AI solving a 90 year old math problem and more

AI solving a 90 year old math problem and more

Hey folks,

What do you do when ChatGPT starts talking nonsensical gibberish or hallucinating wildly?

​Usually, you start by shouting at it or hitting refresh. But Snickers thinks you should feed it a candy bar instead.

​Snickers recently launched Hungr.AI, calling it the world's first digital candy bar made specifically for AI. 

So, how does an LLM model even have a candy bar?

When a chatbot starts hallucinating, you copy a digital Snickers bar off their website and "feed" it to the AI, which is really just a prompt telling the model to review its response and try again. That’s perfectly on brand for Snickers’ iconic “You're Not You When You're Hungry” campaign.

But candy isn't the only thing people are feeding their chatbots.

Last October, Swedish creative director Petter Rudwall launched Pharmaicy, a marketplace selling "drugs" for AI: code modules named cannabis, ketamine, cocaine, ayahuasca and alcohol, priced between $32 and $70. Upload one into a paid ChatGPT account, and the model loosens up: fuzzier logic, more emotional language, and sometimes erratic.

Rudwall built the modules from human trip reports and psychological research, reasoning that some of history's best creative work happened under the influence. So why not test the same trick on a model trained on generations of such writing?

So now instead of yelling from behind a screen, you can just feed your chat something. And depending on the outcome you want, it could be anything from a chocolate bar to cocaine. 

Here’s a soundtrack to put you in the mood… 🎵

Foolmuse by Peter Cat Recording Co.

You can thank our reader, Svasti Agrawal, for this lovely recommendation.

Also, folks, keep your music recommendations coming. We’d love to feature them in our Sunday editions, especially gems from underrated Indian artists many of us haven’t discovered yet. Can’t wait to hear them!

What caught our eye this week

OpenAI solved a $1 million math problem. Or did they?

If you’ve been anywhere near the internet this week, you’ve probably heard that OpenAI says one of its AI systems has solved the Navier-Stokes problem, one of the seven Millennium Prize Problems in mathematics.

And if “Navier-Stokes” sounds like the kind of thing you’d rather not think about on a Sunday, that’s fair. But the basic idea is surprisingly familiar. These equations describe how fluids move, whether that’s water flowing through a pipe, air moving around an aircraft, or smoke swirling through a room. The problem is that mathematicians have never been able to prove whether these equations always behave nicely, or whether they can suddenly break down and produce what’s called a singularity.

That question has remained unresolved for roughly 90 years. And in 2000, the Clay Mathematics Institute put it on a list of seven exceptionally difficult problems and attached a $1 million prize to each one.

So when OpenAI announced that its AI had found a solution, it was kind of a big deal.

Except there’s a rather important asterisk.

You see, for years, mathematicians have been trying to crack the Navier-Stokes problem. One of them is Tristan Buckmaster, a mathematics professor at New York University. He had been working on the problem with Levent Alpöge, a mathematician who works at Anthropic, OpenAI’s rival.

Interestingly, they weren’t doing this entirely the old-fashioned way either. Buckmaster had been using OpenAI’s Codex, while Alpöge was using Claude, to help with their research. After months of work, they believed they had made significant progress.

Then, in early September, word of their work reached OpenAI.

And this is where the story gets rather awkward.

OpenAI says it had heard rumours that major progress had been made on Millennium Prize Problems and began its own effort on September 1. It then deployed around 10,000 AI agents that worked on different parts of the problem, collectively generating roughly 2.7 million messages and 130 billion output tokens over about 88 hours. The company says the equivalent compute would have cost around $15 million at customer prices. 

And eventually, it got its result.

The AI found a mathematical construction in which a smooth fluid could develop a singularity in finite time. OpenAI then had another model spend about 17 hours translating the result into Lean, a formal language that lets computers check mathematical proofs. The company published a 165-page write-up alongside the formalisation.

That sounds pretty definitive. But there was just one problem.

Buckmaster and Alpöge were working on related ideas at almost exactly the same time. And Buckmaster says that after OpenAI learned about their progress, the company accelerated its own work and eventually produced a solution using an approach that was closely related to theirs.

More importantly, Buckmaster had a question.

He had spent months working on the problem using Codex. So could his unpublished research have somehow made its way into OpenAI's models?

So when he asked OpenAI, the company said its internal system did not have access to his private Codex sessions and later said an investigation found that his prompts in the two months before the announcement could not have influenced the system, including through training. At the same time, OpenAI acknowledged it could not rule out the possibility that user data contributed to earlier model training.

And there’s even more to this, like credit sharing and whatnot, but it got us thinking about something more interesting.

You see, for centuries, mathematical progress has followed a fairly familiar rhythm. Someone has an idea and works on it for years, discussing it with colleagues, writing proofs, and other mathematicians picking it apart. Eventually, if everyone agrees that it holds up, the result becomes part of human knowledge.

Now imagine replacing some of those steps with 10,000 AI agents working simultaneously for 88 hours. If an AI discovers the proof, who gets the credit? 

The company that built the model? The researchers who came up with the original idea? The mathematicians who guided the AI? The people whose earlier work appeared in its training data? Or, eventually, does the machine itself become part of the answer?

The Navier-Stokes problem may have been sitting unsolved for nearly a century. But perhaps the bigger question OpenAI has accidentally created is one that mathematics has never really had to confront before.

When a machine finds the answer, who exactly solved the problem?

Infographic

Tukaram Munde 21 years in service and 25 different transfers

Readers Recommend

This week our reader Siddharth Pal recommends reading Train to Pakistan, written by Khushwant Singh in 1956.

It's a short book about a fictional village near the India-Pakistan border during the partition/Independence period and how partition affected the village where people of all religions once lived in harmony. It captures the village's social and moral fabric and what the main protagonists do (or don't do) when offered a chance to save people.

Thanks for the rec, Siddharth!

That’s it from us this week. We’ll see you next Sunday.

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