5 Responses to “Lindsay Graham”

1. 1 1 nobody.really
   August 3, 2026 at 3:18 am

   >Say what you will about him…

   Ok. He was a dick.

   (Thirty yrs ago, Mike Doonesbury gave a speech introducing presidential candidate Steve Forbes, culminating with “Call me a fool! Call me a crazy dreamer! But I truly believe that Steve Forbes will be the next president of the United States!” The meagre audience dutifully responded with “Fool!” “Crazy dreamer!”

   Sometimes you get what you ask for.)

2. 2 2 Steve Landsburg
   August 3, 2026 at 9:40 am

   nobody.really: I do not dispute this.

3. 3 3 nobody.really
   August 4, 2026 at 4:43 am

   Next topic (again pulling from memory):

   I recall you waxing eloquent about mathematics, and an irreducible, hard-to-articulate quality called “elegance,” involved in mathematical proofs. I came away with a sense that a hedonic quality was central to advanced mathematics.

   Today (August 4, 2026), I received Noah Smith’s post “The end of the age of heroes.” The post notes that AI is making great strides in mathematical discoveries—and that this is triggering a sense of loss and despair among mathematicians. The joy of the enterprise is not in HAVING the answers, but in FINDING the answers.

   This sounds like a scene from Hitchhiker’s Guide to the Galaxy, with professional philosophers objecting to the supercomputer Deep Thought searching for the meaning of life, the universe and everything. We’re supposed to laugh at these self-interested philosophers. But I can’t help but share the vague sense of loss of the mathematicians.

   My own mathematics background was more humble, but I recall the sense of satisfaction in a sudden flash of insight. As my studies grew more challenging, I began shifting away from real internalization to simply memorizing. That was the beginning of the end of my mathematics career; I was able to pass tests, but the joy was gone. So I find it easy to project that sense of loss onto the mathematicians in Smith’s post.

   I’d be interested in hearing your take on this. (Maybe start a new thread for that discussion.)

4. 4 4 nobody.really
   September 22, 2026 at 4:35 pm

   https://www.nytimes.com/2026/09/22/science/math-ai-history-understanding.html?unlocked_article_code=1.DFE.Fwr6.BFYceE8tDK-2&smid=url-share

5. 5 5 Steve Landsburg
   September 22, 2026 at 5:26 pm

   nobody.really: Of course you’re way off topic here, but this seems to be a point in history where pretty much everyone seems to be bending the rules on this topic. So I will say this:

   I haven’t yet read the article you posted. But my take on the topic is this: Eighteen months ago, ChatGPT scored 4/90 on my economics final exam, and I thought that for the foreseeable future, AI would be a joke. Now I will not be surprised if it solves the Hodge conjecture.

   AI is great at solving problems, and not just by brute force. Claude found a counterexample to the Jacobian conjecture that you can write down in a few lines, but it didn’t find it by checking trillions of polynomials; it found it by some beautiful out-of-the-box geometric thinking. So AI is great at solving problems in exactly the same way that many great mathematicians solve problems.

   But here is what I have **not** seen: I haven’t seen an AI notice that the category of topological abelian groups is not abelian, and think that’s just *not okay* and then invent condensed mathematics to solve the problem. I haven’t seen an AI do anything comparable to inventing negative numbers, or inventing cartesian coordinates, or rewriting the foundations of algebraic geometry, or inventing K-theory, or figuring out what an infinity-category ought to be, or inventing a good theory of motives strong enough to settle Grothendieck’s standard conjectures. I continue to think we’re very far from this. On the other hand, I’ve been wrong before.