Esteemed algebraic number theorist Professor Frank Calegari gave a public talk titled ‘The secrets of Pi (and other transcendental numbers)’ on 23 November 2022, hosted by SMRI. The lecture took place at the University of Sydney Nanoscience Hub and was followed by a reception for attendees. Attendees interacted with mathematical activities, including evaluating integrals/infinite sums and approximating Pi, as well as demonstrations by students from the Sydney University Mathematical Society (SUMS).

#### Event photo gallery

All photographs by Jayne Ion.

**Talk abstract: **Since antiquity, mathematicians have understood that the ratio of the circumference of a circle to its diameter is a fundamental constant, the real number now known as Pi = 3.141529…Throughout the centuries, the number Pi has come up again and again in mathematics in many totally different contexts — as the special value of various integrals, the solution to questions in probability, and many more places.

In this talk, we will explore a conjecture, formalised by Grothendieck, which explains how seemingly different occurrences of Pi (as well as many other interesting mathematical constants) should all be related. These numbers are linked to some the biggest open problems in algebra and number theory.

**About the speaker**: Born in Melbourne, Frank Calegari attended Melbourne University as an undergraduate and completed his graduate studies under Ken Ribet at the University of California at Berkeley. He has been a postdoctoral fellow at Harvard and was a Fellow of the American Mathematical Institute from 2002-2007, and a von Neumann Fellow of Mathematics at the Institute for Advanced Study from 2010 to 2011.

Frank joined the Faculty of Northwestern University in 2006 and since 2015, he has been a Professor of Mathematics at the University of Chicago. Frank’s numerous awards include a Sloan Fellowship in 2009 and in 2013 he became a fellow of the American Mathematical Society.

Frank’s other interests include coffee, cooking, cricket, and classical piano; he performed live with Zubin Mehta and the Israeli Philharmonic Orchestra.

**About the ****Mahler Lecture Tour**: The Mahler lectures are a biennial activity organised by the Australian Mathematical Society, and supported by the Australian Mathematical Sciences Institute. The tour invites a prominent international mathematician to travel to Australian universities to deliver lectures at a variety of levels, including several public lectures.