Pi Day Is Upon Us Again and We Still Do Not Know if Pi Is Normal

Abstract

The digits of π have intrigued both the public and research mathematicians from the beginning of time. This article briefly reviews the history of this venerable constant, and then describes some recent research on the question of whether π is normal, or, in other words, whether its digits are statistically random in a specific sense.

Additional information

Notes on contributors

David H. Bailey

DAVID H. BAILEY. In June 2013, David H. Bailey retired from the Lawrence Berkeley National Laboratory (LBNL), after 15 years of service, although he still holds a Research Fellow appointment at the University of California, Davis. Prior to coming to LBNL in 1998, he was a computer scientist for 15 years at the NASA Ames Research Center. In the field of high-performance scientific computing, Bailey has published research in numerical algorithms, parallel computing, high-precision computation and supercomputer performance. He was the first recipient of the Sidney Fernbach Award from the IEEE Computer Society, and more recently the Gordon Bell Prize from the Association for Computing Machinery.

Bailey is also active in computational and experimental mathematics, applying techniques from high performance computing to problems in research mathematics. His best-known paper in this area (co-authored with Peter Borwein and Simon Plouffe) describes what is now known as the “BBP” formula for pi. In two more recent papers, Bailey and the late Richard Crandall demonstrated a connection between these formulas and a fundamental question about the digit randomness of pi. Bailey has received the Chauvenet Prize and the Merten Hesse Prize from the Mathematical Association of America, in each case jointly with Jonathan Borwein and Peter Borwein.

Jonathan Borwein

JONATHAN MICHAEL BORWEIN is a Laureate Professor of mathematics at the University of Newcastle, NSW Australia. His research interests include functional analysis, optimization, high performance computing, number theory, and he is one of the leading advocates of experimental mathematics. He has authored over a dozen books and more than 400 articles. With more than 5500 ISI citations, he is an ISI “highly cited mathematician.”

Prof. Borwein received his D.Phil. from Oxford University in 1974 as a Rhodes Scholar. He has worked at Dalhousie University (1974–1991, 2004–2009), Carnegie Mellon University (1980–1982), the University of Waterloo (1991–1993), and Simon Fraser University (1993–2003). He is a fellow of the Royal Society of Canada, the American Association for the Advancement of Science, the Australian Academy of Science and a foreign member of the Bulgarian Academy of Sciences. Jon was a Governor at large of the Mathematical Association of America (2004–2007), is past president of the Canadian Mathematical Society (2000–2002) and past chair of NATO's scientific programs. He currently chairs the Scientific Advisory Committee of the Australian Mathematical Sciences Institute (AMSI). In 1993 he shared the Chauvenet Prize with David Bailey and his brother Peter. Among many other achievements, he is known for co-authoring the Borwein–Preiss variational principle, and Borwein's algorithm for pi.