9 ms·

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

by lacker 17d ago

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.

d_sem 17d ago
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
aerodexis 17d ago
You don't think frontier mathematics is already secret?
- 0xWTF 17d ago
  How to admit you're in finance without admitting you're in finance?
  - computerfriend 17d ago
    Or signals intelligence.
  - leonidasrup 17d ago
    Or Cryptanalysis. " The National Security Agency is the largest employer of mathematicians in the U.S. " https://www.scientificamerican.com/article/mathematicians-and-computer-scientists-shrug-over-the-nsa-hacking/ https://www.scientificamerican.com/article/mathematicians-an...
  - short_sells_poo 17d ago
    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).
    - fingerlocks 17d ago
      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
  - 69nanoseconds 17d ago
    > 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.
    - computerfriend 17d ago
      This is mostly true, but there are exceptions (e.g. Renaissance Technologies).
      - 69nanoseconds 17d ago
        > 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.
        computerfriend 17d ago
        > RenTech uses/used unpublished frontier mathematics to predict the market No, more like, some differential geometry and gauge theory. The topics that Jim Simons worked on.
    - aerodexis 17d ago
      I wouldn't be surprised if it's marketing all the way down.
rkagerer 17d ago
Was the term "frontier mathematics" always in use, or did it just become a thing after the advent of contemporary AI?
- pixl97 17d ago
  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.
  - w4der 17d ago
    Google trends shows it spiking last year: https://trends.google.com/explore?q=frontier%20mathematics&date=all&geo=Worldwide https://trends.google.com/explore?q=frontier%20mathematics&d...
    - pixl97 17d ago
      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.
  - goodmythical 17d 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.
itemize123 17d ago
unfortunately, the worse of both can be true at once.
thaumasiotes 17d ago
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.
- watwut 17d ago
  Like yeah, result is that one group politicians are minimized and others maximized. Which makes total sense unlike the "too much frontier math" nonsense.
  - thaumasiotes 17d ago
    > Like yeah, result is that one group politicians are minimized and others maximized. Which groups are those?
    - watwut 17d ago
      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".
      - thaumasiotes 16d ago
        So... you just didn't bother reading the second half of my sentence? According to you, there is no discourse about politicians using gerrymandering to give themselves safer seats.
oersted 17d ago
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.
- veunes 17d ago
  This seems right as long as the AI output is legible enough to reverse-engineer
  - mitxela 17d ago
    And especially when it isn't. Reading uncomplicated unobfuscated Python is easy, but the people who reverse-engineer Denuvo or Nvidia GPUs are gods.
veunes 17d ago
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.
eru 17d ago
> 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?
- schoen 17d ago
  > 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#Classified_discovery https://en.wikipedia.org/wiki/Public-key_cryptography#Classi... I guess that's kind of a long time in computer technology terms.
samirillian 17d ago
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
Phemist 17d ago
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.

by lacker 17d ago

d_sem 17d ago

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

aerodexis 17d ago

You don't think frontier mathematics is already secret?

0xWTF 17d ago
How to admit you're in finance without admitting you're in finance?
- computerfriend 17d ago
  Or signals intelligence.
- leonidasrup 17d ago
  Or Cryptanalysis. " The National Security Agency is the largest employer of mathematicians in the U.S. " https://www.scientificamerican.com/article/mathematicians-and-computer-scientists-shrug-over-the-nsa-hacking/ https://www.scientificamerican.com/article/mathematicians-an...
- short_sells_poo 17d ago
  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).
  - fingerlocks 17d ago
    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
- 69nanoseconds 17d ago
  > 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.
  - computerfriend 17d ago
    This is mostly true, but there are exceptions (e.g. Renaissance Technologies).
    - 69nanoseconds 17d ago
      > 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.
      - computerfriend 17d ago
        > RenTech uses/used unpublished frontier mathematics to predict the market No, more like, some differential geometry and gauge theory. The topics that Jim Simons worked on.
  - aerodexis 17d ago
    I wouldn't be surprised if it's marketing all the way down.

rkagerer 17d ago

Was the term "frontier mathematics" always in use, or did it just become a thing after the advent of contemporary AI?

pixl97 17d ago
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.
- w4der 17d ago
  Google trends shows it spiking last year: https://trends.google.com/explore?q=frontier%20mathematics&date=all&geo=Worldwide https://trends.google.com/explore?q=frontier%20mathematics&d...
  - pixl97 17d ago
    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.
- goodmythical 17d 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.

itemize123 17d ago

unfortunately, the worse of both can be true at once.

thaumasiotes 17d ago

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.

watwut 17d ago
Like yeah, result is that one group politicians are minimized and others maximized. Which makes total sense unlike the "too much frontier math" nonsense.
- thaumasiotes 17d ago
  > Like yeah, result is that one group politicians are minimized and others maximized. Which groups are those?
  - watwut 17d ago
    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".
    - thaumasiotes 16d ago
      So... you just didn't bother reading the second half of my sentence? According to you, there is no discourse about politicians using gerrymandering to give themselves safer seats.

oersted 17d ago

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.

veunes 17d ago
This seems right as long as the AI output is legible enough to reverse-engineer
- mitxela 17d ago
  And especially when it isn't. Reading uncomplicated unobfuscated Python is easy, but the people who reverse-engineer Denuvo or Nvidia GPUs are gods.

veunes 17d ago

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.

eru 17d ago

> 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?

schoen 17d ago
> 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#Classified_discovery https://en.wikipedia.org/wiki/Public-key_cryptography#Classi... I guess that's kind of a long time in computer technology terms.

samirillian 17d ago

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

Phemist 17d ago

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.