Schedule of Plenary Speakers

The plenary speakers for the 2016 ISMAA Annual meeting are:

- William Dunham (George Pόlya Lecturer, MAA)
- Richard Laugesen (University of Illinois at Urbana-Champaign)
- Matt Boelkins (MAA, Grand Valley State University)
- John McCarthy (Washington University in St. Louis)

Abstracts

Title: **Two (More) Morsels from Euler**

Speaker: William Dunham, George Pόlya Lecturer, MAA

Abstract: Leonhard Euler (1707 – 1783) is responsible for a stunning array of famous theorems,
formulas, and concepts. In this talk we examine a pair of lesser-known results where his
genius was on full display.

The first is a curious problem from number theory. Euler sought four different whole
numbers, the sum of any pair of which is a perfect square. With characteristic ingenuity,
he came up with this fearsome foursome: 18530, 38114, 45986, and 65570. We’ll look
over his shoulder to see how he did it.

Moving from number theory to analysis, we consider the series of reciprocals of squares– i.e., 1 + 1/4 + 1/9 + 1/16 + … Through his career, Euler gave (at least) three different
proofs that this sums to [(pi)^2]/ 6 . Here we present the argument from his 1755 text on
differential calculus. The amazing thing about this derivation is that he used l’Hospital’s
rule … not once nor twice, but thrice!

These two results, which require only elementary mathematics, are reminders of why Euler is justly considered “the master of us all.”

Title: **Two pictures and a quotation: Dido, drums and isospectrality**

Speaker: Richard Laugesen, University of Illinois at Urbana-Champaign

Professor and Director of Graduate Studies

http://www.math.illinois.edu/~laugesen/

http://www.math.illinois.edu/GraduateProgram/

Abstract:

Why does your cat curl into a ball on a cold night? What did the cat teach Lord Rayleigh? And what might you be missing if you close your eyes at the orchestra?

Title: Fibonacci's Garden

Speaker: Matt Boelkins (MAA, Grand Valley State University)

Abstract:
Why do so many spectacular spirals appear in these coneflower and sunflower pictures? Why are the seeds in each packed so efficiently?

A marvelous combination of plant biology, mathematics, and a computer model enables us to generate seeds according to a fixed angle of rotation, experiment with different angles, and explore patterns in the numbering of seeds. In so doing, we discover some startling connections between a famous number and the ubiquitous Fibonacci sequence that help explain these spiral patterns and the evident beauty that captures our eye.

Along the way, we'll also discuss the nature of mathematics and think about some of the deep observations and questions about mathematics posed by a few of humankind's greatest minds.

How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?'' - Albert Einstein

Title:
**Wondjohnerland. How Pure Mathematics can help Medicine**

Speaker: John McCarthy, University of Washington in St. Louis

Abstract: Our ability to gather quantitative measurements has grown much faster than our ability to analyze it intelligently. This is particularly true in Medicine. Mathematicians all know that applied mathematics and statistics are essential to understand what can be learned from the data. I will discuss some examples of how pure mathematics can also contribute, and argue that the perspective that pure mathematicians bring to the

table can lead to insights that would not otherwise have occurred.