2 August 2024 | 5:58 pm

In a previous blog post, I discussed how, from a Bayesian perspective, learning about some new information can update one’s perceived odds about how likely an “alternative hypothesis” is, compared to a “null hypothesis” . The mathematical formula here is Thus, provided one has (i) A precise formulation of the null hypothesis and the alternative […]

8 July 2024 | 5:09 pm

I’ve just uploaded to the arXiv my paper “Dense sets of natural numbers with unusually large least common multiples“. This short paper answers (in the negative) a somewhat obscure question of ErdÅ‘s and Graham: Problem 1 Is it true that if is a set of natural numbers for which goes to infinity as , then […]

8 July 2024 | 12:11 am

Many modern mathematical proofs are a combination of conceptual arguments and technical calculations. There is something of a tradeoff between the two: one can add more conceptual arguments to try to reduce the technical computations, or vice versa. (Among other things, this leads to a Berkson paradox-like phenomenon in which a negative correlation can be […]