### Mathematics you thought you knew

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, October 23, 2024 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker

**Please Note:** Further notes on the talk: “Mathematically, what is 5 feet divided by 2 secs?” In other words, how do we make this question mathematically rigorous? The answer was initiated by Newton, carefully explained by Hölder in 1901 using axioms of a quantity space, and finally generalized by Hassler Whitney in the 1960s. Whitney’s explanation is a bit idiosyncratic and hard to understand in terms of modern vector bundle theory. Jim Madden and I reworked it so that it makes sense in terms of tensor products of 1-dimensional vector spaces with a chosen basis element.

Mathematically, what is a 5 feet divided by 2 seconds? Is it 2.5 ft/sec? What is a foot per second? We go through several examples of basic mathematical terms you learned in elementary, middle, and high school and understand them at a deeper, graduate student level. You may be surprised to learn that things you thought you knew were actually put on very weak mathematical foundations. The goal is to learn what those foundations are so that you can bring these basic ideas into your classroom in a non-pedantic-but-mathematically sound way.