Mathematics as Metaphor - Curtis McMullen (Harvard University)

TL;DR

Mathematics is both a part of nature, governing the laws of the universe, and an artifact of human culture, influenced by language and communication.

Transcript

hello hi I'm Steve kerkhof I'm the chairman of the math department here at Stanford and I'd like to welcome you to tonight's lecture by professor Curtis McMullen who's a Cabot professor of mathematics at Harvard this public lecture is one of a series that sponsored by the math department and the Stanford math Research Center it's also a very specia... Read More

Key Insights

• 👮 Mathematics exists in both the natural laws of the universe and as a cultural artifact.
• 💨 Tiling provides a useful way to understand and represent mathematical concepts, such as surfaces and knots.
• ❓ Quantum topology and the Jones polynomial offer insights into the relationship between quantum physics and mathematics.

Summary & Key Takeaways

• Mathematics exists in the laws of the universe, such as general relativity and quantum mechanics, as well as in human culture as a means of communication and understanding complex systems.

• The Platonic solids, such as the cube and dodecahedron, have recurring presence in mathematics and are associated with the elements of nature and the structure of the solar system.

• The concept of tiling, or arranging shapes to fill a space, can be used to represent surfaces of different geniuses, such as the torus and surfaces with handles.

• Knot theory and quantum topology provide insights into the nature of three-dimensional space and the interaction between quantum physics and mathematics.