On Tuesday, April 28, Anatoly Vorobey will be speaking on How Modern Math Is Different, and we'll have the usual chance to chat with other interesting people.
Mathematics has been rapidly growing and changing over the last 250 years. This continued progress, however, has not been level or uniform. In this talk I will describe a quiet revolution that happened in math on and around the end of the 19th and the beginning of the 20th century. Just a few decades saw a decisive change in how mathematics "works", in several different aspects:
* How mathematicians see math and its goals;
* How mathematics sees its relationship with other sciences;
* How mathematicians approach the goals of rigor and precision;
* And most of all, what kind of entities math is "built out of", what are its basic building blocks.
None of these changes ever made it into the typical curriculum for high school or below. Some of these changes are felt by science and engineering students as they begin their undergraduate studies, but most of them are only apparent to professional mathematicians. I will attempt to describe as simply as I can what is it that makes modern math different from the 19th century math or from other sciences. No particular math material beyond the high school curriculum will be assumed.