Norman Wildberger Might Do it
Are finite multisets the foundation for mathematics?
Norman Wildberger might be the guy to place mathematics on firm foundations.
In the story I’m telling about history, our present dark age was precipitated by the foundations of mathematics being undermined in the late 19th century. The castle was destroyed and never rebuilt.
Wildberger is trying to rebuild the castle, finally.
Despite my criticism of set theory, I have actually become persuaded that set theory is indeed the foundation for math — but finite sets, not infinite sets!
The fact that his upcoming book is titled: "Box Arithmetic: A Finite Multiset Foundation for Mathematics" made my spine tingle.
It’s way, way, way too early to say whether he’ll accomplish the mission. But he’s the only person I’m aware of with technical sophistication who has possibly found the right foundations.
I felt excited and obligated to tell you, dear reader, the day his video came out :).
(For what it’s worth, if this does check out, I will likely be spending a large amount of energy, and part of my career, fleshing out the implications of this work.)
You've got it exactly right. Wildberger is the man with the intelligence and vision — and courage! — needed to, as you put it yourself, "replace" mathematics as we currently know and teach it. It's a monumental job, and it's no wonder Wildberger has been largely marginalized by the mathematics (and philosophy of mathematics) "establishment". If I were a young man (I'm 75, with health issues), I would certainly want to be an active participant in this important work. Please do give serious consideration to doing so yourself! -- Jerry Balzano. Prof Emeritus, UC San DIego
This was very interesting. Thanks!