Personally this is a watershed moment for researchers and grad students I know. All of them are close sourcing WIP repos, not putting their progress in LLMs, or have lab level initiatives to self host models.
I am building a federated hosting platform that I plan to opensource for this exact reason for our company and similar users. I would love to talk to these teams (we are a small team at Duke and a health care company).
I'm a mathematician. I have a lot of trepidation about these tools and what they mean for the future of the profession.
That said... most of us are not working on problems as famous as Navier-Stokes. Even if OpenAI could scoop me based on my back-and-forth with ChatGPT, which I presume they could if they threw $15 million worth of compute at it, I highly doubt they'd bother.
The fact that anyone has to make that trade off with that through process shows a company and culture that is untrustworthy. OpenAI isnt open, isnt a non-profit, isnt for the benefit of humanity, and isnt even for the benefit of users at this point, its users are vassals providing training data so their models can reach ASI first.
I am going all in on sovereign ai even if its worse, these companies have shown they not only dont deserve trust but are actively stealing past and present intellectual property from humanity and users.
But consider they could decide that they want to scoop more regular research work too. They could automate it with just a few LoC. Even if you opted out in the ToS, you'd have to file a massive lawsuit just to enforce it. And the actual fine would be inconsequential to OpenAI.
I think going forward, any researcher should consider anything submitted to an LLM to be copied/stolen.
I think they spent millions pursuing strategies to attack that particular problem? I don't think it takes 15 million for their model to get trained on your chat logs. This is probably all automated internally. If they did scoop your ideas, it would likely get incorporated into their model without any conscious decision making. And if you're not a high profile academic, nobody will hear about it.
If you mean move to products with ZDR policies, OK, very fair and I agree. If you're talking the equivalent of carpenters should give up pneumatic air guns because hammers are more authentic, then that's silly. These are tools, and like any tool how effective they are can come down to how well you use them.
Should they give up pneumatic air guns if the company that supplies then can then control what you build with them, how you build with them, and secretly copies all your designs for their own use. Sure its a good tool, but its also becoming a trap.
It is capitalism doing capitalism stuff, but more fundamentally technology is allowing for more centralized control of more things by fewer people. Regardless of ideology, increasing concentration of power has bad outcomes for people (except the ones in power).
I mean, yes, there are a lot of things that are often omitted in mathematical writing and it's up to the reader to infer them (that's "mathematical maturity"). When textbooks discuss intervals, such as [a,b] for example, should the author specify the interval is nondegenerate/nonempty each time? That is, should we repeatedly see "a<b" as part of the hypothesis? Degenerate cases are often not the primary interest of the particular area or theorem you're studying. We don't usually care about functions with empty or singleton domains. And, yes, you could say a lot of results are technically false due to those degenerate/trivial cases. But usually it just means the author didn't want to clutter their writing, or it's not significant to the rest of the theory.
The post proposes a counterexample of a function with a empty domain A. Some authors do actually specify that the domain should be nonempty in this theorem. This is a common result. Others authors don't. It's not a huge deal.
yea this is something I've been wondering about. I'm not too keen on the finance aspect, but I understand that the big players aren't turning a profit. OpenAI is still losing money. I've seen some discussion related to increased token costs. If that continues, isn't dependence on their services a risk?
I remember watching a documentary which talked about feedback loops in the climate. It might have been in the context of history. If the ocean warms up enough, it causes the CO2 in the ocean itself (either in the deposits or the gas saturated in the water) to get released into the atmosphere. Maybe I'm not using the right technical words, but there is a certain amount of CO2 that sits within the ocean that is separate from the atmosphere. In any case, after a certain point it becomes a feedback loop: warmer climate -> more CO2 joins the atmosphere -> warmer climate.
We don't even need the oceans temperature to rise, as the arctic tundra permafrost melts the amount of plant material ready to release its CO2 is massive. Some estimate think it would double the amount of our total emissions if all of it defrosts.
But this did lead to one of the more ridiculous head line from a few years back.
Thawing Permafrost Is Artificially Chilled to Stabilize Alaska Oil Pipeline
Warmer water holds less dissolved gases of all kinds, including CO2. You can see this yourself by heating water in your kitchen. Well below the boiling point, you can observe tiny bubbles, which are composed of nitrogen and oxygen dissolved in the water coming out of solution. The oceans will eventually become carbon sources, not carbon sinks, if they warm enough, but that's not projected to happen this century.
However, there are regions of the oceans which currently absorb lots of CO2 which will absorb much less as time goes on. One important example is the AMOC, which, by turning over lots of water, helps sink surface dissolved CO2 into the deeper ocean. In recent years, oceanographers have observed a weakening of the AMOC, which was predicted but is happening much earlier than expected. This is one of the important planetary tipping points, which could cause a dramatic shift in the planet's climate.
But don't worry -- the Trump administration is defunding programs like the Office of Oceanic and Atmospheric Research, decommissioning the Ocean Observatories Initiative, and is planning to shutter NOAA's research arm altogether -- thus solving the problem once and for all.
And one scary observation related to this is that warm water will also hold less oxygen for marine life, literally throttling that part of our life-support.
>If they are truly rare, then they are likely not valuable,
Sometimes I don't even know how to respond to comments here. I don't want to be rude, but you just have to give this a moment of thought. Is all the media that you find valuable common? I know that's not the case for me based on my own experience.
the argument for the existence of pi or e doesn't connect as easily to something as "tangible" as a polynomial equation, but the arguments are still out there
I know, it's just less obvious and probably not at all convincing for a person with no mathematical knowledge. Even talking about (1+1/n)ⁿ is not easy without a bunch of calculus.
I think the argument for pi should be somewhat straightforward since people usually do trigonometry in high school? I don't know an argument for e that doesn't involve some kind of calculus.
>It seems to me something like history might be more at risk. In mathematics a wrong result can be checked. With something like history checking answers is not always so easy.
Isn't that exactly why we need historians? How do you fact check an interpretation of evidence or of history? I would never trust a chatbot for its take on history, and that's partly due to the fact that we've seen how political it can get. In the worst case, the communication of history can be used to misrepresent cultures and limit freedoms. How we interpret history informs our present day policies. There's no way we'll ever leave that to a computer.
If I need a mathematical solution to my problem (my fusion reactor is not working) it is not quite good enough to know that some theorem is correct. I need to know how it applies.
If I want to use some argument about history (US Civil War fought for human rights, states right, protect interests of wealth) there may not be a simple/single correct answer. I could ask an expert historian to help me build my argument (whatever it might be) or maybe a chatbot. Would it matter, I am still getting the answer I want? Maybe law is field that is in the most danger. We have always had lawyers arguing every side of every case, often pointing to the same laws to justify their argument.
The field of math (and other hard sciences) might stand to benefit from AI. It might be a powerful new tool. Tractors did not destroy agriculture.
Art, political science, history, others, do not have right answers to all questions. I am not saying AI replacing these fields would be a good thing. I think it could easily be a disastrous thing. Just saying if a field is going to disappear it might be because there are no right ways to do it and many may just opt for the easy and cheap answers.
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