I remember when I first became an engineering manager. It felt pretty strange at first to be standing up in front of an audience, describing what our team's code did, how it worked, and how we ensured it was high quality. Being the final approver who decided whether the new service was ready to go into production or not. Because I didn't really understand it, the way that I had when I was writing all the code myself.
With AI, now every software engineer gets to feel this way.
The question is the right one. "Why are we even doing all this?"
Why, indeed, is society funding pure mathematics? Many mathematicians are complaining that they do not like AI and their jobs are less fun when AI is involved. But does that matter? Should that matter to the institutions who fund mathematics research?
To me it seems that we fund pure mathematics because we believe that some pure mathematics will end up being useful. Turing was doing "pure mathematics" when he invented the Turing machine, because we didn't have another word for it, yet.
So, which is going to be more useful - the sort of pure mathematics that AI does in 2026, or the sort of pure mathematics that humans do in 2026? That is the debate I would like to see.
Usefulness and efficiency should serve all humans, rather than privileging the feelings of elites accustomed to receiving accolades for their intellectual capabilities.
In theory it would be possible to formally verify the soundness of the borrow checker. Maybe with AI advances we'll be able to do that in the near future. I mean, how much more complicated can it really be than proving Navier-Stokes?
You take hardware properties as axioms (for instance, ARMv6 cache coherency is specified in detail as part of the lengthy spec, even though you have no guarantees that the hardware actually is faithful to the spec)
You can formally verify that the algorithm has the desired properties, though. If the hardware requires additional properties for soundness, then that would only be an error in the properties, not in the proof. (Of course, that would no longer prove soundness on that hardware.)
It seems like there are several different parts to the discovery of the "structure of DNA" and different people contributed.
1. DNA is helical
2. DNA is a double helix
3. The ACGT copying mechanism
Part 1 was Franklin and Wilkins. Part 3 was Watson and Crick. Part 2 is the part under debate, to what degree was the double helix clear from just Franklin's imaging?
But really, how much does it matter? It seems like the four of them each contributed a lot. The Nobel prize only went to the other three, in large part because Franklin died before it was given out.
> But really, how much does it matter? It seems like the four of them each contributed a lot.
In today's standards, or at least what I am used to, Franklin and Wilkins should be co-authors of the "Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid" Watson & Crick paper. But they only got this note at the end: "We have also been stimulated by a knowledge of the general nature of the unpublished experimental results and ideas of Dr. M. H. F. Wilkins, Dr. R. E. Franklin", not even talking about the image but giving the impression that they had an unimportant talk while having an informal tea.
But they (W & C) include this text: "The previously published X-ray data on deoxyribose nucleic acid are insufficient for a rigorous test of our structure. So far as we can tell, it is roughly compatible with the experimental data, but it must be regarded as unproved until it has been checked against more exact result". They suck for this: they could ask Wilkins & Franklin to include the X-ray that is sufficient to base their claims, add them as authors, and make a better article. But they choose to "be stimulated" by the perfect picture 51 and claim ignorance afterwards.
> But really, how much does it matter? It seems like the four of them each contributed a lot. The Nobel prize only went to the other three, in large part because Franklin died before it was given out.
A Nobel can only be split among 3. Agree with the rest of your post.
A Nobel Prize has never been awarded posthumously. The 1974 change was explicitly codifying a practice that had already been in-place — not awarding dead people.
Other comments suggest that Franklin would have eventually gotten there on her own. Her work was key to the discovery as we know it, which wouldn't have happened without it. To me, that's the whole story.
Specifically the antiparallel base matching was the important bit, agreed, but minor nitpick. The first alpha helix wasn't solved until 1951, so one year earlier. Their ubiquity was very novel.
Watson used his credibility to advance unscientific eugenics theories for years. The impropriety suggested by the circumstances surrounding the discovery of the structure of DNA serves to undermine the arguments of people who are liable to think, "Well, he was smart enough to make one of the most important scientific discoveries of all time, how could he get race theory wrong?".
Watson's shadow would not extend so far if Franklin's role were known - not just because it would have diminished his, but also because her presence would have undermined attitudes that marginalized non-white-men, in the field of science and beyond. It matters a great deal, unfortunately. And it's a tough pill to swallow for a lot of people who have their pride wrapped up in what he represents.
I remember once at Google someone complained that GoogleBot hacked them and deleted their data, and it turned out that GoogleBot was just crawling the pages, and they had unfortunately designed their website so that there was no authentication, page URLs were generally secret, and GET requests to certain URLs were treated as requests to delete data. So once one URL leaked the site got crawled and a lot of data was deleted....
It sounds like you might be thinking of the Google Web Accelerator incidents with 37signals.
If that’s the case, then the delete links were behind authentication, but DHH assumed that meant it was okay to ignore the HTTP spec. and use GET for unsafe actions. Lo and behold, authenticated users with the GWA browser plugin installed deleted all their data.
Then, instead of learning from the mistake and fixing his bug, he tried to detect GWA and hide from it. Sure enough, that failed and users experienced data loss for a second time. He still continued to blame GWA, calling it “evil” and “scary”. You’d think he’d be smart enough to figure out that he needs to follow the HTTP spec., but he couldn’t admit to being wrong.
Different incident that AFAIK did not become public. But yeah, I bet things like this happened a lot. In 2005 people were still getting used to the idea of a robot crawling their website regularly.
Yes, I worked for a bit on site at a datacenter in Fort Worth and was surprised by how many ex-nuclear-submarine engineers there were. I guess it's similar, you have a lot of high tech equipment in an environment where the climate is closely controlled.
Offering Luna for cheap is like restaurants giving you free bread and water. They're pretty sure that you're going to end up eating the expensive stuff on the menu.
Do you have a source for that? Are they raising more money or receiving more money for AI-oriented products or are they actually making more money on consumer/B2B end products?
Well you mention Android, iPhone, Nintendo, and Microsoft. Those are the biggest companies, and many of them don't even use the best coding tools. So they are not going to be the ones improving.
On the other hand, look at the YC companies. I think the last batch or two is growing revenue faster than any batches ever before. Those are the companies that are being sped up a huge amount by AI.
It’s hard to imagine a company more all in on ai than Google. The pressure to use it is intense and they are throwing ai at basically every problem. If a proposal doesn’t have ai in the title somewhere it has no chance of funding.
I don’t really think it has made Google products better, but it is absolutely the expectation.
I have a sneaking suspicion Nintendo's recent docked VRR support may have been an AI assisted endeavor. It even has proper LFC support which the PS5 does not..
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.
With AI, now every software engineer gets to feel this way.