Well, actually not all of us, really just me (I?). I was listening to a vaguely interesting podcast this morning about David Bessis' book Mathematica, which (apparently?) emphasises the importance of intuition in mathematical thinking rather than logical proofs. In particular, the idea was that being a good mathematician is learning to train your intuition to agree with the reality, battering it into the right shape when you make a mistake instead of just giving up. It can then be a useful guide and inspiration when exploring new mathematical concepts. What most struck me about this idea of 'training your intuition' was that this was analogous to machine learning (LLMs/AI/whatever). You don't really care about the steps or formally proving something, you're just trying to make the outputs of the system agree with reality. Our big advantage over LLMs in this context being that for us reality is more than 'all the text on the internet'. But then I got to thi...
One of my work colleagues has recently moved to Sydney, and was asking me about schools. Public? Selective? Catholic? Private? The second greatest topic of conversation in our blessed city after housing. There are no good answers; I think the most I can contribute is a biased, almost completely unresearched and probably fundamentally incorrect take on why it's such a mess. In the before times, there were three systems. If you were rich, you went to a fancy private school; in such times, this was tautological. All private schools were fancy. Otherwise, if you were Catholic you went to a 'systemic' Catholic school for a smaller amount of money, and if you were neither rich nor Catholic you went to your local government school. Then, the systemic Catholic schools started running out of money as the nuns and monks aged out and they couldn't afford to actually pay teachers, so they extorted the government of the time into funding them since it would be cheaper to do this tha...