I recall several mathematicians (possibly including Terence Tao) mentioning that fields in mathematics have become so specialized and isolated that a conference like the ICM feels more like a collection of mini-conferences. An expert in one area can barely understand a talk in another.
Modern AI feels like a godsend to mathematicians. It helps them break down boundaries and connect concepts in ways a mere mortal couldn't imagine.
The examples in the posts suggest that the past does not contain all the patterns, or information in general, about the future. If so, isn't it natural that point forecast will fail in some cases?
> So, so, so much politics and public reputation management. Zhang should have never had to suffer like that.
Very true. Unfortunately, when there are people, there will be politics. I remember when reading Yau's autobiography, I kept marvel how much calculation, or "politics" if you will, that Yau mentioned or implied in the book.
> My guess is the outcome would have been the same for the same reasons?
At least Zhang didn't have to spend 7 years working on the Jacobian conjecture. He said in an interview that he always wanted to work on number theory. Moh asked him to work on Jacobian, and he obliged.
Interestingly, Yitang Zhang of the twin-prime-conjecture fame spent 7 years working on the Jacobian conjecture under the advisor Tzuong-Tsieng Moh at Purdue. A key step in his thesis used a corollary of Moh's. It turned out that the corollary was incorrect. As a result, Moh refused to write any recommendation letter for Zhang, and Zhang couldn't find any teaching or research job and ended up spending years working at a Subway[1].
Imagine Zhag had ChatGPT in 1986 when he started working on the Jacobian Conjecture.
[1] Of course now this has become an inspiring story. That said, the story definitely invokes complex emotions. The best way to describe it is probably this Chinese poem, which I have no idea how to translate: 庾信平生最萧瑟，暮年诗赋动江关
> - PC office productivity software destroyed expensive professional products.
I agree with the lesson too. Just to be precise, wouldn't the current model war be more akin to open-source office suite versus MS office suite? If so, then the cheaper option didn't really win. That said, the open-source alternatives didn't really feel the same as MS Office, and it took them a long time to reach the feature parity (or did they ever?). In contrast, the open-weights models are getting close enough to the SOTA models, and users can easily switch from one to another without feeling any difference for mojority of the tasks.
I wonder how Chinese companies can make their models so much cheaper than the US companies. I'm not sure government subsidies are the answer. Subsidizing a single company with a few billion dollars, maybe. Subsidizing at least three companies with 10s of billions of dollars annually? Do we have proof of that? I assume we can't pin it on the lower cost of engineers in China, either. The top engineers are not that cheaper, and isn't engineering cost a small fraction of the cost of the model companies? Besides, if engineering cost is the driving force, can we really say that the US companies have a technical edge?
> open models is what will kill Anthropic and OpenAI.
Maybe killing Anthropic is a good thing? Anthropic believe that they are the moral god and they get to determine what we can do and can't do, and they get to tell us what model to use and what not to use. I find it very counterproductive.
If we look at how AI solves those Erdos problems or IMO problems, we can see a clear pattern: AI is like a perfect cramming human being: it has seen and memorized pretty much all the known problem sets and the solution patterns. It knows all the areas of maths - a feat that even the best mathematicians in the world can achieve. So AI can link an obscure solved problem in one area to a hard problem in another, leading to amazing new solutions[1].
I think we can use AI similarly: asking AI for ideas that we haven't thought of before, and asking AI to connect the dots in new ways. To do these two effectively, though, we will need deep conceptual understanding of what we work on, and strong intuition to further refine the answers given by the AI.
That is, we don't offload our thinking. We just augment it with AI. It's like playing the game of ABC: given a letter, and name all the movies starting with it. One can be very familiar the movies but still fail to recall most of the titles. AI can exactly help with that type of recall.
[1] That's why OpenAI's model could solve the hardest problem (problem 6?) in 2025's IOI, but failed to solve the easiest one for human (problem 3?).
There is a difference between reading a short article and reading an actual book. Reading short articles gives you quick facts and situational awareness, but it doesn't build wisdom.
My personal theory is that wisdom comes from deep, long-form reasoning. You can't get it just by skimming short articles or memorizing isolated facts. When we read a deep and comprehensive book, the real value is the mental labor. It forces us to follow a long, complex argument, spot subtle patterns, and actively debate the author in our heads. We have to weave different facts together to see the bigger picture.
This kind of "hard reading" actually changes our brain by building new neural connections. Wisdom goes beyond collecting information. It's more about the cognitive journey of thinking deeply and widely about a topic. Short articles give us data points, but books train us how to think.
Of course, serious researches may tell us otherwise. I don't have any data points outside my personal experience.
> But, at token rates, 10x or 100x the cost of open models or what I was spending on the frontier models a month ago
And we can't ignore the power of "good enough". GLM5.2 may not be as good as the SOTA models, but it can be good enough for most, of not all, of our needs.
Yeah, large volume of comprehensible input is the key. It's just that the frequency of words is of Zipfian distribution, so I thought maybe flash cards could give me more frequent exposure of the important words in less time.
For language learning, I wish there was an audio-first flashcard app that changes up the example sentences every time. Right now, I'm using Anki to learn Japanese vocabulary from N5 to N3[1]. I know the words and the example sentences well enough to read N3-level text, provided I know the grammar. But when it comes to listening, I struggle to understand even N4-level spoken Japanese. Anki just doesn't offer enough variety for me to truly internalize what the sound means in different contexts. Plus, seeing the text before hearing the audio tricks my brain. I think I'm learning the sound, but it's an illusion because I already know the meaning from seeing the word first.
[1] I feel like Anki offers diminishing returns once you get past N3. Advanced words usually have subtle nuances that you can only really pick up through rich context, like in a full paragraph or a TV scene. Native-speaking kids can understand complex words in context because they have a deep grasp of a smaller, simpler vocabulary. That’s why I’m focusing on mastering high-frequency, simple words first to build a learning flywheel. I'm hoping this will eventually let me pick up new words naturally through reading and listening, just like a native kid does.
You're right, there are nuances in different policies. I was referring to the general power and consent that Europeans grant to the EU council. In my naive view their power is unchecked. As a result, we can start with good intent and good regulations, but eventually they will abuse their power as its the nature of power.
Honest question: when Europeans give so much power to EU and usually favor regulations by the government, isn't it natural that the government will try to implement more control? And it looks EU officials do not have to accountable for anything. They will not suffer personally even when their policies wreck havoc. I don't quite understand why Europeans can trust EU at all. Case in point, EU HQs shut down its air conditioning on floors 1 through 7 to prevent electrical overloads, leaving the upper levels used by top officials unaffected. Yet did anyone like Leyen get punished? Note I'm not naive enough to believe politicians don't have special treatment in other countries. But at least in some countries, politicians will not be so shameless that they'd do it in broad day light.
It's great that we have yet another competing models. The more models we have, the less likely we are subject to the ideologies and the controls thereof by the cults like Anthropic. And of course, it drives down the cost of tokens.
Wouldn't toxics like nitrites accumulate over the years? Also, I'd assume the purpose of perpetual soup is to concentrate the aroma and the taste, but is there going to be a diminishing return?
Remember it was reported that OpenAI didn't think that ChatGPT would be successful? OpenAI thought that ChatGPT was yet another toy before its launch. Yet once ChatGPT became an overnight success, Altman started to talk about how AI would be dangerous, how it would displace or even replace jobs. In contrast, Amodei seemed to always believe in what he said. So, can we say that Altman is a opportunistic businessman, and Amodei is a cult leader?
Modern AI feels like a godsend to mathematicians. It helps them break down boundaries and connect concepts in ways a mere mortal couldn't imagine.