Dr. Shirley Gray and Dr. Silvia Heubach, both Professors of Mathematics, gave keynote address during the regional meeting of the Mathematics Association of America (October 22, 2016).
Shirley Gray talk on fusion mathematics aptly integrated her love of math and history. Fusion Mathematics: No treatise of mathematics has attracted more international attention in the past decade than the Palimpsest of Archimedes. The 1998 auction at Christie’s, followed by collaborative work centered at the Walters Art Museum led to traveling museum exhibits, newspaper articles, television specials, and dozens of presentations. Mathematicians and other scholars attracted a new and significant audience. The singed, battered, faded, mildewed, damaged 10th century manuscript—the world’s oldest copy of The Method of Archimedes—sold for $2 million “under the hammer.”
In the true Archimedean experimental tradition, my team of students and faculty decided to look not retrospectively at the content of propositions in The Method but rather in terms of 21st century mathematics and technology. “We believe we participated in every scholar’s quest to have a Eureka moment—we found the Golden Ratio in our attempts to image the footprint of Archimedes.” This discovery led to several publications and a Wikipedia article. But perhaps more importantly, our work in simultaneously embracing computer graphics, computer science, pure mathematics and 3-D printer modeling may reap huge benefits for future research in a new field that we call fusion mathematics.
Silvia Heubach’s talk was entitled The Game Creation Operator. Combinatorial games are games in which both players have full knowledge of the available moves – no chance is involved! We will focus on vector subtraction games, in which two players alternately remove tokens from a number of stacks. The well-known game of NIM is an example this type of combinatorial game. For vector subtraction games, the allowed moves are given as a set of vectors that indicate how many tokens can be removed from the respective stacks. Game positions are described by vectors listing the respective stack heights, so moves and positions have the same structure. This allows us to define a game creation operator that generates a new game by selecting specific positions in the current game and making them the moves in the new game. We will explore properties of this operator and the behavior of the sequence of games it creates for vector subtraction games on any number of stacks, and give more specific results for games on one and two stacks.