“What do tinker toys, laws, and hotels have in common?” Professor VanDieren asked. As it turns out, quite a bit, if the laws and hotels are mathematical laws and hotels. The tinker toys were used as an introduction to the presentation: we had to build several different structures following various rules, such as “no red pieces can be used” or “you may only use purple and yellow pieces.” We used these laws to create models, and we were continuously subjected to more laws that forced us to adapt our structuring techniques and ultimately change the models. Once we had built enough models, Professor VanDieren explained how mathematicians also use laws to create models, just as we had done with the tinker toys—of course, mathematicians have much more complex rules and models to adhere to.
With the hands-on part completed and understood, the presentation then moved onto the arithmetic-heavy ideas: we were presented with the idea of an infinite hotel and how laws regarding infinite models were used to create it. This led smoothly into Professor VanDieren’s explanation of her own work in the field of models and infinity. It was extremely impressive and very abstract, but her headway in the field has been significant. Not only has she worked for years on theorems concerning this concept, but she has also posited the idea of “tameness” in infinite models, setting the foundation for many other mathematicians to be able to delve into the field.
The presentation was intriguing – but very abstract, and ended with Professor VanDieren giving us a sample of one of her ongoing models. It was neat to be able to learn about high-level mathematics, and Professor VanDieren even said she’d be willing to give an encore presentation if anyone else is interested! Anyone with the slightest interest in math should definitely hear her presentation; it’s unlike anything you will ever encounter anywhere.
– Brittany Burmester