Dan Curtin Answers Your Questions

1. What are good books to read to learn the history of mathematics?

One of the best is a textbook: A History of Mathematics, by Victor Katz. A good shorter one is Math Through the Ages: A Gentle History for Teachers and Others, by William P. Berlinghoff, Fernando Q. Gouvêa

2. To you, what is the most interesting mathematical historical moment or discover?

There are so many! The solution of the cubic equation in the early 1500s is important. It led, in part, to the explosion of algebra in Europe leading up to Descartes and ultimately to the Calculus.

3. Who is your favorite mathematician?

Rafael Bombelli of Bologna.

4. What new things are being discovered/pursued in math history? What's hot?

Right now the social history of how mathematics (and science) interacts with the rest of the world, and how mathematical (and scientific) institutions formed so that what had been largely a pursuit of individuals became to some extent more of a group effort.

5. Who do you believe to be the contemporary greats, who will represent our era going forward?

Too many to name: Ingrid Daubechies jumps out. Her work on wavelets is well-thought of and she has provided leadership, including the Presidency of the International Mathematical Union. Somewhat younger is Terence Tao- spectacular work on number theory, and a gifted musician too!

6. Is there an application for your skills outside of academia? [ael: I presume that the student is not referring to your skills as Irish Musician, Guinness drinker, or Step dancer....]

I never tested this! I do have solid mathematical skills. The history requires analytic skills in the much more uncertain world of texts and critical analysis of cause and effect. There are many fields, such as the actuarial world, where careers start with applying mathematics, but eventually, at the highest level, require people skills and more general analytic knowledge. Maybe more down to earth - mathematics majors and history majors are always welcome in law schools.

7. If you could teach any class what would it be?

At last an easy one: MAT 385, The History of Mathematics!!

8. What was the most memorable experience in your career?

There are so many here as well. So many students that I enjoyed getting to know, most were great, but I even remember fondly the few who drove me nuts! For a single memory, it was receiving, in 2013, the national Distinguished Service Award from the Mathematical Association of America. You do the work because it needs to be done, and it is often fun (among the tedium) not for the recognition, but I do have an ego, after all!

9. Do you think that there are still formulas we haven't discovered ourselves, that the ancients knew?

Depends on what you mean by ancient. If you mean Ancient Greece and earlier, I don’t think so, but ancient civilizations did have different ways of looking at things that can spark ideas. Once we reach the time of Descartes and Fermat (1600s,) and after, there might well be a few things, especially among some of the less studied mathematicians.

10. Do you think that we should be incorporating more history of math discussion when teaching to younger students? If so, what do you think would be best to teach to give a better understanding of the standard curriculum?

Practically I think incorporating snippets of historical material as different topics come up is the way to do it for younger students. If time allows you could show them the different techniques the ancients used, explain why they wanted to solve these problems. It is also fun to take problems from ancient books and solve them using today’s methods. A bit ahistorical, but fun, and leads some students to wish to find out the actual history.

11. Related: how do you think a better understanding of math history would affect math students?

For any subject the history adds depth to our understanding. To many students mathematics seems like an abstract grab bag of tricks that dropped out of the sky. Giving some of the history can help put the ideas in context. By hearing of the struggles actual mathematicians had to undergo to find these methods, the students may appreciate them better and understand why they don’t necessarily get the idea without much effort.