Primes

Primes have been known at least since the time of the Rhind Papyrus (1550 BC) and thoroughly studied since Euclid (300 BC). Around 1800, Gauss and Legendre conjectured that the number of primes between 1 and x is asymptotic to x/ln x, as x tends to infinity. It took many brilliant mathematicians nearly a century (and many incorrect proofs) to prove that result (Hadamard and De La Val ee Poussin, 1896). The road to this proof gave rise, among many other things, to what is still considered the most important unsolved problem in mathematics, the Riemann Hypothesis. In this talk, we discuss (very informally) various aspects of number theory and illustrate those with pictures and theorems about primes. We focus on questions like, how many primes are there? What are the gaps between them? Why do we need to know about complex analysis if we study number theory? We’ll address the “schism” between algebraic and analytic techniques. Some of the techniques to study prime transformed into what are now established branches of mathematics (complex analysis, and abstract algebra). This talk is accessible to anyone with a basic understanding of undergraduate calculus and undergraduate linear algebra. The emphasis is not on proofs but on intuition and visual cues. 

Speaker

ISA Visiting Fellow - J.J.P. Veerman

Portland State University, Oregon, U.S.A.

Visit Prof. Veerman's web page

PhD students and researchers who are interested may request an attendance certificate.