Last week, I gave a talk titled “Proofs Without Words” during the second episode of our Friday Afternoon Mathematics Undergraduate Seminar (FAMUS). I gave a nearly identical talk two years ago in FAMUS, but I think my delivery was much better this time.

The title might be misleading as I actually spoke quite a few words. Perhaps a better title would have been “Visual Proofs”. The essence of the talk was that I would present the audience with a figure that was meant to convey both the statement and proof of a theorem and then I would try to get them to guess what the corresponding theorem was. It was a lot of fun. If you are interested, here are the slides. I removed the pauses, so if you want to play along, you’ll have to cover up the theorem statement before you see it. My favorite is the one on slide number 6.

The content of my slides was inspired or came directly from the following sources:

Most weeks in FAMUS, the host interviews a faculty member. This time I had the opportunity to interview Dr. John Hagood. This was an absolute pleasure for me as John has had a huge impact on my career. When I did my MS degree at NAU, I had John for three different courses. Without a doubt, he is the best teacher I have ever had. When I started teaching, I attempted emulate him as best I could. I eventually developed my own style, but John has had a lasting effect on my teaching. It was really nice to be able to convey this to the audience in his presence. Thanks John!

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 226: Discrete Math
  MAT 690: CGT

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Land Acknowledgement

  Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.