"It would be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.'"
About this Quote
The nightmare here isn’t that a computer gets smarter than us; it’s that mathematics stops being a human language. Graham points to a future where truth becomes cheap but meaning becomes scarce: you press a button, the oracle replies “yes,” and the most celebrated unsolved problem in number theory collapses into a sterile fact. The punchline is the second clause: “you won’t be able to understand the proof.” That’s the real discouragement, because in math the proof isn’t a receipt stapled to the answer. It’s the story of why the answer had to be that way, a chain of ideas you can walk, audit, and ultimately own.
Graham is writing from inside a culture that treats understanding as the prize. Mathematicians don’t just want results; they want concepts that travel, techniques that generalize, intuitions that can be taught. A machine-generated proof that’s formally correct but cognitively opaque would sever that pipeline. It would turn the Riemann hypothesis into a black-box theorem: certified, uselessly so.
The line also anticipates an anxiety that’s now mainstream in AI: verification without comprehension. Even if we can check each step mechanically, “understand” means something else - compression into human-sized ideas, not a million-page argument or an alien formalism. Graham’s subtext is a defense of math as a communal, aesthetic enterprise. Without intelligible proofs, we don’t just lose an answer; we lose the discipline’s method of making new answers.
Graham is writing from inside a culture that treats understanding as the prize. Mathematicians don’t just want results; they want concepts that travel, techniques that generalize, intuitions that can be taught. A machine-generated proof that’s formally correct but cognitively opaque would sever that pipeline. It would turn the Riemann hypothesis into a black-box theorem: certified, uselessly so.
The line also anticipates an anxiety that’s now mainstream in AI: verification without comprehension. Even if we can check each step mechanically, “understand” means something else - compression into human-sized ideas, not a million-page argument or an alien formalism. Graham’s subtext is a defense of math as a communal, aesthetic enterprise. Without intelligible proofs, we don’t just lose an answer; we lose the discipline’s method of making new answers.
Quote Details
| Topic | Artificial Intelligence |
|---|
More Quotes by Ronald
Add to List
