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- Hacker News
- "Logistical component A is constrained by abstract concept B." am I being a dick, or is this not extremely interesting to read? TBF I've probably over-consumed this particular category of argument recently.by alansaber
- I miss articles actually written by Tao.by bananaflag
- I'll be a golden age for mathematics and science, especially science.
It'll not necessarily be that great for every mathematician or scientist.
by weinzierl - Obviously a golden age.
I’m not bitter about this anymore — it’s been a long time. But the story holds something.
Back in the day, I knew I was talented at mathematics, and I wanted to pursue a research career. For a freshman research class, I selected a problem that was intentionally outside my comfort zone, and came up with some cool ideas. It wasn’t publication quality, though the course wasn’t really expecting publications.
Framing the problem in a way that it could be solved with calculus turned out to be a key insight. I turned to Wolfram, since the integrals were beyond what I as a freshman could have done myself, and I understood that the insight that produced the solution was my original work. I don’t think anyone in the class could have done those integrals. The instructor himself couldn’t tell me what was wrong with them if anything. Yet, he was unimpressed and subtly dismissive or critical.
Today, I might have been in the wave of researchers developing AI for mathematics work. The instructor could have been proud of shaping mathematics through his mentorship. The university might have invited me for talks. Instead, I ended up leaving mathematics as a field altogether. Now, I write software for a bank.
The world is as rich as we make it. Don’t let your opportunities and potential expire. Embrace the materials that are available to work with, or someone else will and they will out compete you and you will have missed the moment.
I get that there’s a romantic idea of what mathematicians do, and the field changing creates a sort of identity crisis. I would argue that the field has entered a new era. Exploring and shaping this era of mathematics is the opportunity of a lifetime. Embrace it, drive it, and make your mark.
by odyssey7 - Some great thoughts, many of which extend beyond mathematics.
One in particular, about sharing secrets, that had not crossed my mind (I have found that virtually no one ticks the "do not train on my data" box...):
> Similarly, it seems that mathematicians already concerned and guarded about what they write in research statements and research proposals. After all, an administrator or a reviewer may upload those documents into an LLM to get help in writing a report, thus potentially compromising the confidentiality of unpublished research.
by nestorD - My read on Terence Tao's comments of late is that professional mathematicians are principally upset about AI-submitted math papers lacking the kind of broad teaching content that high quality human math papers offer. While the answer might be correct, AI math papers don't teach the reader in the way a human author would have. Professional mathematics is not just about solving problems; it's just as much about spreading knowledge so that others can program their human brains with the same understanding that the paper's author had when they wrote the paper (and achieved the result).
In other words, the crisis in mathematics (as I read it) is that AI can solve without teaching. The result may be impressive, but if the only beings that can move math forward in future are machines grinding away on billions of scenarios that no human would have the patience to undertake, this leaves those in the profession wondering about their place in it.
by ttul - These are all great points but I'd also point out that the 'dark age' scenario is a highly competitive scenario, while the 'golden age' scenario is a highly collaborative one.
I don't think technology will fizzle out in either scenario. In the 'dark age' highly competitive scenario, you will still have those who 'understand what is produced' seeking progress and advancement. They will cohort with whoever/whichever organization is producing the best, most validated results.
I don't think knowledge would be become alien to human understanding, it would just become highly concentrated again as it was in the past. In the past, only the wealthy and noble could afford to spend time on education.
And usually, those who went deep into any field and provided contributions to science were those who had time to devote entire lives to the study or pursuit of knowledge. We still have these issues today, and these issues will always be present.
There is a supply chain of economy, and we provide different rewards based on the value of what is produced. The jobs never go away, the desire for prestige, greed, etc., never goes away. It's why economies exist, and it's why everyone is considering the value of LLMs, and their place in economies, and academies (presumably which exist to advance human understanding/appreciation, but also to prepare younger generations for future work).
- Authorship and credit seem like anti-patterns in math. One of the least accessible parts of math to me is that literally everything is named after people. Navier-Stokes? Who? I don't really want to know to be honest, I'd rather the ideas and information be framed with a prioritization towards understanding, not author's reputation. I feel the same way about all of the Greek notation, it's 2026, can we not use something in regular circulation to broaden the audience?
Maybe AI can actually drastically improve this situation by bridging the gap between those "in the club" and those who want to do something useful with mathematical ideas.
by grandpajoey