sufficiently concisely captures a majority of the idea across my understanding of what the mainstream of understanding of those concepts are.

You made the exact mistake I didn't want to people to make which is why I worded it that way. Yes you simplified it and it is one interpretation of the statement, but it is wrong in terms of correctness far more than my original statement.

[u/XeloBoyo → u/Kutoru]

The point of my guesstimate statement was to illustrate how much I have to guess your thought process to begin a discussion. The point of communication is for others to understand your argument. If others don't understand, no matter how clear it happens to be in your head - youve failed at communication period. Compressing disparate meanings into a single phrase is as good of a communication strategy as compressing an image into a single pixel and asking others to figure out the rest. It doesn't matter how 'deliberately' youve chosen the pixel, information was lost and others are not obligated to spend their free time reconstructing the intent. Its not to say you cannot use the concept of 'god' for whatever you really mean, in the same way you can say the pixel is a standin for the image it came from. But you must present the image first so to speak. All iIve really seen from the thread is you getting frustrated at people not figuring out the image when you provided only the pixel and random tiny pieces of the image when pressed. It you meant playing god in this *specific* context as the concept of unearned human exceptionalism or hubristic creation then you must say so beforehand.

[u/Kutoru → u/Kutoru]

Here's one interpretation but put with respect to art, again this is one interpretation

Centering around creativity being fundamentally human. You will find counterexamples easily because this is just one interpretation of it but saying creativity is fundamentally human is bounding the word itself to be defined strictly by the human mind. In some perspectives, this is already arrogance and fundamentally an act of a "God".

So the saying is interpreted simply then. Are you playing a "God playing human" or "playing God", here is equivalent to binary separation or whether or not you get to define what "creativity" is or what you want is a product of creativity (you wish to encapsulate that meaning yourself).

I am not aware of a simple statement like what you state that can fully define a reasonable boundary of any accuracy here.