Bruce J. Petrie

Ph.D. Candidate

Supervised by Craig Fraser
Institute for the History and Philosophy of Science and Technology (IHPST)
Victoria College
University of Toronto
Toronto, Ontario, Canada
M5S 1K7
b.petrie@utoronto.ca

Education

Research Interests

"Each new major achievement in the theory of transcendental numbers is linked with the emergence of a new method." [1]

When the prominent mathematician David Hilbert gave his famous 1900 Paris Address he claimed “We know that every age has its own problems, which the following age either solves or casts away as profitless to be replaced by new ones…The deep significance of certain problems for the advance of mathematical science in general and the important role which they play in the work of the individual investigator are not to be denied." During the address, Hilbert listed ten problems (although twenty-three later appeared in print) that would direct mathematical research for the new century. One of his ten problems concerned the transcendence of two numbers 2^sqrt(2) and e^PI. In 1900, transcendental number theory was the frontier of mathematical research.

My doctoral dissertation will be an investigation of an important topic in the history of modern mathematics, the origin and development of transcendental number theory. A transcendental number is not the root of any polynomial with rational coefficients. A polynomial is defined to be an expression involving a sum of powers in one or more variables multiplied by coefficients, ex. a*x^n + b*x^(n-1) + c*x^(n-2) +... . In 1844 Joseph Liouville was the first person to demonstrate a number was transcendental (actually a whole family of them) and thus proved their mathematical existence. My investigation into transcendental number theory will uncover the specific catalysts, intuitions, and motivations of its pioneers (such as Leonard Euler, Johann Lambert, Joseph Liouville, Charles Hermite, and Ferdinand von Lindemann). I will examine how the concept of transcendence arose in mathematics and reveal what Liouville needed to conceive his approximation theorem and the first family of transcendental numbers. It is my agenda to not only expose the new methods mentioned by Fel'dman and Shidlovskii but also to trace their origins.

[1] Fel’dman, N. I. & Shidlovski, A. B. "The Development and Present State of the Theory of Transcendental Numbers”, Russian Math. Surv., 1967, 22 (3), 1-79.

Current Projects and Upcoming Presentations

Awards

Teaching Experience

Professional Associations

Unpublished Contributions and Previous Presentations

EUREKA!

I have been happily married for 6 years and could not have accomplished what I have had it not been for the loving support of my wife. In my spare time, I am an avid World of Warcraft player and if you're really nerdy (like me) you can look up my "main" character here. I also enjoy making machinima movies and display them on my Youtube account and Warcraft Movies Account as well.
Last Update: December 2009