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.
> 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?
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.
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.
(edit: this is books data)ngrams says first use in ~1889 in use for a few years, flatline until re-introduction in ~'66, surprisingly peaking in ~'83, and current sitting at roughly less than half of peak useage.
Though it appears to have gained popularity from 2017-2021, it dipped in '22 and that's as far as ngram goes.
Yea, for sure AI brought it into the mainstream. The terms existed for a long time, but the number of people actually involved in it are really low so it's not going to show up much on trends unless something big happens in the field.
1. People will publish AI generated frontier math making it difficult to identify frontier mathematicians.
2. Trained frontier mathematicians will become scarce
I do think they can happen together like malnutrition and obesity. Pursuit of recognition, intellectual property, remuneration, war machines, etc, will naturally drive new strategies for academics to compete with capital-intensive AI research. One strategy will surely be new types of silo-ing, whether that will kill the post-enlightenment spirit of math we’ve come to love is still an open question
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).
The quant side of finance is stochastic calculus and chaos, that’s what they’re talking about. Mandelbrot himself published a pop-sci book about the new fractal math of the stock market
> 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 new grads or impressing investors). Jane Street and DE Shaw are notorious for this.
> This is mostly true, but there are exceptions (e.g. Renaissance Technologies).
Nope.
Let me guess: you listened to The Man Who Solved the Market and think RenTech uses/used unpublished frontier mathematics to predict the market.
There are plenty of firms with both higher annual % returns (consistently over 15-20 years) and higher absolute $ returns than RenTech/Medallion fund, especially post-2010. And they’re not using “frontier mathematics”.
A lot of alpha comes from how well you know the VP at the exchange. Not math. Not tech. But good ol’ politics.
Don’t like a market participant? Tell the exchange to issue violations to that participant. Get them banned for a few months.
Fat fingered a trade with wrong price or quantity? The exchange can and does undo a trade after the fact. All in the name of “orderly markets”. Similar to when governments use “national security” as an excuse.
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.
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".
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.
The secrecy will be volumetric. Im sure it will continue to be possible for bullshit to out-generate information. With bullshit being redefined to true, but informationally/conceptually useless proofs.
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.