3 March 21

 Today counts 176 years after the birthday of {Georg Cantor}, the German mathematician who created set theory. I put his name inside curly brackets to symbolize the fact (in standard set notation) that he is the unique member of the set containing Georg Cantor (1845-1918). My tie for today is covered with tiny boxes which you could assemble into whatever sets you choose. Set theory provides the foundation for counting things, which is pretty important for many parts of our lives. I asked my mathematician friend Margaret Yoder for some authoritative quotations about set theory, and she provided this one:

"Set theory has a dual role in mathematics. In pure mathematics, it is the place where questions about infinity are studied. Although this is a fascinating study of permanent interest, it does not account for the importance of set theory in applied areas. There the importance stems from the fact that set theory provides an incredibly versatile toolbox for building mathematical models of various phenomena." -- from Jon Barwise and Lawrence Moss, Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena, CSLI, Stanford, 1996.

So now I hope you can see the incredible versatility of noting that the {small bottles in my left hand} and the {red blocks in my right hand} are well-defined, finite sets that share the same cardinality (the number of distinct elements) as the set containing the first two elements in the set of natural numbers (N), which we associate with the "number 2."

Other dimensions of set theory are revealed in statements like these from the Stanford Encyclopedia of Philosophy: "The axioms of set theory imply the existence of a set-theoretic universe so rich that all mathematical objects can be construed as sets. Also, the formal language of pure set theory allows one to formalize all mathematical notions and arguments. Thus, set theory has become the standard foundation for mathematics, as every mathematical object can be viewed as a set, and every theorem of mathematics can be logically deduced in the Predicate Calculus from the axioms of set theory."

As mentioned in the first long quotation, Cantor's set theory applies especially to studying infinity. "One might say that set theory was born in late 1873, when he made the amazing discovery that the linear continuum, that is, the real line, is not countable, meaning that its points cannot be counted using the natural numbers." (Stanford Encyclopedia of Philosophy)

I could go on and on . . .