Summing it Up | Avner Ash & Robert Gross | Talks at Google

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.

[tomkilleen]

Had a difficult day on Monday, and treated myself to Summing It Up. Video is amazing, and I know the book will equally pleasurable to read.

[JC-jihp]

Currently have only read up to the introduction but the subject matter is gripping.

[pierretruchon]

Very interesting and enlightening  presentation.  I will have to revisit some part of it.  I am surprised that since you talked about Ramanujan and Euler or even the Reiman's zeta function, that you didn't talk about the sum of all integers that is said to be equal to -1/12...