Comment by hintymad | Hacker News Reader

Comment by hintymad | Hacker News Reader

> On the other hand, none of the proofs so far seem to contain “alien ideas,” a move-37, or completely novel arguments or new concepts that were not present in the literature in some form or another.

I have the same optimism as Prof Tao. That said, I can understand why so many mathematicians have been so upset or stressed out. It turned out much of the mathematical work is about clever combination of existing methods - this already requires enormous amount human ingenuity and years of dedicated learning. Unfortunately, or maybe fortunately, AI can be very good at knowledge transfer and finding combination of existing ideas to solve seemingly impossible problems. Even though mathematicians are extremely smart and capable, only a small number of them are capable of truly inventing "alien ideas", discovering new ground-breaking mathematical structures, or coming up with new problem-solving techniques. That is, AI can eat many mathematicians' cake. That said, I'm still hopeful. Mathematicians still understand mathematics deeply. If someone can prompt AI to solve an important problem, that person is more likely a good mathematician than an average joe like me. So, I think mathematicians do have a bright future: leverage AI, and make more and bigger math discoveries. It's still the same north star: we must know, and we shall know. It's just that with AI, we will know sooner and more.

I was recently working on a project where I had to come up with a novel solution to a problem the company was facing. The problem has been solved before, but in suboptimal ways that wouldn’t work for this specific company. I came up with a pretty interesting solution, one that combines different statistical methods, and was a little more complicated, but gave better results.

I asked Claude what it thought about the technique. It hated it. It loathed the idea that I was not sticking with traditional methods that were pointed to in papers and pre-existing open source packages. Even after talking through the idea and how it was better and showing it the results, it was weirdly hesitant to admit it was a valid method, simply because it seemed nervous that the idea was novel.

I don’t have a real moral to the story, I just thought I would add my anecdote here.

Real humans react the same way. The best argument you can pull to do something at work is to show that someone else already does it.

Interesting! My experience is that Claude has a tendency to always suggest the true and tried, but likes off-center ideas when I present them. Fable especially has a "yes, and!" attitude where it understands and plusses the idea.

I had a similar experience with not being able to convince Claude of a different approach to a problem. Then I shared the idea with Codex and it liked it. As another commenter said, you can have the same thing happen with humans.

It's pretty much the same story with software development. There are two camps and the bigger camp got hit hard. Nowadays I feel entitled to use the "software engineer" title. Essentially, all the decisions-making and nuanced trade-offs which AI is not capable of making; that's engineering. AI can only do programming and code analysis... At least so far.

That said, in the past couple of month, AI has gained a lot of ground on the 'project management' front in terms of planning capability for a lot of simple to medium-complexity projects. It still needs a lot of help for more complex projects. Just today, it almost fooled me into making a major structural mistake but thankfully I asked the right question and saved myself a lot of future problems; it was essentially dancing around a critical point and giving me the illusion that the critical point had been addressed but only when I phrased my question in a particular way, I understood the core issue was not addressed.

> I have the same optimism as Prof Tao.

This is not written by Tao, but by Álvaro Lozano-Robledo.

It's quite amusing that this mistake gets made on every single one of these guest posts when the first words on the page are "This is a guest post by Álvaro Lozano-Robledo" and the first paragraph starts with "I would like to give Terry my heartfelt thanks for giving me the opportunity to contribute a post to his blog." It's pretty clear that everyone is skimming these at best. Maybe he should put the disclaimer in a bigger font or something.

Though it’s very funny to imagine Tao suddenly acquiring a massive ego:

> At any given time in the history of mathematics, there have been mathematicians … whose mental capacity for mathematics seems completely super human (e.g., the owner of this blog, among many others).

Ouch! I don't know how I missed that. In fact, I thought it was the opposite: a guest post by Tao for Álvaro Lozano-Robledo

It's interesting, what would be Tao's views on the creativity question. Like, I don't find the empirical observation of LLMs now, the notion these proofs are mostly "just" sophisticated grinding, to be a strong indicator of what could/couldn't happen.

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