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Studying the original manuscripts that developed mathematical ideas played a key role in Ralph C. Huffer Endowed Chair in Mathematics and Astronomy Ranjan Roy’s latest research.
Earlier this year, Roy published Sources in the Development of Mathematics, a textbook in which he discusses the evolution and development of mathematical ideas. In the book (which took him 10 years to research and write), he focuses on some important mathematical discoveries in history and charts the origin of these discoveries. He traveled to England’s Cambridge University to study 400-year-old original manuscripts, many of which were in Latin, German, French, and Russian. One mathematician that Roy studied there was Leonhard Euler, who created the theory of hypergeometric series and q-series.
Roy was surprised in the course of his research by how long it took to develop and perfect many of the most basic mathematical concepts, methods, and practices. For example, it took a hundred years of effort from the keenest mathematical minds, including Gottfried Leibniz, the Bernoulli family, and Euler, to develop the elementary functions in the form that they are now taught in pre-calculus and calculus.
Students will get to read more about Roy’s research — and Euler’s theories, as well as those of other mathematicians — because he will be using the textbook this spring in a capstone course called Development of Mathematics, which focuses on the development and evolution of mathematical ideas.
Roy’s book teaches that not all interesting mathematical ideas, theories, and proofs of formulas and theorems developed by mathematicians of the past have been written about in textbooks and may not have entered mainstream mathematics. It is a common practice among people in literature and philosophy to study the earlier practitioners of their disciplines; mathematicians could profitably do the same, according to Roy.
Roy is currently working on a second book on the development of mathematics that is not yet titled, but will serve as a continuation of Sources in the Development of Mathematics. Researching math is unique from researching other topics, according to Roy, because it is not dependent on being translated to English.
“With math, the neat thing is (that) there are formulas you can look at to see what (the writer is) doing (even when you don’t know the language),” Roy said. “I was reading a paper by Euler and saw a formula at the top and a formula at the bottom and saw a way of getting to the bottom from the top. A translator confirmed what I thought.”
While the formulas guide the reader and provide a general outline before translation, Roy noted, it is still necessary much of the time to translate in order to read math in different languages.
Source: Ranjan Roy is a professor of mathematics. He typically teaches courses in calculus, linear algebra, real analysis, computer analysis, and some special topics. He was Beloit College’s “Teacher of the Year” in 1986 and 2000. Roy was named a Distinguished Teacher of Mathematics in 2001 by the Mathematical Association of America, which also awarded him the Allendoerfer Prize for expository writing in 1990. His research interests include algebraic number theory, hypergeometric series, differential equations, and the history of mathematics. Roy can serve as a media contact for information related to his research and teaching