I recently read an interesting article titled How a Math Genius Hacked OkCupid to Find True Love. It tells the story of a PhD researcher who, tired of being ignored on a dating site, applied contemporary machine learning algorithms to find his optimal target groups of women and the optimal profiles to attract them. I was amused and horrified at the same time.
Suppose you have a set of observations (measurements) and want to assess how well they fall into an ideal target range. Here are a few thoughts on how to go beyond the most obvious measure: percentage of “in-range values”.
My 2012 New Year Wish has some beautiful mathematics: beautifully simple, beautifully abstract, and beautifully mysterious. Want to peek under her skirts?
Our long journey through the infinite lands is coming to an end. What end is there to infinity, you ask? I’d have to put on a theologian’s hat to answer that. But as a mathematician, I can answer a question much more daring: what end is there to infinities?
Can there be any fact more shocking than that there are two infinities, one bigger than the other? Well, take a guess… But to crack the mystery underlying the existence of two different infinities, we first need to learn a little more from set theory… Monkeys, sheep, and leopards return!
Let’s challenge our notion of infinity by stating a downright crazy idea… and then proving it beyond any doubt.
We know that the natural numbers 1,2,3,… go off to infinity. But what happens when we consider negative numbers -1,-2,-3,… as well? How many numbers do we get? And what about fractions? Do we have multiple infinities?
Let’s quickly recap the most important (and weird) properties of the “natural numbers infinity” we call <$\aleph_0$>.
Back in spring I started a series on interesting mathematical topics for the layman. Now I’m back with some fresh stuff. I’m still aiming to explain thrilling areas of pure mathematics to a non-mathematical audience.