10 of Today’s Most Influential Mathematicians

Mathematics has continually expanded into more and more powerful and abstract areas of study. Professional mathematicians understandably specialize, and only a few truly great mathematicians can honestly be said to understand most of the field. Yet, in the end, mathematics remains counting. The study of numbers (and numerical treatments of structures, shapes, and changes) is one of the most powerful fields of study-one of the central discoveries of all of humankind-that has made possible modern science and technology, from abstract physics to the blueprints for an iPhone or automobile. Math runs the world. And in this list, we’ll get introduced to the most influential-and brilliant-mathematicians in our modern world.

In what follows, we look at influential mathematicians over the last decade. Based on our ranking methodology, these individuals have significantly impacted the academic discipline of mathematics within 2010–2020. Influence can be produced in a variety of ways. Some have had revolutionary ideas, some may have climbed by popularity, but all are academicians primarily working in mathematics.

1.Keith Devlin

Devlin is formerly a Consulting Professor of Mathematics at Stanford University and now co-founder and Executive Director of Stanford’s Human-Sciences and Technologies Advanced Research Institute, founded in 2006. He is also a member of Stanford’s Center for the Study of Language and Information (CSLI), an important research center for work in computational linguistics, computer science, and mathematics. Devlin received his bachelor’s (special) in mathematics at Kings College, London and his Ph.D. in Mathematics from the University of Bristol in 1971.

Devlin is a prolific writer about mathematics and related scientific disciplines, writing both for specialists and a general readership. He has authored over 30 books during his storied career as a mathematician, and 80 research articles! No wonder, then, that in 2007 Devlin was awarded the Carl Sagan Prize for Science Popularization. These days, Devlin’s research is focused mainly on applying media and other technologies to help students and others learn about math. For instance, he is co-founder and president of BrainQuake, a company that makes video games to facilitate learning mathematics. He is also known as the “Math Guy” on NPR’s Weekend Edition Saturday, where he is a commentator.

Devlin became a Fellow of the American Mathematical Society in 2012.

2.Terence Tao

Tao is arguably the greatest living mathematician, and has been called the greatest mathematician of his generation. Born in South Australia, Tao was a child prodigy, the youngest person ever to win a medal in the International Mathematical Olympiad-he was ten. He has since won the Field Medal, the “Nobel Prize” for mathematicians. Terence Tao holds the James and Carol Collins Chair in Mathematics at the University of California, Los Angeles (UCLA).

At the age of 14, Tao attended the Research Science Institute, a summer seminar for talented high school students hosted by the Massachusetts Institute of Technology (MIT). At the age of 16, he received his bachelor’s and master’s degrees in mathematics at Princeton University. He received his Ph.D. from Princeton at age 20. He joined UCLA at the age of 24 and became the youngest person ever appointed to full professor by the university.

Tao’s focus is on partial differential equations, a nonlinear area of calculus, or the mathematics of change. Those who know him are quick to point out that he has an impressive grasp of seemingly all of mathematics-a rare feat, particularly today in an age of specialization. He has also done important work in fields as diverse as probability theory to number theory. As fellow mathematician Timothy Gowers put it when reviewing one of Tao’s books, “it is not easy to find gaps in Tao’s knowledge, and if you do then you may well find that the gaps have been filled a year later.”

Tao has won numerous awards, including but not limited to the Field Medal (referenced above), in 2006 a MacArthur Award (the “genius” award), Fellow of the Royal Society (2007), and in 2009 he was inducted into the American Academy of Arts and Sciences.

3.Ian Stewart

Stewart is Emeritus Professor of Mathematics at the University of Warwick, England. Stewart received his bachelor’s of arts degree (first class) in mathematics from the University of Cambridge in 1966 and his Ph.D. in Mathematics at the University of Warwick in 1969.

Stewart is a gifted mathematician who is also a writer of popular science and science fiction. A fertile mind, his primary focus in mathematics is a subfield of the study of dynamic systems known as catastrophe theory. He has also published widely on diverse topics in mathematics, including his book on chaos theory, Does God Play Dice: The New Mathematics of Chaos, published in 1989. Over the years, he has written nearly 100 articles for the well-known science and mathematics publication Scientific American. He even has his own iPad app, Incredible Numbers by Professor Ian Stewart.

Stewart received the Michael Faraday Medal in 1995 for “communicating science to UK audiences,” the mission of the Medal. He was elected a Fellow of the Royal Society in 2001.

4. John Stillwell

Born in Melbourne, Australia, John Stillwell holds the title of professor emeritus at the University of San Francisco. Though Stillwell came to USF in 2002, he spent the bulk of his career at Monash University in Melbourne from 1970–2001. Stillwell earned his PhD at Massachusetts Institute of Technology in 1970.

Stillwell is best known as a source of knowledge and education in mathematics. He has been influential as the author of numerous books on subjects in mathematics, including the history of math in the last two centuries, the foundations of mathematics, algebra, number theory, and geometry. His books are both widely-used textbooks, and popular publications, such Mathematics and its History, Yearning for the Impossible and Reverse Mathematics.

For his work, Stillwell has received awards and honors including the Chauvenet Prize of the Mathematical Association of America, the book award of the Association of Jesuit Colleges and Universities, and was invited to speak at the International Congress of Mathematicians in 1994.

5.Bruce C. Berndt

Berndt is the Michio Suzuki Distinguished Research Professor of Mathematics at the University of Illinois Urbana-Champaign. Berndt received his undergraduate degree from Albion College in Michigan in 1961. He received his master’s and Ph.D. in Mathematics from the University of Wisconsin–Madison. With the exception of a year as visiting professor at the University of Glasgow in Scotland and a one-year stint at the Institute for Advanced Study at Princeton, Berndt has enjoyed his long and stellar career teaching and researching mathematics at the University of Illinois.

Berndt is world-famous as one of the greatest analytic number theorists, a core area in mathematics exploring the properties of number systems, such as the integers. He is perhaps best known for working out the results of the singular genius Srinivasa Ramanujan, a “prophet” of mathematics discovered by talents in the United States after solving some of the world’s most difficult problems in mathematics without the benefit of formal and extensive mathematical training. Berndt received a coveted Steele Prize for his work on Ramanujan’s notebooks, and also serves as editor of the Ramanujan Journal.

Berndt was named Fellow of the American Mathematical Society in 2012. In 2012, SASTRA University in India also awarded him an honorary doctorate.

6.Timothy Gowers

Gowers is Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, UK. He also holds the Rouse Ball Chair in Mathematics at Cambridge (Roger Penrose holds this Chair at the other granting institution, Oxford), and is a Fellow of Trinity College, Cambridge. Gowers received his early training at King’s College and Eton, where he was a King’s Scholar. He received his Ph.D. from Trinity College, Cambridge University in 1990.

A British mathematician, Gowers’ work has been primarily in functional analysis, and in particular in the vector construct known as a Banach space. He has also performed fundamental work in combinatorics and number theory (of combinatorial number theory), proving a number of important lemmas and results, as well as introducing the concept of a quasi random group in 2005. Most recently, Gowers has taken up the perennial problem in mathematics, the conjecture that “P does not equal NP,” or in other words that complex problems in computational theory (NP problems) cannot be reduced to a simpler class of problem, known as P.

Gowers also helped to popularize mathematics, writing a book for a general readership in 2002 titled Mathematics: A Very Short Introduction. Interestingly, he also served as a consultant on the movie Proof in 2005. He is also active in encouraging collaboration on difficult problems in mathematics online.

Gowers won the Fields Medal in 1998. He was knighted by the Queen (British Monarchy) for his services to mathematics in 2012.

7.Peter Sarnak

Sarnak is a permanent faculty member in Mathematics at the Institute for Advanced Study (IAS). The IAS is located on 1 Einstein Drive in Princeton, New Jersey, an address inspired by Albert Einstein’s famous tenure there in the early and mid-20th century. Some of the greatest mathematical minds in modern times have called the IAS home, like John Von Neumann of early computing fame. Sarnak is thus in good company, past and present. Sarnak is also the Eugene Higgins Professor of Mathematics at Princeton University.

Sarnak received two bachelor’s degrees in mathematics from the University of the Witwatersrand in South Africa in 1975 and 1976 and his Ph.D. in Mathematics from Stanford University in 1980. He works on problems in analytic number theory, and his contributions have had important applications to other scientific areas like physics and computer science. Sarnak also invented a field known as “arithmetical quantum chaos,” and performed work leading to a solution to a famous unsolved problem in mathematics known as Hilbert’s Eleventh Problem after mathematician David Hilbert, a 19th century mathematician who issues a challenge to mathematicians at the turn of the 19th century as a list of twelve unsolved problems.

Sarnak has won numerous awards during his outstanding career in number theory, including the George Polya Prize in 1998, and most recently a Sylvester Medal in 2019.

8.Martin Hairer

Sir Martin Hairer is currently a professor of mathematics and Chair in Probability and Stochastic Analysis at Imperial College London in the Faculty of Natural Sciences, Department of Mathematics. Previously, he held roles at the University of Warwick, and the Courant Institute of New York University. An Austrian Citizen born in Geneva, Switzerland, Hairer completed his BS in mathematics at the University of Geneva in 1994. He stayed there for his MS and PhD in physics, completed in 2001.

Hairer is known as the leading name in stochastic partial differential equations, with significant implications for areas including quantum field theory and spatial modeling. In his research, Hairer has produced groundbreaking results in the construction of stochastic systems, stochastic analysis techniques, and his theory of regularity structures, fueling further research and advancement.

For his work, Hairer has received awards and honors including the 2014 Fields Medal, the Whitehead Prize, an Advanced Research Fellowship with the Engineering and Physical Sciences Research Council, Fellowship with the Royal Society, and holds the honorary title of Knight Commander of the Order of the British Empire.

9. Andrew Wiles

Wiles is Royal Society Research Professor at the University of Oxford. He became an overnight sensation when he proved one of the most famous conjectures in all of mathematics, known as Fermat’s Last Theorem, after the 17th century mathematician Pierre Fermat. Wiles received his bachelor’s degree in Mathematics from Oxford and his Ph.D. in Mathematics from the University of Cambridge. He spent a year at Princeton University’s Institute for Advanced Study and then became Professor of Mathematics at Princeton University. He has taught back and forth between Princeton and Oxford for much of his stellar career.

Wiles became interested in Fermat’s Last Theorem as a child of ten, he recalls, and his later professional career became a quest to find a proof of the famous centuries old conjecture in number theory. When he proved it true in 1993, not just the world of mathematics but the entire world and the media reported the accomplishment (technically, it wasn’t completely proved until 1994). Wiles thus enjoys status among mathematicians as having solved a problem many thought true, but essentially unprovable before him.

Not surprisingly, Wiles has received many honors and awards for his career in mathematics, including the Fermat Prize (no surprise), the Wolf Prize, and a Copley Medal. He was awarded a MacArthur Fellowship in 1997.

10. Roger Penrose

Penrose is Emeritus Rouse Ball Professor of Mathematics at the University of Oxford. He is also Emeritus Fellow of Wadham College, a constituent college of Oxford, and an honorary Fellow of Saint John’s College, Cambridge. Penrose received his bachelor’s in mathematics (first-class degree) from University College, London, and completed his Ph.D. at St. John’s College, Cambridge in 1958.

Along with the late Stephen Hawking, Penrose is one of a select few mathematicians (or mathematical physicists, in the case of Hawking) who are generally known and “famous.” Over his impressive career, Penrose has developed sophisticated mathematics to analyze Einstein’s “space-time,” contributing greatly to our understanding of fundamental physics. His exploration of mathematical singularities has expanded our understanding of core phenomena like the Big Bang and Black Holes. Penrose used advanced mathematics to develop a theory of how energy can be extracted from a Black Hole, now called the “Penrose process” in his honor. He is also known for his contributions to tiling theory, another area of mathematics dealing with shapes and topologies. He discovered the eponymous Penrose tilings in 1974. He is also known for Penrose Diagrams, causal diagrams connecting points in spacetime.

In addition to his ongoing and fundamental contribution to mathematics and mathematical physics, Penrose is a successful popularizer of difficult concepts in the sciences. His The Road to Reality: A Complete Guide to the Laws of the Universe, published in 2004 is a readable tour of the laws of physics for interested non-specialists. He is also known for his foray into the problem of consciousness (what is the nature of conscious experience?), writing two widely-read books on the subject, where he argues that consciousness arises from quantum events in the brain.

Penrose was elected a Fellow of the Royal Society in 1972. Among his many other accomplishments, he won the prestigious Eddington Medal with Stephen Hawking in 1975, and the Albert Einstein Medal in 1990. In 1994, Penrose was knighted for his outstanding service to science and mathematics.

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References: academic influence