Although this course is old—I took it in 1997—it is always evolving in small ways. For the last several years, students brought literary works involving mathematics to our attention and we discussed various themes present in these books, our lives, and the history of mathematics. Unofficially, we have also found time for students and myself to consider mathematical topics not covered in JTG: the platonic solids, logarithms, slide rules, pythagorean triples, Fermat’s Last Theorem, the millennium problems.
This semester we are going to canonize this extra-curricular work and make some official space and guidelines for it. We will call this “Show and Tell”. The one thing I don’t like about the name—or the term presentation—is that it implies a passive audience. There is a saying, “To learn you must do”.
So how do these work? You will pair off and choose topics. On the assigned day, you get a bit less than half the class time to show us a world we do not yet know. You will also need to turn in something small and permanent to represent your investigation.
This reminder can be a paper-based version of your talk, it can be your slides from a ppt., or it can be a video of the talk. It can be a website, or blog post. Media and format do not matter to me, but it should represent what you learned and hoped to share as well as document your resources so another could follow your tracks and take the next step.
Show and Tell Topics
There are many possible topics. Here are a few possibilities: Fictional works where math plays a big role in the storytelling
- Curious Incident of the Dog in the Nightime
- Proof
- Wild Numbers
- Logicomix
- Uncle Petros and the Goldbach Conjecture
- The Mind-Body Problem
JTG itself brings up more topics than it really goes into. So offhand mentions or other questions emerging from JTGmay be good sources of topics to choose from. We already poke a couple holes in the story of mathematics Dunham gives us in JTGby suggesting that instead of Chapter 5 a group should cover a development in ancient math that does not come from the Greeks, but this story has many parts. Investigating additional non-European mathematics could be a great thing to do, and to get you started in that direction, you may want to check out a great book we are reading a bit of, The Crest of the Peacock.
There are also loads of interesting, accessible mathematical topics present in other “popular” books and other media.
- The Mathematical Experience
- The Cult of Pythagoras
- Yearning for Impossibility
- Beyond Numeracy
- Numberphile
- Vi Hart’s videos.
- 3 Blue 1 Brown
This class however is not just a collection of random mathematical facts, and you should remember this as you look for topics. This class is about seeing the content of math in a meaningful extra-mathematical context. This can be its historical development or changes through time. It can be something that is too often hidden from us, or a set of assumptions that is never questioned. Your topic can focus on how math is done, written about, or interacts with other areas of thought. It is especially interesting when we can see more than one perspective on a mathematical idea since we usually assume that math is monolithic in character.
Some of the books already mentioned are good sources for these kinds of ideas:
The Mathematical Experience – What math really is, how it works, and how it fits into society.
Descartes Dream – The particulars and consequences of mathematizing the world The Cult of Pythagoras – The prevalence of myth (as in false story) in how we think about math and its history.
Yearning for Impossibility – The constructive role that impossible ideas play in the development of math.
Just as we look at math in terms of its development in history and role in society, JTG teaches us to look at math in terms of the role it plays in biography, the individual lives of those who do it. While the fictional works lie somewhere between in that their biography is inspired by but distinct from living persons, there is a lot out there that mixes math and biography.
Loving and Hating Mathematics – Biographical vignettes organized into themes about math and society.
Interviews with current mathematicians on Numberphile, Nova, etc. in relation to current and difficult problems, the meaning of math, etc.
What do I do?
Please, dig deeper than finding a video to bring in. A good video is a great first step, but there is more to do. I do not think “Show and Tell” will live up to its potential if it just ends up being a forum for people to bring in cool videos. Even though the time available is a bit limited, we should aspire to more than being entertained or scratching the surface. Hopefully we together begin to get at the difference between glossy, patronizing treatments and those that dig a bit deeper and ask more from their audiences.
This goes just as much for reading JTG—and maybe digging into video can show you new perspectives on digging into text. Our goal is not to efficiently assimilate a set of facts, methods, etc. and reproduce them for a grade. Instead, we have a chance to work together to learn what math means, how to communicate with it, how to be curious about it, how ideas grow, and how to get to know each other through these kinds of inquiry. Watching a video, reading a book, following a proof presentation are parts of this, but if we take them for the whole, we miss the soul of what we can do together. Here are some questions to ask each other as you work on these “Show and Tell”s.
Why is this topic interesting? Not every bit of math is terribly important in our everyday affairs, but it still needs a context for us to understand why we should bother with it. This can be historical, personal, practical, philosophical etc.
What is there for us to do? Since you cannot learn math without doing it, what do we get to do, either during the presentation, before, or after?
How does this connect to math, themes, questions, we have brought up elsewhere? If this obviously connects to a topic we have already entertained or that will come up, it is pretty insensitive to not make something of this.
What resources did you use? Be specific about where your stuff comes from and provide links when possible. How do you know your source has a fair claim to authority? e.g. if I were to present on the weird idea that 1+2+3+… = -1/12, I would want to do some Googling to make sure this wasn’t just poppycock. This isn’t just pedantic either. Sometimes what makes the story interesting is who thought what, when, and how this came to change.
Why are we better off for knowing this? How can this change how we see the world and how it works? Again, this doesn’t need to be vital to everyone’s everyday life, but there should be some clear consequences, even if it’s only to math itself. Who is this important to and why? What does it change for them?
What do we watch/read, what you do, and do we have an active role?Many possible sources are interesting videos. Having us simply watch them in class is not the best use of large chunks of our time together in most cases. If it’s a short video, you could have us watch it for homework, or you could find excerpts, or otherwise break up the viewing. A proof is not just a bit of logic, it is also a kind of performance. It can be good or bad in many ways, one of which is length. How an you give us something to do as well?
Terminology Most mathematical ideas seem to be naturally held in our heads in a form of visualization. When explaining to someone else, you are trying to help another see. This is hard to do when you use indirect (“this one”), vague, or incorrect names for objects and operations.
Starting discussions This is especially important to think about for what an Honors class is supposed to be. How can a discussion be productive, and not just a lot of hot air? The answer is not as easy as in the case of a math problem. The aim is to provide participants a path between obviousness—yes or no questions—and aimlessness—“What do you think about this?”. Discussions need structure and goals if they are to be productive. Even once you know this, it is not an easy thing to design one.
