Logical difficulties in modern mathematics (2012)
Did the guy ever deliver on his promise to create a better system?  I thought the problems he was pointing out was motivation for a better system (that united the naive understanding and rigor better?), but the further into the article I got, the more it just seemed like a list of complaints.<p>Having 1) studied &quot;naive statistics&quot; when I was young and 2) learning the full-on measure-theory version a la Bourbaki, and now 3) using applied statistics every day, I can say the naive version is the most useful by far.  Yes, there is hand waving, but the hand waving works, and you really don&#x27;t get into that much trouble unless you try to be pathological.<p>I admit, it would be great to have a version where the naive intuition (many of which are motivated by empirics, physics, and real world situations) and the theoretical definition matched better.  Even still, I don&#x27;t think the formal treatment is appropriate as an introduction -- it&#x27;s an unnecessary hazing on learning minds when they can get most of the value with a bit of hand waving.