This week: 2026 ASN award winners announced, ChatGPT vs. mathematics, the single most important rigor-enhancing practice in all of science, and more.

Congratulations to the 2026 ASN award winners!

The registration deadline for the 11th evolutionary demography conference June 18-26 has been extended until June 1. I don’t work on the ecology and evolution of structured populations myself, or on human demography. But I have friends who do, and they all love this conference. So if you work on those things, I encourage you to look into attending.

“The most important ‘rigor-enhancing practice’ is caring about getting things right, and without that nothing else matters.” Adam Mastroianni brings the heat. Wow. I covered some of the same ground in this recent post, but not like this. That brief quote doesn’t really do the post justice.

I’m late to this, but here are proposed updates to the regulations of the Canadian Panel on Responsible Conduct of Research. These regulations govern how researchers who receive TriCouncil research funding, and the universities employing those researchers, are supposed to respond to allegations of scientific misconduct. One proposal is that there’d be no statute of limitations on allegations. Another is that institutions would be obliged to investigate and hold accountable respondents who are no longer affiliated with the institution. A third is that institutions would be free to consider anonymous allegations, and allegations “in the public domain” , so long as sufficient information is provided (think of PubPeer comments). A fourth is that institutions would be obliged to define retaliation against good-faith accusations (e.g., suing an accuser, or spreading malicious rumors about an accuser) as a form of misconduct. If implemented, I don’t know that these proposals are going to change anything all that much. Offhand, these seem broadly like good ideas to me, though I’d agree with Adam Mastroianni that the rules matter less than having good people to implement and enforce them.

This week in unsurprising results: a new preprint finds that people prefer interacting with sycophantic LLM chatbots that validate their beliefs. Chatbot users also rated sycophantic chatbots as more unbiased. And the only way for the chatbots to get users to take on board information that contradicted their pre-existing beliefs was to present that information as validating the user’s other beliefs. I’m not too worried about this (though what do I know, obviously), because hasn’t it ever been thus? I mean, it’s not as if lots of people wanted to be contradicted back in the pre-LLM days. And it’s not as if people don’t already have lots of ways to avoid having their beliefs contradicted.

Recently I linked to news that off-the-shelf ChatGPT had proven an open, and fairly well-known, conjecture in mathematics, despite not being specifically trained or tailored to do mathematics. Further, it had done so using a method of proof that impressed human mathematicians–it would’ve been called “creative” and “insightful” if a human mathematician had done it. Finally, the proof had not been memorized from the training data (i.e. the proof wasn’t already published in some obscure venue that was in the training data but that human mathematicians didn’t know about). Well, now ChatGPT has done it again, and this time it’s done it for one of the central conjectures in discrete geometry (!) It’s a very famous conjecture that was posed by the Paul Erdős in 1946. Literally every expert in discrete geometry has tried and failed to either prove it or refute it at some point. No less than Fields Medalist Timothy Gowers says that we’re now at the point where mathematicians are going to have to fundamentally rethink how they go about their work, individually and collectively.* (UPDATE: Here are some very interesting comments from a mathematician on why ChatGPT could come up with these proofs while humans couldn’t. That’s excerpted from this longer preprint with comments from a number of mathematicians. Very very interesting throughout.)

Still true. Heartbreaking that it’s less true than it once was, because the Trump administration is trying to make it not true at all. But still true.

*Aside: some of the reactions to Timothy Gowers’ Bluesky post about the proof are a good illustration of the link in the previous paragraph. People who hate AI for whatever reason really don’t like hearing that AI is ever useful for anything, and so will reach for any excuse to deny that AI is ever useful. You might think that “AI is genuinely useful for some purposes,” and “AI is a bad thing for the world on balance” would be easy thoughts to hold in your head at once, especially when you’ve just been told that AI is genuinely useful for mathematics by literally one of the world’s greatest mathematicians. But apparently not, at least not for the sort of people who talk about AI on Bluesky. Apparently, Bad Things must be Bad always and everywhere, otherwise they’re not truly Bad, I guess? Maybe Timothy Gowers should’ve found a way to spin this proof as somehow confirming something else that AI haters on Bluesky believe (“Here’s why this proof shows that Elon Musk is terrible.”)**

**Aside to the aside: obviously that aside is far from the most important or interesting thing in the world! What can I say? Like many people who write words on websites, nothing annoys me quite like (some) other people who write words on websites. Consider this your invitation, if one were needed, to tell me how annoying I am sometimes.