Avner Ash and Robert Gross: "Summing it Up" | Talks at Google

source: Talks at Google    2016年9月26日
Summing it Up: From One Plus One to Modern Number Theory
Summing It Up, published in May this year, is a book about number theory, for the proverbial "general audience", concentrating on sums and series. It begins with very simple questions about whole numbers, such as "what is the sum of the first n k-th powers" and "how many ways can you break up a positive whole number into whole number parts" and shows how such questions lead naturally to the use of calculus and infinite series. The more advanced methods, besides providing new insight into the original questions, lead to further ideas and new questions. The book ends by discussing "modular forms", which are certain infinite series that were crucial in the proof of Fermat's Last Theorem.
In this talk, the authors will attempt to explain what is number theory, through examples, notably Bernoulli numbers. They will discuss the question "why might (should?) a normal person be interested in number theory?" (Spoiler alert: there is no final answer to that question.)
The authors are both professors of mathematics in Boston College. They both do research in number theory and they both have strong interests in books of all sorts, reading them as well as writing them.