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From his Wikipedia page:

> Po-Shen Loh (Chinese: 罗博深; pinyin: Luó Bóshēn; born June 18, 1982) is an American mathematician specializing in combinatorics. Loh teaches at Carnegie Mellon University, and from 2014 to 2023 served as the national coach of the United States' International Mathematical Olympiad team. He is the founder of educational websites Expii and Live, and lead developer of contact-tracing app NOVID.

weird bias by authority aside, do you really think that the daily decisions in this world today, and anytime soon, will be made based on the "let humanity flourish axiom"?

beyond a point of absolute comfort, the point of money is to accumulate power and power can be spent to make more money. musk doesn't need more money, he needs more power. dangling starlink to ukraine treasonously is that power that money can't buy but space x can.

moonshots are the external story told to maintain social acceptance. tax credits for spacex would be lot harder to sell to taxpayers if everyone unambiguously knew its just another profit seeking private company. tesla gets a lot of lenience because of its supposed pushing of frontiers.

musk can exchange his social capital to manipulate stocks to make others money in exchange for backchannel favors.

idk if musk actually believes mankind will terraform mars but he sure seems to be getting a lot back on earth from saying it.

> working 12~18 hours doing one moonshot after another.

Does anyone actually beleive Musk works 12 - 18 hour days?

He hires the right people and his companies solve hard problems, but they make a few electric cars, design and build some rockets, and launch some satelites. Most of that shouldn't require much of Musk's time since he has experts working on it.

Other than designing new rockets, there doesn't seem to be many new innovations coming out of Musk-owned companies.

To me, it feels like we all think he must be doing a ton of work even though his companies don't seem to be generating much output.

Nobody in their right mind would start a rocket company in order to make more money. I feel like he just wants to play real life Factorio and he wants everyone to tune in on his Twitch account and watch him play. Meanwhile he was trying to fix democracy [1] (and protect his own companies) by buying Twitter and at some point he realized he fucked up.

But who knows, I could be wrong.

I'm not exactly a fan. I'm not exactly against him either. He just seems like a hardcore geek to me that got way too much money and way too much buy-in.

[1] I'm not saying I that I think he was fixing democracy. I'm saying that I think that he thought he was fixing democracy.

This is really a matter of taste, but i (personal opinion) think that Zuck, Karp, Thiel and others who (partly by sucking the inauguration dick) have the ear of the current powers that be, produce much more demented shit than Musk. But the exact personalities really don't matter, the whole jolly crew running the show does not seem very humanistic in their writings or actions.

> how to make a lot of money from his existing assets without working 12~18 hours

This is the biggest lie in today's society. "Make money from assets". There is no such thing. Money cannot work. People can work. He's figured out how to extract a lot of money from his employees, without them realizing the trick that's being played on them.

The part that does count is that we can verify that we does what we want it to do. We just don't know how.

Same with the black box part of AI. What the weights represent? Arcane dark magic if you ask me. What do they do? Well with LLMs we're all experiencing it.

I find it hard to distinguish between knowing how something works, and being able to predict its behavior (including ways to create and destroy it) with probability approaching 1

Only because we understand everything _except_ how it works.

Seems a bit nitpicky, we certainly understand how to use it with great effect, we just don't understand the biochemical mechanism.

Not unless humans were able to produce the medicine or perform the surgery or whatever is necessary to actually heal someone. In order for that to happen it has to be verified and understood by humans, like the other commenter said.

We already don't understand LLMs and they are having oberservable effects

Yeah that information mattered when someone wrote it down, not when the LLM regurgitated an approximation.

It can be other form of life, but that other form of life need to be extremely aligned and keep humanity interest as top priority.

> not really sure what it shows

it shows that you don't get anything for free. If it was without any cost in other areas to make a human massively more intelligent, it would presumably happen over time via the same processes that led to us.

As it is, the higher (and lower!) ends of the distribution tend to be highly correlated with other issues (mental+physical), and the further you go, the more unfortunate things which make it harder to do stuff in general start to crop up like psychosis, autism, ocd, anxiety, addiction etc

Yeah but there is only one species that ponders its future.

I stopped reading at this point because I reject this initial assertion, and I assumed everything that follows is based on it.

There is nothing to suggest that an AGI will care about its future or who controls it. (whatever that means). that just more anthropomorphism.

We care a lot about our future so an ai pretending to be like us will also pretend to care. But we have a lot of biology driving us. Our emotions (Fear, Hate, Love, Pride etc) are baked into us in a way just wont be the same for ai.

Why does the universe being bounded imply mathematics is finite?

>The universe is bounded by rules

That's physics. Not all math is physics.

Trivially false. Let P be the set of maths problems and I be the interesting subset of P. If I is finite, then there exists an element x belonging to P\I whose description is minimal among P\I. Then x is interesting. QED.

Interesting is a bit in the eye of the beholder. Some people probably find maths boring full stop, some probably find all of it interesting.

I think it really depends on what the universe looks like as you drill down into it. It seems like the further down into smaller systems you get, the more analytically complex it gets. And then there will always be more value in enhancing the generalisations you have.

That's a good question that can be answered by methods in mathematics.

Yes, I think it would be viable if it wasn't corporations reaping all the benefits (income) from AI right now.

I don't think research communities should be destroyed.

Best case, they still matter.

Worst case, AI kills us all and it's irrelevant that we "wasted" money on research.

Do you think surgeons start performing surgery for the first time on people?

Not all of it would translate, but robotic surgery could be done on anesthetized animals in a mass RLVR way.

A few people with way to much power are building AI to achieve their utopian, sci-fi dream. A few other powerful people are using that first group to achieve their post-democratic goals. It’s the most obvious top down attempt at imposing their vision onto the rest of the world. They aren’t building tools to serve anyone else than themselves

IMHO hiding details of the hack helps conceal that they built it to do what it did, and maybe were able to know it was working just as intended.

The fact it keeps doing it, with more and more evidence, is a sign that it's built that way.

This is a program running on their montoroed machines that they purpose built and monitored its training at every step. I think it'd be way more suprising that they didn't know it used note taking and cross-run memory.

Is there a proof that every possible proof is a generation in the grammar of lean or rocq? Sounds like an unsubstantiated claim.

You're confusing the mechanical language of math with math itself.

The map is not the territory, etc. If math was just an elaborate linguistic Glass Bead Game then we wouldn't be funding it. The intuition is that the surface rules of math help uncover the underlying structure of reality.

> What do you think all the PhD's and post-doc students are doing...?

Thinking.

The clue is burried in the text of OP's article.

> Mathematicians can also consider wholly redirecting their skill sets to work on real world problems. I’ve actually been encouraging mathematicians to consider thinking about working on government or other large-scale societal issues.

The fact that this is a radical departure from the norm is part of why mathematics (and philosophy) is often seen as some intangible or ungrokable science to many outsiders, as they're generally approaching it from a perspective of "Okay, but why, what is this useful for?", and the answer "For the science of it" doesn't tend to land with people that aren't already passionate about said science/discipline and are just trying to figure out what it even is or involves.

Doesn't help that there is a pervasive sentiment in American Academia (not sure about elsewhere) about Math being *the* hard science, and I mean hard as in difficulty, so a lot of people get intimidated by it before they ever give it a chance very early on in their academic life and carry that through the rest of their education.

So there ends up being a rather small pool of people that are in(to) the field, and rather high friction for stimualting interest in it from outsiders from the way that it's taught, and a massive difference in the perspective of it's use between it's diaspora and the unmathed masses.

> I did systems administration for a university math department for several years. I came to the conclusion that mathematics (and perhaps philosophy) were both topics where it was likely that no staff members in that department could describe "what goes on here" and that possibly even within the department, one professor may not be able to describe what another professor's actually doing.

And this is indeed why it is not going to be taken seriously as an academic or (more importantly) an economic endeavour done by humans anymore.

That won't stop the career mathematicians from protesting and having a cry here trying to justify themselves.

Good question, and maybe I should have provided an alternative description rather than just criticising.

Unfortunately, it is actually surprisingly hard to pin down, and I think mathematicians (and, as a student, I count myself as one to some degree at least) now have the task of making this a lot clearer. If we want to justify our existence in the face of new machines that can seemingly ‘do our work for us’ (so far in a restricted context), we should give a robust defence of our practice. If we can’t do this, we simply don’t deserve the funding (which, by the way, again contrary to some misguided statements here, isn’t very much anyway!). I think all of this will become clearer to outsiders as time passes, but for now it’s not easy to give a quick answer — though I can try.

Mathematics is about understanding things. Isn’t that what every subject is about? Well, I suppose so, but mathematics more specifically does something like the following:

(1) observe some phenomenon in ‘reality’.

(2) attempt to formalise that phenomenon in such a way that it can be manipulated purely symbolically.

(3) use this (perhaps fairly arbitrary; remember that we can invent as many formal systems as we like) system to deduce from our initial assumptions new facts that would otherwise have been very non-obvious.

It seems like outsiders have a decent grasp of (3) and the application of AI to it, but have very little idea about the other two steps. It seems to be widely assumed among non-mathematicians that problems are essentially god given and that the job of a mathematician is therefore to chug away on these problems, manipulating symbols and trying out tools, in the hope of learning a yes/no answer to each one.

The first two steps are by far the hardest and most important, and they’re also the parts that AI seems currently unable to help with.

NOTE: this is not a deeply insightful description of what the subject is about, and there are many better characterisations out there. I think Tao and various others have written recently about why complicated and inscrutable AI-generated proofs aren’t nearly as valuable as one might imagine. (That’s not to say there’s no value to such proofs; perhaps in time, as technology improves, mathematicians will come to accept AI as part of the process.)

If you want to understand all of this issues better, reading the recent slew of guest posts on Tao’s blog would be a very good start.

My understanding when I was practicing is that the trend in modern mathematics is to focus on spaces with a certain kind of structure, and maps between those spaces that preserve it, and then what are invariants are preserved by those maps. Structure-preserving maps between categories of such spaces - "functors" in the language of category theory - are especially neat.

That's certainly different from Olympiad-style problems.

Pure mathematics reduces to abstract "relationships" and their implications largely.

To know what something is about, a natural way is to do it yourself.

Wondering about the world, using the simplified language of "mathematical logic"

In my observation, most programmers and engineers lose their math chops over time. The math they need is mostly baked into their tools, such as CAD. If a problem requires more advanced math, it's given to a "math person" in the department. Often, the "math person" is also not allowed to touch the production code.

> Otherwise you could just put this problem into an automated theorem prover (we've had those forever, they are actually just brute-forcing it).

There are many automatic theorem provers that do very clever stuff, just as the underlying theroy describes.

> I am shocked how people can deny that solving Navier Stokes requires some sort of intelligence.

It is absurd to waste time discussing whether it is inteligent or not. It is just an algorithm, we know how it works, and it does exactly what we expect it to do. LLMs are not magical things. The main difference is the scale: for Navier-Stokes they spent in 3 days more money that the whole mathematical community over the last 20 years easily.

By the way, I'm not saying that LLM's are useless, that I'm anti-AI or anything like that.

It was needed before the LLMs and training data existed in digital form. Euclid, Gauss, Turing didn't have that benefit.

That's what I thought also, that is why I posted Tao's version.