What words come to your mind when you think about geometry? Lines? points? Boredom? When I was in High School, I was only moderately interested in geometry and mathematics. Most of the time it seemed like drudgery and I also was not sure I was very good at mathematics anyway.

Eventually I realized there was a whole exciting and, quite frankly, mind bending world of modern geometric mathematics. Nowadays when I think of geometry, here are some of the words and phrases that come to mind (you may be surprised).

1. Orders of infinity (yes some infinities are bigger than others)
2. Musical spaces and geometries, heavy metal electric guitar, fret board geometry.
3. “Square circles” at the edge of the universe, curved space.
4. Computer graphics, virtual reality.
5. Psychedelic atoms of reality, symmetries, gauge group representations, spin, quantum mechanics.
6. Non-Euclidean, curvature, topological twisting, torsion.
7. Fourth dimension, fifth dimension etc. Flying through infinite dimensions.
8. Curved space-time, time travel, black holes.
9. Parallel universes.
10. Fractals, objects whose dimension can be a fractional number like 2/3!
11. Decomposing reality into its frequencies.
12. Physics.
13. Minimal surfaces, soap bubbles, microscopic life. (See here: http://www.miqel.com/fractals_math_patterns/visual-math-minimal-surfaces.html)
14. Eternal truth.
15. Crop circles, aliens, juggling.

Some questions we will answer:

• What does electric guitar have to do with flying through infinite dimensions of a so called Hilbert space? What exactly does “dimension” mean anyway?
• What is non-Euclidean geometry?
• What is “the calculus” and why is it just about the greatest intellectual achievement ever?
• What does vibration have to do with the shapes of things? (the quantum mechanics of flowers, rocks, and minds)
• Do parallel lines really never meet?
• How can we tell if space is curved and what does this even mean?
• When is the sum of the interior angles of a triangle not equal to 180 degrees?

We all know that mathematics is the foundation of all the hard sciences and of engineering and therefore leads to, well, money among other things. However, what I plan to demonstrate to anyone who attends my talks and workshops is that mathematics is intrinsically interesting and exciting to the point that many would do it even if there were no money to be made. Of course, there is plenty of money to be made.

Alien Forest in Neoplatonic Mathworld

For further information email:  jeffrey.lee@ttu.edu

Back to:  TTU Summer Math Academy