I have seen two worries recently:
1. People will publish so much frontier mathematics, humans won't be able to understand it all
2. Frontier mathematics will all be kept secret
Fortunately, these seem like they can't both happen at once.
I have seen two worries recently:
1. People will publish so much frontier mathematics, humans won't be able to understand it all
2. Frontier mathematics will all be kept secret
Fortunately, these seem like they can't both happen at once.
There are many conjectures that we know are almost surely true, but we don't know why, and explaining why is the main purpose of the mathematician when publishing a proof.
The fact that we don't know why is a clue pointing at some area of math that we haven't discovered yet. The hope is always that it will uncover some hidden fertile valley that will lead to lots of new discoveries. But the proof of the conjecture itself, without understanding, is really not that valuable.
My point is that even if AI discovers many new truths, there's still plenty to do for the mathematical community, in dissecting it and building useful abstractions to understand it, abstractions that can be leveraged for further exploration and uncovering new questions.
This seems right as long as the AI output is legible enough to reverse-engineer
And especially when it isn't. Reading uncomplicated unobfuscated Python is easy, but the people who reverse-engineer Denuvo or Nvidia GPUs are gods.
> 1. People will publish so much frontier mathematics, humans won't be able to understand it all
That already happened before AI.
> 2. Frontier mathematics will all be kept secret
Gauss kept lots of frontier mathematics in his drawer. In the 20th centuries government spy agencies developed public key cryptography long before that was known to the public. To give just two examples.
It's not the end of the world.
And what do you care, if someone keeps frontier mathematics a secret, if you can ask DeepSeek version 10 in 2030 to prove the Riemann hypothesis for you?
> long before that was known to the public
About 4-6 years earlier, depending what you want to count, although the inventors may also have been less clear on its importance or applications compared to the later public inventors.
https://en.wikipedia.org/wiki/Public-key_cryptography#Classi...
I guess that's kind of a long time in computer technology terms.
Was the term "frontier mathematics" always in use, or did it just become a thing after the advent of contemporary AI?
It's been in use far longer than LLMs. Thought I'm not exactly sure when it came into common use. I'm pretty sure I've heard the term on Nova decades ago.
Google trends shows it spiking last year: https://trends.google.com/explore?q=frontier%20mathematics&d...
I think the worry is:
1. People will publish AI generated frontier math making it difficult to identify frontier mathematicians. 2. Trained frontier mathematicians will become scarce
You don't think frontier mathematics is already secret?
How to admit you're in finance without admitting you're in finance?
> How to admit you're in finance without admitting you're in finance?
Tell me you have no clue about quant finance without telling me you have no clue about quant finance.
You probably think it’s abstract topology and Ito calculus, when in reality it’s linear regression and PCA. If you’re lucky, maybe you’ll see a sigmoid function.
If someone in finance is using LLMs, it’s for marketing purposes (recruiting students, or impressing investors). Jane Street/DE Shaw are notorious for this.
Or Cryptanalysis.
" The National Security Agency is the largest employer of mathematicians in the U.S. "
https://www.scientificamerican.com/article/mathematicians-an...
99.99% of finance is freshman level math if at that. Then 99.99% of the remaining 0.01% is somewhat more complicated but still not frontier level.
There are very-very few cases where you need truly advanced math in finance. The problems that need solving are generally vastly more pedestrian.
You need to deal with terrible data quality, terrible formats, noise in every aspect of your work, disruptions, lack of standards, inability to generate new data (and repeat experiments), conflicting and often opaque incentives, technical problems ranging from shitty APIs to having to squeeze nanoseconds out of your network stack, etc.
These are all difficult problems, but they are crucially not frontier math problems (by and large).
Or signals intelligence.
Seems perfectly possible to get the worst of both worlds: more mathematics than anyone can read, and less access to the mathematics people actually care about.
unfortunately, the worse of both can be true at once.
That's also what the gerrymandering discourse is like. Gerrymandering is a threat to civilization because it means political parties will minimize their electoral margins, and because it means politicians will maximize their electoral margins.
Like yeah, result is that one group politicians are minimized and others maximized.
Which makes total sense unlike the "too much frontier math" nonsense.
> Like yeah, result is that one group politicians are minimized and others maximized.
Which groups are those?
The whole point of gerrymandering is to split districts so that votes for the other party are diluted. The whole point is to create many districts where your party is majority and then a few districts for the rest of the opposition.
If you are good at it, end result is that minority can keep majority of the seats and power. So, as there are two parties, the groups are "likely to voted republicans" and "likely to vote democrats".