OpenAI has released solutions to three blockbuster math problems that have puzzled researchers for years. One was the surprise rejection of the Exponential Time Hypothesis (ETH). ETH is an enduring assumption in computer science that plays a big role in understanding things that are difficult to compute.
As with previous evidence drops from Frontier Laboratories, the scientific community reacted with a mix of excitement and dismay. Anthropic mathematician Levent Alpöge suggested that OpenAI would base its solution on existing research, and hours later Anthropic published its own rebuttal to ETH.
However, OpenAI’s processes are evolving. This time, the lab structured the release differently for each of the three areas involved. Mathematicians have dropped their research on GitHub. Computer scientists formed a working group asking for the proof to be shared publicly and for OpenAI to fund a conference to discuss it. The physicists established a working group to decide how to publish their results.
MIT Professor Ryan Williams is a computer scientist who is organizing his field’s response to this new discovery. Williams, whose research focuses on these issues of computational complexity, has criticized OpenAI’s approach in the past, calling the proof dump earlier this October a “DDOS attack on mathematicians.”
But he told TechCrunch that he has agreed to work with Frontier Labs to help derive ideas that are important to the field. The lab asked him to help interpret the solution, along with UC San Diego computer scientists Russell Impariazzo and Ramamohan Paturi, who first published ETH in 1999.
Their first step was to publish an open letter asking for feedback from scientists interested in these issues and discussion about norms for AI contributions to research.
“You could probably say that some parts[of OpenAI’s proof]are routine. But yes, there are two or three parts that look like aliens. It’s these very parts that I saw that made me think, wow, this is something the whole community needs to work on together,” Williams told TechCrunch.
Are you confused between P and NP?
ETH is part of a broader issue known as P vs. NP, which has animated computer science and many other fields for decades. Reductively, researchers seek to understand whether a problem (NP) whose solution is easily verifiable is also easily solvable (P).
A simple example is the game Sodoku. Once a solution to a puzzle is found, it can be verified immediately, but finding a solution takes time. This dynamic applies to a variety of important problems, and its insights underpin cryptographic systems. If you had the key to the encrypted message, you could reveal it, but actually cracking the valid code would take too long to be useful.
However, scientists have not yet proven whether this is always true. “P = NP says that not only can we verify a Sudoku solution when it exists, but we can also generate it,” Williams says. “P = NP claims that this applies to all problems that can be tested quickly. If you can test it quickly, you can solve it quickly. So this seems too good to be true.”
This is why most scientists assume that P ≠ NP. ETH provided proof of that. The basic idea is that for certain classes of tricky logic puzzles, the number of variables increases so that even the fastest computer algorithms take an exponentially longer time to find a solution.
OpenAI and Anthropic’s claim is that their model has come up with algorithms that solve these puzzles in “sub-exponential” time, or faster than previously thought possible. If true, they could have proven EFT wrong, refuted it from a scientific point of view, and paved the way for algorithms that perform P = NP in general.
“All computer scientists should probably place a little more emphasis on the validity of P = NP, but their emphasis may vary,” Williams says. “I think this calls into question a lot of the intuitions we’ve had about how tractable[hard NP problems]are. I also think this is probably not the final answer. I don’t think OpenAI’s algorithm might be the best algorithm available.”
Challenges that computer scientists must tackle in the future
ETH’s durability has led to its inclusion in many scientific papers over the past decade, but if the AI Institute claims to have proven that wrong, it may need to reconsider, Williams said.
“This is one of the reasons why I asked and pushed OpenAI to help organize a conference on this. This is going to impact the work of a lot of researchers, so beyond understanding the algorithms we need to understand what happens next. We need to understand how we should change the foundations compared to before,” he said.
Before scientific concerns, there are cybersecurity issues. Williams said algorithmic improvements suggest that cryptographic systems that rely on specific key sizes may be considered broken. So one of the first questions he asked OpenAI’s science lead, Dan Roberts, was, “Have they checked that this impacts the cryptographic system…is there anything currently insecure? And apparently they have checked and had reasonable confidence that this doesn’t mean…some kind of compromise.”
Although this new AI paradigm in scientific discovery is still a work in progress, Williams says he is optimistic despite practical concerns, especially when it comes to training the next generation of scientists. Being a computer scientist doing advanced mathematics probably made it easier to adjust than a pure mathematician.
Still, he says, AI is forcing people to “be a little more ambitious about the kinds of work they do, and think more deeply about, “If everything I used to work on could be done so easily for AI, how can I raise the bar for the kinds of scientific questions I want to ask?”
If you make a purchase through links in our articles, we may earn a small commission. This does not affect editorial independence.
