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OpenAI Says Its AI Broke a 27 Year Old Computing Assumption · DX Today | No-Hype Podcast & News About AI & DX

• 0:00
  SPEAKER_00: Welcome to the DX Today Podcast, your daily deep dive into the AI ecosystem.
• 0:04
  SPEAKER_00: I'm Brian, and joining me as always is Jessica.
• 0:07
  SPEAKER_01: Thanks, Brian.
• 0:08
  SPEAKER_01: Today we are talking about something that sounds like science fiction.
• 0:12
  SPEAKER_01: Because OpenAI says its internal models produced three brand new results in mathematics, computer science, and physics this week.
• 0:20
  SPEAKER_00: I have to admit, my first reaction was the same one I have to every big announcement, which is that I want to see the receipts before I get excited about anything at all.
• 0:28
  SPEAKER_01: That is fair.
• 0:29
  SPEAKER_01: And the good news is that there are actual receipts this time, at least for some of it.
• 0:34
  SPEAKER_01: So let me walk through what the company is claiming before we start poking holes.
• 0:38
  SPEAKER_00: Please do, because I suspect most of our listeners, like me, have not thought about harmonic analysis or complexity theory since a very long and very painful semester in college.
• 0:48
  SPEAKER_01: The first claim is in computer science.
• 0:49
  SPEAKER_01: The company says its models disprove something called the exponential time hypothesis, which researchers have treated as a working assumption since it was formalized back in 1999.
• 0:59
  SPEAKER_00: Explain that one for me in plain terms, because the name sounds important, but I could not tell you what it actually says or why anyone should care about it.
• 1:07
  SPEAKER_01: Roughly, it says that a whole family of hard logic puzzles cannot be solved much by the stir than by checking almost every possible answer.
• 1:14
  SPEAKER_01: And an enormous amount of theoretical computer science has been built on top of that assumption.
• 1:19
  SPEAKER_00: So if the assumption falls, then every result that quietly leaned on it suddenly has a crack in its foundation.
• 1:26
  SPEAKER_00: Which sounds like a big deal for the people working in that field.
• 1:30
  SPEAKER_01: Exactly.
• 1:31
  SPEAKER_01: Ryan Williams, a complexity expert at MIT, told Al Jazeera that a confirmed refutation would be a major development, and his team is now verifying the proof alongside the two researchers who first stated the hypothesis.
• 1:43
  SPEAKER_00: Before anyone panics, I want to ask the practical question.
• 1:47
  SPEAKER_00: Does this mean the encryption protecting my bank account just stopped working?
• 1:51
  SPEAKER_00: Or is this one of those results that lives entirely on a whiteboard?
• 1:55
  SPEAKER_01: It lives on the whiteboard for now.
• 1:57
  SPEAKER_01: The new method is still slower than polynomial time, so it does not show that P equals NP.
• 2:03
  SPEAKER_01: And every report I read says everyday encryption is not affected by it.
• 2:07
  SPEAKER_00: That is reassuring.
• 2:08
  SPEAKER_00: And it is also the part that gets lost when a headline says an AI broke a famous hypothesis, because people hear broken and immediately think of something dangerous or something they need to fix.
• 2:18
  SPEAKER_00: Right.
• 2:19
  SPEAKER_01: And Williams himself said there are no short-term real-world applications, although the proof introduces a new technique that could eventually make a range of fundamental problems more efficient to solve.
• 2:29
  SPEAKER_00: Let me try a picture for the listeners.
• 2:31
  SPEAKER_00: Imagine a lock with a huge number of possible combinations, and the old assumption said you basically have to try nearly all of them, no matter how clever you are about the order.
• 2:41
  SPEAKER_01: That is a good picture.
• 2:43
  SPEAKER_01: The new result says you can skip a meaningful slice of those combinations as the lock gets bigger.
• 2:48
  SPEAKER_01: And the method even counts how many combinations work rather than just finding a single one, which is an unusually strong form of the result.
• 2:55
  SPEAKER_00: Okay, that is the computer science piece.
• 2:59
  SPEAKER_00: What is the second claim?
• 3:00
  SPEAKER_00: Because I saw the word Kakeya in a few headlines and honestly assumed it was a new kind of sushi.
• 3:06
  SPEAKER_01: It is a puzzle about how small a shape can be, while still containing a line pointing in every direction.
• 3:11
  SPEAKER_01: The bigger target is the local smoothing conjecture, which Christopher Sogi proposed in 1991, and which implies the Kakea conjecture.
• 3:19
  SPEAKER_00: And how far had human mathematicians gotten on that one before the models showed up?
• 3:23
  SPEAKER_00: Because I assume people have been working on it for more than three decades now.
• 3:27
  SPEAKER_01: They had made real progress.
• 3:29
  SPEAKER_01: A team proved the two-dimensional case around 2019, and Hong Wang and Joshua Zhaal settled the Kakeya question in three dimensions just last year, which was celebrated as a landmark result.
• 3:39
  SPEAKER_00: So the claim is not that the machine finished one more dimension, it is that the machine proved the whole thing in every dimension at once, which is a very different level of ambition.
• 3:49
  SPEAKER_01: That is the claim.
• 3:50
  SPEAKER_01: Alex Yosevich, a mathematician at the University of Rochester, whose own doctoral advisor was Soga, called it a historic development and said he felt joy and optimism along with a small twinge of sadness.
• 4:02
  SPEAKER_00: I find that twinge of sadness to be the most human detail in this whole story, because it captures what a lot of experts in every field are feeling right now about these tools.
• 4:11
  SPEAKER_01: It really does.
• 4:13
  SPEAKER_01: And the third claim is the most ambitious of all: an existence proof for quantum chromodynamics, the theory of how quarks and gluons interact, which is connected to one of the famous Millennium Prize problems.
• 4:24
  SPEAKER_00: Wait, are they claiming the million-dollar prize?
• 4:27
  SPEAKER_00: Because if a chatbot is collecting prize money from the Clay Institute, that would be a very different story from the one we are telling today.
• 4:34
  SPEAKER_01: No, and they are careful about it.
• 4:36
  SPEAKER_01: The prize problem has two parts existence and something called the mass gap.
• 4:41
  SPEAKER_01: And the company is not claiming the mass gap, so the prize money stays on the table for now.
• 4:46
  SPEAKER_00: Good.
• 4:46
  SPEAKER_00: That kind of restraint actually makes me trust the rest of the announcement a little bit more, because overselling is usually the first warning sign I look for in these situations.
• 4:55
  SPEAKER_01: Then you will like the timeline too.
• 4:57
  SPEAKER_01: The company says the physics work came first, with the simplified version on September 9th and the full theory nine days later, and the other two results arrived in the middle of this month.
• 5:07
  SPEAKER_00: I also want to know how long the machine actually spent on these problems, because there's a big difference between a lucky afternoon and a research program that ran for months with enormous amounts of computing power behind it.
• 5:18
  SPEAKER_01: The company has not given compute figures for these three results.
• 5:21
  SPEAKER_01: For an earlier batch of smaller results, it said each one averaged about three hours of reasoning time, but nobody should assume the same is true for work of this size.
• 5:30
  SPEAKER_00: That missing number matters to me because the cost of a discovery tells you whether this is something every university will be able to do next year, or something only a handful of very rich labs can afford to run.
• 5:41
  SPEAKER_01: I agree that cost is the hidden variable here.
• 5:44
  SPEAKER_01: If a discovery like this needs a giant data center for weeks, it concentrates scientific power in a few companies.
• 5:50
  SPEAKER_01: But if it gets cheap, it could spread to every math department on Earth.
• 5:54
  SPEAKER_00: Now here's where I put on my skeptic hat.
• 5:56
  SPEAKER_00: How do we know any of this is actually true rather than a very convincing document full of math that looks right but falls apart on inspection?
• 6:04
  SPEAKER_01: That is the key question.
• 6:06
  SPEAKER_01: And the answer is a tool called Aline.
• 6:08
  SPEAKER_01: It is a proof assistant, a program that checks every logical step of a proof mechanically.
• 6:14
  SPEAKER_01: And the company says the computer science and math results were both checked that way.
• 6:18
  SPEAKER_00: That sounds like a strong guarantee, but I have run enough real systems to know that a perfect check of the wrong specification can still give you a perfectly wrong answer with total confidence.
• 6:28
  SPEAKER_01: You're exactly right.
• 6:30
  SPEAKER_01: And the company admits it.
• 6:31
  SPEAKER_01: Lean confirms that the formal statement was proven, but humans still have to confirm that the formal statement really matches the famous conjecture that mathematicians actually care about.
• 6:40
  SPEAKER_00: That is the gap where I would focus all my attention if I were reviewing this, because a single definition written slightly differently could turn a historic proof into a proof of something much less interesting.
• 6:51
  SPEAKER_01: And there is precedent for concern.
• 6:54
  SPEAKER_01: Earlier this month, a sign error invalidated an argument in one of their machine-written manuscripts.
• 6:59
  SPEAKER_01: Three manuscripts were withdrawn, and 14 others had to be corrected after the fact.
• 7:15
  SPEAKER_01: Agreed.
• 7:15
  SPEAKER_01: But the numbers also show how much remains unchecked.
• 7:19
  SPEAKER_01: Of roughly 700 top-line results in their research repository, only about 300 or around 42% have been formally verified so far.
• 7:28
  SPEAKER_00: So the honest summary is that these three results look very promising.
• 7:32
  SPEAKER_00: A couple are mechanically checked, and none of them has gone through normal peer review or independent confirmation yet.
• 7:38
  SPEAKER_01: That is the honest summary.
• 7:40
  SPEAKER_01: And I think the more interesting story might be how the company chose to release the work, because it is trying something that has not really been done before at this scale.
• 7:48
  SPEAKER_00: You mean the shepherds?
• 7:50
  SPEAKER_00: I saw that word in the announcement, and it struck me as an unusual choice of vocabulary for a technology company talking about scientific research.
• 7:57
  SPEAKER_01: Yes.
• 7:58
  SPEAKER_01: For each result, the company picked a group of outside experts to guide the release.
• 8:02
  SPEAKER_01: Williams and his colleagues handle the complexity result, and the company says it will fund a conference if that group wants one.
• 8:08
  SPEAKER_00: And the physics result is with a group led by David Gross, the Nobel laureate, which tells you they understood that physicists would want one of their own to vouch for it before anyone took it seriously.
• 8:19
  SPEAKER_01: Right.
• 8:20
  SPEAKER_01: And that group decided to hold back the raw machine output so they can write their own interpretation first.
• 8:25
  SPEAKER_01: While the mathematics result was posted directly to a public code repository for anyone to inspect.
• 8:30
  SPEAKER_00: So we have three different release models for three different communities, which is either very thoughtful or a little chaotic, depending on how charitable you want to be about it this morning.
• 8:39
  SPEAKER_01: I lean toward thoughtful.
• 8:41
  SPEAKER_01: There are no non-disclosure agreements.
• 8:43
  SPEAKER_01: The company says it claims no academic credit, and participation is voluntary and unpaid, which removes a lot of the obvious conflicts of interest.
• 8:52
  SPEAKER_00: But I will push on one thing.
• 8:54
  SPEAKER_00: Choosing who gets to see the work first is still a form of power.
• 8:58
  SPEAKER_00: And the company itself admits that picking the first shepherds creates an information advantage for a small group of people.
• 9:04
  SPEAKER_01: That is a fair point.
• 9:06
  SPEAKER_01: And it connects to the money side.
• 9:08
  SPEAKER_01: This is a company valued at more than$800 billion, currently raising capital, and a scientific breakthrough is about the best marketing story imaginable.
• 9:17
  SPEAKER_00: That is exactly why I want the verification to be boring and slow and thorough, because the incentive to declare victory early is enormous when you are talking to investors and competitors at the same time.
• 9:27
  SPEAKER_01: And the competition is real.
• 9:29
  SPEAKER_01: Last month, Anthropic announced an enzyme similar to the gene editing system called CRISPR, and scientists were split, with some excited and others saying the significance had been exaggerated.
• 9:39
  SPEAKER_00: So we are now in an era where the frontier labs compete on scientific discoveries, not just on benchmark scores, and that changes what counts as a product launch in this industry.
• 9:49
  SPEAKER_01: It does.
• 9:50
  SPEAKER_01: And I think the second order effects are where this gets really interesting.
• 9:54
  SPEAKER_01: Because if machines can generate serious proofs quickly, the bottleneck in mathematics moves from discovery to verification and understanding.
• 10:02
  SPEAKER_00: That is the Monday morning question for me.
• 10:05
  SPEAKER_00: If I am a graduate student or a professor, what actually changes in my work next week, as opposed to 10 years from now when everything is settled?
• 10:13
  SPEAKER_01: Next week, the job shifts toward reading, checking, and explaining machine output.
• 10:18
  SPEAKER_01: Yosevich said many pure math problems came from physical questions, and those questions can now be explored much faster than before.
• 10:26
  SPEAKER_00: I can see that being a real gift for people who love asking good questions, and a real threat for people whose whole career was built on grinding through technical proofs that a machine now does overnight.
• 10:36
  SPEAKER_01: Both can be true, and there is also a talent angle.
• 10:40
  SPEAKER_01: Universities will need people who are fluent in proof assistance, like Lean, and I expect that skill to become one of the most valuable things a young mathematician can put on a resume.
• 10:49
  SPEAKER_00: That makes sense to me, and it mirrors what happened in software, where the people who understood testing and verification became more valuable once the amount of code being written started growing faster than anyone could read it.
• 11:00
  SPEAKER_01: And for businesses, the practical payoff is further away.
• 11:04
  SPEAKER_01: Better algorithms could eventually help with scheduling, routing, chip design, and imaging, but foundational results usually take years to reach real products.
• 11:12
  SPEAKER_00: So my takeaway for our listeners is simple.
• 11:15
  SPEAKER_00: Watch what Williams and his group say over the next few weeks, because their verdict on the complexity result will tell us far more than any press release ever could.
• 11:23
  SPEAKER_01: And mine is that the way this was released may matter as much as the math itself.
• 11:27
  SPEAKER_01: Because if open verification by outside experts becomes the norm, it could set the template for every lab that follows.
• 11:34
  SPEAKER_00: That's all for today's episode of the DX Today podcast.
• 11:37
  SPEAKER_00: Thanks for listening, and we'll see you next time.