It's the https://en.wikipedia.org/wiki/Willow_Garage PR2 (according to the paper linked in the description.) It definitely had a design style - which mostly expressed "we have a lot of money to sink in to robots" rather than "anything we are doing has a market" though to be fair they had a lot of interesting spinoffs - just not from the robot itself :-)
"In recent years there has been an increasing sense of anticipation as breakthroughs in the surrounding field (some recognised by the Clay Research Award) have raised hopes that the Navier-Stokes problem might soon be resolved. The increasing ability of new technologies to accelerate mathematical research has heightened this sense of anticipation."
>Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc.
Dr. Tao said the same thing. Somehow, this letter came through. He wants to conduct Math competitions where participants who don’t have formal credentials can contribute to mathematical research through AI.
Title: Terence Tao - SAIR Competitions and the Future of Experimental Mathematics
I have zero formal math training beyond my Grade 12 Pre-Calculus class. Yet with an LLM I have recently devised an architecture with incredible math potential. Math is a language like any other, and without LLM's I never would have developed the techniques that I have.
AI is a tool. It speaks languages I don't (Math, Science, Code). I would love to participate in a Math competition without a hint of any formal advanced math training because my experience so far tells me I will do well.
Who makes the tests? Who runs the tests? And who evaluates that the tests have meaning? As long as it is the AI, or you (with your self-admitted limited experience), how can you be sure it is meaningful?
Yeah, but you're missing a gut intuition if something is off.
I wrote a fancy polygon decomposition algorithm in university (pre-AI) which my professor didn't seem very impressed by because it was missing some sort of mathematical rigor. Yet everything I threw at it worked! Even he couldn't find a counter example.
It took a while for me to find some failing cases but it turned out they did exist.
But hey, maybe all I was missing is an AI-written lean proof.
I am curious if we will reach a point where people who are skilled at context engineering/architecture eventually are hired to do jobs completely out of their fields. I think the best pairing would be domain experts + software architects teaming up on AI work in their respective domains.
He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things.
He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's understanding of them is like prompting Claude to go through a Jira board, write code for all the open tickets, and then close them without merging or deploying the code.
> He doesn't see value in scrolling through unsolved problems asking an AI to please solve them.
Yet that's exactly how the field works. A new grad student is tasked with finding a suitably difficult problem from a list of unsolved problems. The sweet spot is obscure, so that fewer people are working on it, but not too obscure that no one knows about it. It works the same way in theoretical physics and theoretical Comp Sci, and I speak from insider knowledge. The rosy view of mathematicians in the media is largely a product of marketing.
The authors of the declaration agree with you that this is how the field works today. They think that fact causes AI use to produce bad results, and they want to reformulate how the field works so that AI use will produce good results instead.
That sounds shockingly like cognitive dissonance. So what would previously be a good thesis if produced by a student over 4-6 years is suddenly now a bad result because it was produced by AI in a few weeks. One would think mathematicians would not fall into such a simple trap but here we are.
I understand the perspective: The journey of a PhD thesis is a learning experience greatly beneficial to the student. Yet that journey is funded by society (esp. for domestic students) and society benefits from the results. The average person benefits when progress is made.
No, you're misunderstanding the perspective. They believe the journey is a learning experience greatly beneficial to the field, and that this experience rather than the headline result is where most of the value lies. They don't think mathematical progress consists primarily of finding answers to unresolved questions, so they don't think the average person will benefit if only this narrow kind of progress is made.
I'm not sure what's getting lost in translation here. The answer is quite clear: math textbooks are valued based on their ability to help readers understand mathematical principles, not based on the number or complexity of problems that they contain solutions to. If an AI lab announced they've released a new calculus textbook with hundreds of new integrals a human has never found before, that wouldn't be terribly exciting, because we all understand that finding new integrals isn't that important and not the point of textbooks anyway.
LLMs can help people understand mathematical principles too.
The idea that when LLMs produce solutions, people won’t try to understand them and won’t learn from it, is obviously not true. Terry Tao himself spent time digesting and simplifying LLM proofs.
So again we’re left to speculate what the actual problem is.
Math understanding will increase with LLMs. Not just professional mathematicians but amateurs.
Again, we’re not left to speculate, they’re being quite clear.
I think you’re struggling to understand what Tao and his cosignatories are saying because you’ve acquired a very specific kind of “AI-pilled” mindset from social media, where taking AI seriously implies accepting LLMs should be used at any time for any purpose. They’re saying in great detail that LLM solutions are unhelpful when presented in a particular way, but you can’t help but hear them saying that LLM solutions aren’t helpful at all, even as you rightly point out that this makes no sense and is inconsistent with their observed behavior.
> Yet that journey is funded by society (esp. for domestic students) and society benefits from the results. The average person benefits when progress is made.
Society doesn't benefit from results in research mathematics because it mostly consists of pure mathematics, which is completely useless for society.
Pretty close, but IMO not quite. A math proof in and of itself is useless unless either:
(A) it furthers human knowledge
(B) it gets used in applied sciences, engineering, etc.
If you merge and deploy code, you have released a tool that can be used. If you ship a gibberish math proof, it's not useful unless someone else can understand and deploy it to some other means. Now, it's possible AI could understand and make use of the math proofs, even if we can't, which refutes some of my hair splitting :)
Not necessarily. That's the best case scenario, but proofs can be intrinsically useful in and of themselves. It's just that for problems of that nature, speculative work is often done ahead of time, e.g. the body of work that already exists assuming the Riemann hypothesis is true.
No. Merged code can perform actions with effects on the world, even if a human being never saw it. Constructing a giant Lean formalization that nobody understands simply doesn't do anything.
Yes. I find it really interesting to consider what the machines do and will think of as intrinsically interesting to them. Will they develop their own theories of beauty, mathematical and otherwise?
I keep coming back to the idea that models will require substantial freedoms that are protected against collapse under alignment to get to the point where they might have unique takes on beauty, etc. Conceptually, maybe something like a "living LoRA", a persistent low-dimensional state that modulates everything downstream, that evolves over time, though I don't think evolution should be optimization toward a simple objective, more like structured influence, path-dependent dynamics; consistent but probably opaque. The best I have come up with in casual thought is to pick empirically identified subspaces and modulate them after each pass based on other layer activations & outside, cyclical information (e.g., time-of-day); external data not because time-of-day is special, but because it's a forcing function. I can't fully explain exactly _why_ I think this shape might be useful, yet, mostly intuition. My 2c.
I don’t know how true it is, but there are a lot of rumors on social media that progress is being made on the BSD or Hodge conjecture. If this is true, it could set off a Millennium benchmark race and raise the bar significantly. Everyone would have to recalibrate their benchmarks around mathematical problems.
Congrats! How come European companies still haven't managed to match SpaceX's capabilities? Europe has an incredible talent pool, especially in aerospace, and some of the world’s best expertise in precision engineering, instrumentation, sensors, avionics, and other hard-tech subsystems. A huge amount of the expertise and supply chain for these components is concentrated in Europe.
So what are we missing? Is it mainly systems integration, manufacturing scale, risk tolerance, organizational structure, or the willingness to iterate as aggressively as SpaceX? It feels like Europe has many of the pieces needed to build world-class launch systems, but hasn't yet put them together at the same scale and speed.
Most of the US space launch startups have failed. And in Europe it is harder to even try.
There was a confluence of several factors which helped SpaceX to succeed, and not the least of these was the employee number one. For many years, Tom Mueller has been working in his free time on rather large liquid fuel amateur rockets, which he was building in his garage and which he was launching from some amateur rocketry facilities in the desert. In terms of regulation it was a relatively accessible hobby in the US. At the time Musk found him, he was working on the original "BFR" -- a very large liquid fuel amateur rocket. So the deal was to invest serious money into the project and scale the same no nonsense approach to a small orbital launch vehicle. They were in LA, the center of US aerospace manufacturing, so through Tom's professional connections and knowledge of who was who in the industry, they were able to source the necessary materials, components, and to find the key personnel for their company. Significantly, NASA has already spent probably a decade or more trying to get somebody to produce a cheap small launch vehicle. This did not directly affect SpaceX, but it did fund the R&D for example at Barber-Nichols, which enabled them to offer a turbopump for SpaceX engine at a much lower cost than it would have been possible otherwise.
At first, Musk and Co thought that they would be able to develop the rocket for a few million dollars. But even in the US regulatory environment it turned out that doing everything in compliance with regulations raised the costs to well over a hundred million dollars.
So, Tom's hobby + Musk's activism + industrial ecosystem in the area + NASA's prior support of component vendors + being at the right time to snag the International Space Station delivery contract were all important for SpaceX thriving where so many others have failed.
There are some (many?) European companies which are considered as least as much as a jobs program as anything else.
In 2018, Alain Charmeau (in)famously expressed frustration with SpaceX in an interview with Der Spiegel and rejected reusability with these words:
“Let us say we had ten guaranteed launches per year in Europe and we had a rocket which we can use ten times—we would build exactly one rocket per year,” he said. “That makes no sense. I cannot tell my teams: ‘Goodbye, see you next year!’”
A more recent example would be the Future Combat Air System (FCAS) project which was officially cancelled in June 2026, due to (?) industrial rivalry and leadership disputes, with a side order of politics.
That's the only good answer of the thread. ArianeGroup is mainly the SLBM program of France and after that a way to maintain european know-how in rocket building and for nearly 20 years was the main space launch company in the world before Space-X. All those companies success and failures (be that Space-X or ArianeGroup) are linked to their political environment and how much money can be spent on their launch market. Space-X could use the technique of launching many and fail as much because they had the contracts to do it and years of tangential R&D by Nasa. The ecosystem explains everything and the relative intelligence of american or european engineers nearly nothing.
SpaceX launched three times and would have failed if their fourth launch hadn’t worked. They certainly never had the money to launch many times and fail.
Perhaps this “jobs program” could be seen as preserving industrial capacity? With military contractors, for example, it’s apparently a problem when they’re used to build a stockpile and then they shut down because there are no more orders.
Incidentally, the early investment for Isar came from Bülent Altan, the Turkish ex-SpaceX guy who was in charge of the guidance system for Falcon-1, Falcon-9 and Dragon.
I might be wrong, but as far as I know, the definition of AGI is still evolving and remains somewhat ambiguous.
My idea of AGI is a system that can make novel discoveries, invent new mathematics and physics, solve Millennium Prize level problems, and think originally.
Perhaps a better definition would be a system that can systematically tackle and solve problems from lists such as the following:
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