Claude 独立攻克图论猜想,高德纳对此震惊发文,反映 (English)

Generated: 2026-06-21 22:32:40

---

Don't Panic, Mathematicians Haven't Lost Their Jobs Yet — AI Is Just a Handy "Cyber Mule"

Yesterday while scrolling on my phone, I saw some news that almost made me spit coffee all over the screen.

"Claude Independently Solves Graph Theory Conjecture — Knuth Shocked!"

Wow, that headline was a masterpiece — it sounded like the opening of a sci-fi movie and the dawn of AI domination all rolled into one. To make it even better, when you clicked through, the author of The Art of Computer Programming, 88-year-old Turing Award winner Donald Knuth, opened with: "Shock! Shock!"

Feels like watching a movie trailer, right?

But hold your horses. As someone who's written a tech column for ten years, I know this game inside out. If the headline isn't blown out of proportion, who's going to click? So today I really want to walk through this whole thing from start to finish — what exactly did AI do? And what does it mean for the rest of us?

---

Let's Break Down What Actually Happened, Without Getting Swept Up by the Hype

The story is actually pretty simple.

Knuth was writing an update for his legendary book and ran into a problem: in an m×m×m cube grid, can you split all the edges into three disjoint cycles, with each cycle visiting every vertex exactly once?

He'd only figured out the case m=3. Everything beyond that had him stuck. Then his friend Filip Stappers suggested: why not let AI take a crack at it?

So Claude Opus 4.6 stepped up. After 31 rounds of iteration, it eventually found a construction.

See, nothing too crazy so far, right? But here's the kicker —

Who came up with the approach? Stappers. Who planned the route? Also Stappers. Who pulled AI back every time it hit a wall? Still Stappers. Who corrected AI every time it started talking nonsense?

Right again: Stappers.

Knuth himself used a perfect analogy: in this case, AI was like an "electric screwdriver" — it can help you get the job done, but it's not some independent genius inventing new things.

Then the media got hold of it and turned it into "Claude independently cracks graph theory conjecture." Can you see how far off that is?

I even saw an article claiming Claude demonstrated "rigorous logical exploration" — guess what? Out of 31 iterations, more than a dozen ended up in dead ends. Some "rigor".

So the real point here was never "how smart AI is," it's "how humans made AI work for them."

---

What Did AI Actually Do? Basically, a "Cyber Whiteboard"

At this point, I've got to show you what Knuth's original paper actually says — it's surprisingly honest about the process.

Here's how Claude tackled it: first it tried linear functions, didn't work. Then quadratic functions, still no. Finally it went brute force and crashed.

On the 15th attempt, something clicked — it realized the graph was a Cayley graph (one with special symmetry), and introduced framing called "fiber decomposition," turning the 3D problem into a jump problem between layers.

So that framework was the right call, right? From there it searched for specific rules within that framework, and finally on the 31st attempt, it found a construction it called "bump" and wrote some Python code.

Knuth took that code, ran it for all odd m from 3 to 101 — all passed. He then rigorously proved the construction's generality and even found that there are actually about 760 similar solutions; Claude had found only one.

So bottom line: the human decides where to go, AI tries if this path can work.

Let me tell you, this is a math version of human-machine collaboration. Stappers set the homework, AI did it. After it was done, Knuth the teacher graded it all.

By the way, Claude couldn't handle the even m cases at all. It brute-forced solutions for m=4, 6, and 8, but couldn't generalize a pattern. Later, another researcher got GPT-5.3-codex to generate code for big evens, but that solution was so complicated that humans still haven't finished proving it.

So there you have it: when AI does math, it has a fatal flaw — it can find solutions but often can't explain why they work.

---

Don't Rush to Praise, Don't Rush to Dismiss

I've been testing several AIs on math problems recently, and honestly, the results are all over the place.

For well-structured problems — say, number theory or combinatorics with clear templates — AI performs pretty well. I threw a few IMO questions at them, and some models came up with solutions more concise than the official ones.

But the moment I switched to problems requiring "inspiration" or "analogical thinking," AI started fumbling. And not in the obvious way — it'll package its mistakes seamlessly and then push a wrong intermediate conclusion forward for another dozen steps.

Knuth's paper also mentions this: Claude often missed key points and would charge down wrong paths. Stappers had to keep calling it back.

This reminds me of when AlphaGo played Lee Sedol. A lot of people said back then, "AI plays Go on brute force, not intuition." Later, when the game records were studied closely, many moves turned out not to be calculated at all — they were felt.

But honestly, I feel differently about AI doing math than I do about Go.

Why? Because Go has fixed rules and a search space that's large but finite. Math is different — its core is about building concepts, finding the right question, not the right answer. You can let AI find solutions within a given framework — fine. But ask it to define its own framework? It's helpless.

The Knuth case falls exactly on this line. Claude was verifying and searching within the framework Stappers gave it, not