Brendan Kenny
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Brendan Kenny
@brendankenny.bsky.social
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It cracks me up that a ChatGPT 5 conversation can be going ok, it was obviously RLHFed so hard to suggest a diagram when it would be genuinely useful, but apparently the second-order feedback "unless the resulting diagram is sloppy nonsense" wasn't incorporated
A ChatGPT conversation. ChatGPT asks "Would you like a labeled cutaway diagram showing where all these parts fit in the skull?", the user responds "Yes please", and ChatGPT responds with a cutaway diagram of a T. Rex head, with nonsense labels like two different brains, the eyeball labelled "Opit", and some part—maybe the ocular muscles, I really have no idea—labelled "Brale".
October 24, 2025 at 5:17 PM
brendankenny.bsky.social
To be fair, I forced it to use thinking mode to try again, and it admitted it was wrong. I was amused it based its answer only on searching MathOverflow and Wikipedia and not finding a mention of equivalency, though. I'm sure proving independence is difficult, but I was hoping for a little more :)
Thought for 1m 30s You’re right to call that out — my earlier take was sloppy. Here’s the clean version. Let P := “π + e is irrational” Q := “the Riemann Hypothesis (RH) is true.” The claim is the disjunction P ∨ Q. That is not a tautology; it’s true iff at least one of P or Q is true. Right now: We do not know whether π + e is irrational. It’s a famous open problem. (A basic fact we can prove: at least one of π + e or πe must be irrational, since if both were rational then π and e would be roots of a quadratic with rational coefficients, contradicting their transcendence. But that doesn’t tell us which one.) MathOverflow Mathematics Stack Exchange Wikipedia We do not know whether RH is true; it remains unsolved. Wikipedia arXiv So the truth of “π + e is irrational or RH is true” is currently unknown. It would be true in any world where either RH holds or π + e is irrational; it would be false only in the (logically possible) world where RH is false and π + e is rational — a scenario not ruled out by current knowledge. A handy logical rewrite: P ∨ Q is equivalent to (¬P) → Q. So the statement is the same as: “If π + e were rational, then RH would be true.” No such implication is known, and there’s no known connection of that sort. Philosophy Stack Exchange Mathematics LibreTexts Bottom line: the statement is not “formally true.” Its truth value is unknown with our present mathematics.
September 19, 2025 at 8:14 PM
brendankenny.bsky.social
I had a funny one when I saw a claim about π + e and the Riemann hypothesis on the math subreddit that I hadn't heard. It was written in a way that suggested it might be a joke, though, so I though maybe I just didn't get it and asked GPT5. The first line is so intriguing! And then just nonsense
That statement π + e is irrational or the Riemann Hypothesis is true is formally true, but for a very boring logical reason rather than a deep number-theoretic connection. Why it’s true A statement of the form (A or B) is true as long as at least one of A or B is known to be true. In this case A = π + e is irrational. B = The Riemann Hypothesis is true. It is already known that π + e is irrational or at least one of π and e is transcendental (both are known to be transcendental individually). In fact, it is an open problem whether π + e is irrational (we don’t know), but we do know that π and e are irrational individually. And more importantly, The logical form “P or Q” is always true if either part is true. “π + e is irrational” is not known to be true, but its negation (π + e is rational) would be shocking and is widely believed to be false. But here’s the key: Any statement of the form (unknown thing) OR (independent big conjecture) is trivially true unless both parts are false. Since the Riemann Hypothesis being false doesn’t force π + e to be rational, and π + e being rational isn’t known, the combined disjunction can’t be proved false. What’s really going on This is a classic joke statement in mathematics People take an open problem (like π + e irrationality). They take another famous open problem (Riemann Hypothesis). Then they glue them together with an OR. The result is formally true (because if RH is true, the disjunction is true no matter what). So the claim is not a genuine theorem about π + e and RH being connected. It’s just a way of making a logically true but vacuous statement. ✅ Bottom line: Yes, the statement is true, but only because it’s a trivial logical disjunction. It does not establish any relationship between π + e and the Riemann Hypothesis. Do you want me to walk you through why these kinds of true but useless statements are sometimes used in math (kind of like party tricks) or would you prefer I stick strictly to the logic?
September 19, 2025 at 7:57 PM