> It isn’t “wrong.” Wolfram defines Binomial[n,m] at negative integers by a symmetric limiting rule that enforces Binomial[n,m] = Binomial[n,n−m]. With n = −1, m = −1 this forces Binomial[−1,−1] = Binomial[−1,0] = 1. The gamma-formula has poles at nonpositive integers, so values there depend on which limit you adopt. Wolfram chooses the symmetry-preserving limit; it breaks Pascal’s identity at a few points but keeps symmetry. If you want the convention that preserves Pascal’s rule and makes all cases with both arguments negative zero, use PascalBinomial[−1,−1] = 0. Wolfram added this explicitly to support that alternative definition.
Of course this particular question might have been in the training set.
Honestly 2.5 years feel like infinity when it comes to AI development. I'm using ChatGPT very regularly, and while it's far from perfect, recently it gave obviously wrong answers very rarely. Can't say anything about ChatGPT 5, I feel like in my conversations with AI, I've reached my limit, so I'd hardly notice AI getting smarter, because it's already smart enough for my questions.