Math Club - Ram Murty (Queen's University)
Thursday, February 14th, 2019
Time: 5:30 - 6:30 p.m Place: Jeffery Hall 118
Speaker: Ram Murty (Queen's University)
Title: The Basel Problem.
Abstract: In 1650, Pietro Mengoli posed the problem of explicitly evaluating $$1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots $$ and this had come to be known as the Basel problem. The solution is $\pi^2/6$ and it was discovered by Euler almost a century later in 1734, when Euler was 28 years old.
Euler's proof, though correct, was far from rigorous and had to await further developments in complex analysis to put it on a sure footing. We will give a slick proof that uses only ideas from first year calculus.