# Louise and Richard K. Guy Lecture Series

The Louise and Richard K. Guy Lecture Series celebrates the joy of discovery and wonder in mathematics for everyone. The lecture series was a 90th birthday present from Louise Guy to Richard in recognition of his love of mathematics and his desire to share his passion with the world. Richard Guy is the author of over 100 publications including works in combinatorial game theory, number theory and graph theory. He strives to make mathematics accessible to all. In 2019, the Richard celebrated his 103rd birthday. **Learn more about his life.**

## Sudoku and Mathematics

#### The 19th Louise and Richard Guy Lecture Series

**Title****: **Sudoku and Mathematics

**Speaker: **Peter Cameron, Professor, School of Mathematics, University of St Andrews

**Date: **Thursday, September 26, 2024

**Joining us in person:**

Presentation: 5 - 6 p.m. (MT)

Location: MacEwan Hall Ballroom (3rd Floor MacEwan Students Centre)*On-site registration is available*

**Joining us online (via Livestream)**

Presentation: 5 - 6 p.m. (MT)**View video of presentation****Abstract:** Sudoku was invented by retired New York architect Howard Garns in 1979. But its roots lie much further back, deriving from magic squares, which first appeared in China more than two millennia ago. Since these squares were often thought to have magical properties, including acting as a talisman in battle, they were of great interest, and mathematicians in many cultures investigated them and gave constructions.

One of these was Leonhard Euler, who gave a construction in terms of what he called "Graeco-Latin squares" (and are now called orthogonal Latin squares). His celebrated "36 officers" problem asked whether the 6 by 6 case has a solution. He thought not, but this was not proved for another century.

Latin squares arise now in many areas of mathematics and applications, including statistics, error correction, and cryptography. Statisticians further developed the ideas by inventing the notions of "gerechte design" and "cricial set". If they had put these two notions together, they would have come up with Sudoku. But this was left to Garns. Maki Kaji introduced the puzzle to Japan, where it was named "Sudoku", and New Zealander Wayne Gould turned it into an international sensation.

As well as the history, I will discuss some surrounding areas and further developments.

**Biography: **Peter Cameron was born in Toowoomba, Australia in 1947. He came to Britain in 1968 to do his doctorate under Peter Neumann's supervision. Since then he has held positions at the universities of Oxford and London, as well as a recent part-time position at the University of St Andrews, which he holds currently.

He was the recipient of both junior and senior Whitehead prizes from the London Mathematical Society as well as the Euler Medal from the Institute for Combinatorics and its Applications. He has been an invited speaker at many international conferences including the International Congress of Mathematicians in Kyoto.

His work lies on the borders of algebra and combinatorics, with side interests in logic and statistics. He is currently writing a book on the ubiquitous but mysterious ADE root systems, and has a large project (mostly with Indian mathematicians) about graphs defined on algebraic structures.

In the distant past he was Australian Universities cross-country champion and also ran the London marathon twice.

## Past lectures

**The 18th Richard and Louise Guy Lecture Series**

**Title****: **M.C. Escher's Math side

**Abstract: **Imagery in M.C. Escher's graphic works not only makes obvious use of geometry, but often provides visual metaphors for abstract mathematical concepts. Again and again Escher strived to capture the concept of infinity. He was also fascinated by and a master at depicting symmetry, duality, reflection, relativity, recursion, dimension, and topological change. This lecture (which assumes no mathematical background) will illustrate these mathematical concepts implicit in several of Escher's works, outline the transformation geometry that governs his interlocking figures, and reveal how this "math anxious" artist actually did pioneering mathematical research in order to accomplish his artistic goals.

**Speaker: **Doris Schattschneider, Professor Emerita of Mathematics at Moravian University in Bethlehem, Pennsylvania

**Date: **Thursday, October 5, 2023**Time: **5:00pm MT

**Location: **

- In person location: MacEwan Ballroom. Doors open: 4:30 p.m.
- Online via Zoom

**Biography: **Doris Schattschneider is Professor Emerita of Mathematics at Moravian University in Bethlehem, Pennsylvania. Combining her dual interests in mathematics and art, she has become internationally known for her work on tilings of the plane and her exposition of M.C. Escher’s art. Her book *M.C. Escher: Visions of Symmetry* explores how Escher made and used his drawings of tessellations. In collaboration with graphic designer Wallace Walker, she designed polyhedral forms covered with Escher tessellations that have been published as *M.C. Escher Kaleidocycles*. She has been active in the Mathematical Association of America, serving as Editor of *Mathematics Magazine*, and received their national award for distinguished teaching. She is especially interested in making mathematics visual, and served as Geometer on the project that produced the software *The Geometer’s Sketchpad*. She is a Fellow of the American Mathematical Society.

*Please note that no recording is available for the 2023 lecture due to copyright restrictions.*

**The 17th Richard and Louise Guy Lecture Series**

**Title****: **Richard Guy's Favorite Unsolved Problems

**Abstract: ** Richard Guy loved problems. He loved to share them and to encourage others to explore them. He loved to work with superstars like John Conway and make their ideas accessible to a wider world. But Richard also had a few problems that he obsessed on in his own research, coming back again and again to those problems with new insights and thoughts. In this talk, Dr. Andrew Granville will recall and discuss a few of Richard’s personal favorites.

**Speaker: **Dr. Andrew Granville, Department of Mathematics and Statistics, Université de Montréal

**Date: **Thursday, October 6, 2022**Time: **5:00pm MT

**Location: **

- In person location: Craigie Hall C, Room 105 (seating is limited). Doors open: 4:30 p.m.
- Online via Zoom: Register directly with Zoom

**Biography: **Dr. Andrew Granville is a professor in the Department of Mathematics and Statistics at the Université de Montréal. His broad range of mathematical interests include arithmetic geometry, Diophantine approximation, algorithmic and cryptographic aspects and analytic number theory, and he has more than 160 publications. His writing accomplishments also include a theatrical play and a widely acclaimed graphic novel that explores mathematical themes. Dr. Granville obtained his PhD from Queens University in 1987. In 2002, he joined the Department of Mathematics and Statistics at the Université de Montréal as a senior Canada Research Chair. He was the winner of the 2021 CRM-Fields-PIMS Prize in recognition of his exceptional achievement in the mathematical sciences.

**The 16th Louise and Richard K. Guy Lecture (2021)**

**Title: ***Unsolved Problems in Number Theory*

**Abstract:** Richard Guy's book "Unsolved Problems in Number Theory" was one of the first mathematical books I owned. I will discuss a selection of my favorite problems from the book together with some of the progress that has been made on them in the 30 years since I acquired my copy

**Speaker:**

Dr. Ben Green

Waynflete Professor of Pure Mathematics

Oxford University

**Bio: **Ben Green was born and grew up in Bristol, England. He was educated at Trinity College, Cambridge and has been the Waynflete Professor of Pure Mathematics at Oxford since 2013.

**Date: **Wednesday, September 29, 2021**Time: **Noon – 1:00 p.m. (MT).**Location: **Online

**The 15th Louise and Richard K. Guy Lecture (2020)**

**Title: ***The Notorious Collatz Conjecture*

**Abstract:** Start with any natural number. If it is even, divide it by two. If instead it is odd, multiply it by three and add one. Now repeat this process indefinitely. The Collatz conjecture asserts that no matter how large an initial number one starts with, this process eventually reaches the number one (and then loops back to one indefinitely after that). This conjecture has been tested for quintillions of initial numbers, but remains unsolved in general; it is perhaps one of the simplest to state problems in all of mathematics that remains open; it is also one of the most notorious "mathematical diseases" that can lure professional and amateur mathematicians alike into devoting hours of futile effort into trying to solve the problem. While it is itself mostly a curiosity, and the full resolution still remains well out of reach of current technology, the Collatz problem is a model example of the more general concept of a dynamical system, which occurs throughout mathematics and science; and so progress on the Collatz conjecture can shed some light on the more general problem of understanding dynamical systems. In this lecture we give some of the history of the Collatz conjecture and some of its variants, and also describe some recent partial results on the problem.

**Speaker:**

Dr. Terence Tao

Professor and The James and Carol Collins Chair in the College of Letters and Sciences Mathematics, UCLA

**Bio: **Terence Tao was born in Adelaide, Australia in 1975. He has been a professor of mathematics at UCLA since 1999. Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory. He has received a number of awards, including the Fields Medal in 2006, the MacArthur Fellowship in 2007, the Waterman Award in 2008, and the Breakthrough Prize in Mathematics in 2015. Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society and the National Academy of Sciences

**Date: **Thursday, October 1, 2020**Time: **Doors open at 4:30 p.m.**Lecture: **5 p.m.**Location: **Online

**The 14th Louise and Richard K. Guy Lecture (2019)**

**Abstract:** When you send your credit card number over the Internet, cryptography helps to ensure that no one can steal the number in transit. Julius Caesar and Mary Queen of Scots used cryptography to send secret messages, in the latter case with ill-fated results. Cryptography allows people to share secrets, encrypt messages, and digitally sign documents, and it is used in electronic voting and in cryptocurrencies. Some of the recent exciting breakthroughs in cryptography include elliptic curve cryptography, pairing-based cryptography, identity-based cryptography, and fully homomorphic encryption, all of which are based on advanced mathematics. The talk will discuss cryptography through the ages, and how modern cryptography uses mathematics, especially the field of number theory.

**Speaker:**

Dr. Alice Silverberg

Distinguished Professor of Mathematics and Computer Science at the University of California, Irvine

**Bio: **Alice Silverberg is a distinguished professor of mathematics and computer science at the University of California, Irvine. She has consulted for film and television, has given over 300 invited lectures, writes about Alice's Adventures in Numberland (at https://sites.google.com/site/numberlandadventures/), and occasionally writes mathematically-inspired Scottish country dances. Professor Silverberg's research areas are cryptography and number theory. She earned her undergrad degree summa cum laude from Harvard University, a master's degree and PhD from Princeton University, and a Master of Advanced Study degree from the University of Cambridge. She has been awarded Humboldt, Sloan, IBM, Bunting, and National Science Foundation Fellowships, and has consulted for or done research at a number of industrial labs and research centres including IBM, Microsoft, Xerox PARC, Bell Labs, Sandia National Labs, DoCoMo USA Labs, the Bunting Institute at Harvard University, the Institut des Hautes Études Scientifiques in France, and the Max Planck Institute für Mathematik in Germany.

**Date: **Thursday, Sept. 19, 2019**Time: **Doors open at 4:30 p.m.**Lecture: **5 p.m.**Location: **MacEwan Hall A, Main Campus

**The 13th Louise and Richard K. Guy Lecture (2018)**

**Abstract:** Mathematics can be tasty! It’s a way of thinking, and not just about numbers. Through unexpectedly connected examples from music, juggling, and baking, I will show that math can be made fun and intriguing for all through hands-on activities, examples that everyone can relate to, and funny stories. I’ll present surprisingly high-level mathematics, including some advanced abstract algebra usually only seen by math majors and graduate students. There will be a distinct emphasis on edible examples. Suitable for all ages including keen children.

**Speaker:**

Dr. Eugenia Cheng

Scientist In Residence, School of the Art Institute of Chicago

**Date: **Thursday, Oct. 11, 2018**Time: **Doors open at 4:30 p.m.**Lecture: **5 p.m.**Location: **MacEwan Ballroom, 3rd Floor, MacEwan Student Centre, Main Campus

**The 12th Louise and Richard K. Guy Lecture (2017)**

**Abstract:** Diophantine equations are one of the oldest, frequently celebrated and most abstract objects in mathematics. They crop up in areas ranging from recreational mathematics and puzzles, to cryptography, error correcting codes, and even in studying the structure of viruses. In this talk, Dr. Bennett will attempt to show some of the roles these equations play in modern mathematics and beyond.

**Speaker:**

Michael Bennett

President, Canadian Mathematical Society

Professor of Mathematics, University of British Columbia

**Date: **Thursday, Sept. 21, 2017**Time: **Registration at 4:30 p.m.**Lecture: **5 p.m.**Location: **Science Theatres Building, Room 135

**The 11th Louise and Richard K. Guy Lecture (2016)**

**Abstract:** Mathematics pervades all the sciences, but it also lies at the heart of a number of fields in the humanities. Two such important subjects which go back to ancient times are linguistics and music. In fact, many of the modern mathematical tools used in probability and combinatorics, and tools applied in varied technologies, such as those on NASA space missions, originate in problems encountered by linguists and musicians thousands of years ago. A look at some of these ancient, poetic problems - and their remarkable solutions through the ages - reveals much about the nature of human thought and the origins of mathematics.

**Speaker:**

Manjul Bhargava

Mathematics Department, Princeton University

2014 Fields Medal Winner

**Date: **Thursday, Sept. 15, 2016**Time: **Registration at 4:30 p.m.**Lecture: **5 p.m.**Location: **Science Theatres Building, MacEwan Hall Student Centre, Ballroom

**The 10th Louise and Richard K. Guy Lecture (2015)**

**Abstract:** This talk will demonstrate some of the surprising connections between the mystery of magic and the art of juggling, and some interesting ideas from mathematics. Ronald Graham is chief scientist at the California Institute for Telecommunications and Information Technology and the Irwin and Joan Jacobs professor in computer science and engineering at UC San Diego. He is also an accomplished trampolinist and juggler.

**Speaker:**

Ronald Lewis Graham

University of California, San Diego

**Date: **Thursday, Sept. 27, 2015**Time: **5 p.m. to 6 p.m.**Location: **Science B, Room 103

**The 9th Louise and Richard K. Guy Lecture (2014)**

**Abstract:** One sometimes hears that the indigenous peoples of the Americas are for some reason not predisposed to mathematics. This belief is surprising, as mathematical traditions in the western hemisphere prior to European contact were already rich and extensive. This talk will focus on some of those traditions, primarily Central American but with some information about mathematical traditions in Algonkian cultures such as the Blackfoot. Almost all of this talk will be accessible to any interested listener, with perhaps five minutes in the middle using a small amount of very elementary number theory. Along the way any listener who has ever eaten an 18 Rabbits granola bar will learn why doing so celebrates indigenous mathematics.

**Speaker:**

Edward Doolittle

First Nations University of Canada

**Date: **Thursday, Sept. 18, 2014**Time: **5 p.m. to 6 p.m.**Location: **KNB 132

**The 8th Louise and Richard K. Guy Lecture (2013)**

**Abstract:** How could there be something we don’t know about arithmetic? It would seem that subject was sewed up in third grade. But here’s a problem we don’t know: What is the most efficient method for multiplication? How many different numbers appear in a large multiplication table? Come learn about these types of problems and recent progress.

**Speaker:**

Carl Pomerance

Dartmouth College

**Date: **Thursday, Sept. 12, 2013**Time: **5 p.m. - 6 p.m.**Location: **SB 103

**The 7th Louise and Richard K. Guy Lecture (2012)**

**Abstract: **Doodling has many mathematical aspects: patterns, shapes, numbers and more. Not surprisingly, there are often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.

**Speaker:**

Ravi Vakil

Stanford University

**Date: **Thursday, Sept. 20, 2012**Time: **5 p.m. - 6 p.m.**Location: **SB 103

**The 6th Louise and Richard K. Guy Lecture (2011)**

**Abstract: **To write a musical canon - be it "Three Blind Mice" or the climax of a Bach fugue - one constructs a melody that can act as its own harmony. Thinking about this task leads us to look at musical structure from points of view usually associated with science and mathematics, not the arts. The lecture will be illustrated with diagrams as well as musical examples form various eras and genres (including at least one improvised on the spot), and will require no technical background in either music or mathematics.

**Speaker:**

Noam Elkies

Harvard University

**Date: **Thursday, Sept. 22, 2011**Time:** 4 p.m - 5 p.m.**Location: **MFH 162

**The 5th Louise and Richard K. Guy Lecture (2010)**

**Abstract: **When I was six years old, my father Martin Demaine and I designed and made puzzles as the Erik and Dad Puzzle Company, which distributed to toy stores across Canada. So began our journey into the interactions between algorithms and the arts (here, puzzle design). More and more, we find that our mathematical research and artistic projects converge, with the artistic side inspiring the mathematical side and vice versa. Mathematics itself is an art form, and through other media such as sculpture, puzzles, and magic, the beauty of mathematics can be brought to a wider audience. These artistic endeavors also provide us with deeper insights into the underlying mathematics, by providing physical realizations of objects under consideration, by pointing to interesting special cases and directions to explore, and by suggesting new problems to solve (such as the metapuzzle of how to solve a puzzle). This talk will give several examples in each category, from how our first font design led to building transforming robots, to how studying curved creases in origami led to sculptures at MoMA. The audience will be expected to participate in some live magic demonstrations.

**Speaker:**

Erik Demaine

Massachusetts Institute of Technology

**Date: **Thursday, Sept. 16, 2010**Time: **4 p.m. to 5 p.m.**Location: **Murray Fraser Hall 162

**The 4th Louise and Richard K. Guy Lecture (2009)**

**Abstract: **In the summer of 1965, I worked as a student programmer for Richard Guy and Jack Kenyon generating G-sequences of Nim-like games and searching for patterns in these sequences. Since then, methods for finding repeated subsequences of a sequence have been shown to have consequences in areas as varied as computational biology and prevention of hacker attacks on computer systems. I will focus on Teiresias, a pattern search method due to Isidore Rigoutsos of IBM Research and colleagues. Recent results obtained using this system are causing us to revise our understanding of how genes and proteins work together.

**Speaker:**

William Pulleyblank

Vice President of the Center for Business Optimization,IBM, New York

**Date: **Thursday, Sept. 17, 2009**Time: **4 p.m. - 5 p.m.**Location: **ST 135

**The 3th Louise and Richard K. Guy Lecture (2008)**

**Abstract: **Combinatorial Games like Chess, Checkers and Go (no dice or cards allowed) have been played for millennia. People, especially those who like to win, have developed strategies for some individual games, consider the number of Chess books, but it was only in 1902 that the hint of a foundation for an abstract theory of Combinatorial Games was published. It took 35 years, 75 years or 105 years (depending on your point of view) to get the theory right. I'll explain, by examples, the development of the theory also with an emphasis on the people involved, many of whom are still alive, Richard K. Guy included. This lecture requires no background in mathematics.

**Speaker:**

Richard Nowakowski

Dalhousie University

**Date: **Thursday, Sept. 18, 2008**Time: **4 p.m. - 5 p.m.**Location: **ENA 101

**The 2nd Louise and Richard K. Guy Lecture (2007)**

**Abstract: **What makes a knot? How would you tell a friend over an old-fashioned telephone just which knot you're holding, supposing of course that your friend is just as captivated by mathematics as yourself? Can two knots cancel? I'll show how some such questions can be answered by hand-waving, and some more by childish arithmetic. Be prepared to dance!

**Speaker:**

John Horton Conway

FRS, John von Neumann Distinguished Professor of Mathematics, Princeton University

**Date: **Thursday, Sept. 20, 2007**Time: **2 p.m. to 3 p.m.**Location: **ST 141

**The 1st** **Louise and Richard K. Guy Lecture (2006)**

**Abstract: **One version of the classic travelling salesman problem seeks to determine whether or not, in any given graph, there exists a "Hamiltonian path" which traverses every node exactly once. In the general case, this problem is well-known to be NP Hard. In one interesting subclass of this problem, the nodes are taken to be the first N integers, {1,2,3,...,N}, where there is a branch between J and K iff J+K is in a specified set S = {S[1], S[2], S[3],...,S[M]}. Or, given S, for what values of N does a Hamiltonian path exist? How fast can the elements of S grow such that there exist solutions for infinitely many N? The answer to the second question turns out to be a close relative of the Fibonacci numbers, for which we construct solutions by observing the path of a billiard ball which travels at 45 degree angles to the sides of its table. Using the same billiard ball methodology, we also find some particular solutions when S is the set of squares or the set of cubes.

**Speaker:**

Elwyn Berlekamp

University of California, Berkeley

**Date: **September 2006**Time: **N/A**Location: **N/A