I'm definitely a layman compared to you guys when it comes to maths (or 'math' as Geeker and Darla might say), but I've always had a fascination with probability theory and am a fan of Thomas Bayes. I love how counter-intuitive it can appear.
For example, the number of people needed before there's a greater than 50% chance that 2 people will share the same birthday.
Or the famous Monty Hall problem. In fact, in Bernoulli's Fallacy that I mentioned earlier, it publishes several of the angry and derisive letters and complaints that Marilyn vos Savant received for pointing out what must to you guys seem obvious. I think one was from the entire maths faculty at an Ivy league college.
Another is the total misunderstanding, not least by doctors, as to what a drug having a 1% false positive rate actually means.
I am starting to go down a bit of a rabbit hole, though - I suppose it was inevitable! I'm now somewhat obsessed with the 'crisis in statistics', P-values, null hypotheses etc. and the staggeringly low replication rates of previous studies.