Lloyd Nicholas Trefethen (born 30 August 1955) is an American mathematician, professor of

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

and until 2023 head of the Numerical Analysis Group at the

Mathematical Institute, University of Oxford The Mathematical Institute is the mathematics department at the University of Oxford in England. It is one of the nine departments of the university's Mathematical, Physical and Life Sciences Division. The institute includes both pure and app ...

. He was elected a Member of the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

in 2025.

Early life and education

Trefethen was born 30 August 1955 in

Boston, Massachusetts Boston is the capital and most populous city in the Commonwealth (U.S. state), Commonwealth of Massachusetts in the United States. The city serves as the cultural and Financial centre, financial center of New England, a region of the Northeas ...

, the son of mechanical engineer Lloyd M. Trefethen and codebreaker, poet, teacher and editor Florence Newman Trefethen. Trefethen attended

Phillips Exeter Academy Phillips Exeter Academy (often called Exeter or PEA) is an Independent school, independent, co-educational, college-preparatory school in Exeter, New Hampshire. Established in 1781, it is America's sixth-oldest boarding school and educates an es ...

. He obtained his bachelor's degree from

Harvard College Harvard College is the undergraduate education, undergraduate college of Harvard University, a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Part of the Harvard Faculty of Arts and Scienc ...

in 1977 and his master's from

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

in 1980. His PhD was on ''Wave Propagation and Stability for Finite Difference Schemes'' supervised by Joseph E. Oliger at

Career and research

Following his PhD, Trefethen went on to work at the

Courant Institute of Mathematical Sciences The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute ...

in New York,

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

, and

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

, before being appointed to a chair at the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

and a Fellowship of

Balliol College, Oxford Balliol College () is a constituent college of the University of Oxford. Founded in 1263 by nobleman John I de Balliol, it has a claim to be the oldest college in Oxford and the English-speaking world. With a governing body of a master and aro ...

. His publications span a wide range of areas within numerical analysis and applied mathematics, including non-normal

eigenvalue In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a ...

problems and applications, spectral methods for differential equations,

numerical linear algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathemati ...

fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...

, computational

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

, and approximation theory. He is perhaps best known for his work on pseudospectra of non-normal matrices and operators. This work covers theoretical aspects as well as numerical algorithms, and applications including fluid mechanics, numerical solution of partial differential equations, numerical linear algebra, shuffling of cards, random matrices, differential equations and

lasers A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of radi ...

. Trefethen is currently an

ISI highly cited researcher The Institute for Scientific Information (ISI) was an academic publishing service, founded by Eugene Garfield in Philadelphia in 1956. ISI offered scientometric and bibliographic database services. Its specialty was citation indexing and analysis ...

. Trefethen has written a number of books on numerical analysis including ''Numerical Linear Algebra'' with David Bau, ''Spectral Methods in MATLAB'', ''Schwarz–Christoffel Mapping'' with Tobin Driscoll, and ''Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators'' with Mark Embree. He is the leader of the

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...

-based

Chebfun Chebfun is a free/open-source software system written in MATLAB for numerical computation with functions of a real variable. It is based on the idea of overloading MATLAB's commands for vectors and matrices to analogous commands for functions a ...

software project. In 2013 he proposed a new formula to calculate the BMI of a person: :

\text = 1.3 \times \frac

(

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

)

Books

* ''Numerical Linear Algebra'' (SIAM, 1997) with David Bau * ''Spectral Methods in Matlab'' (SIAM, 2000) * ''Schwarz-Christoffel Mapping'' (Cambridge, 2002) with T. A. Driscoll * ''Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators'' (Princeton, 2005) with Mark Embree * ''Trefethen's Index Cards'' (World Scientific 2011) * ''Approximation Theory and Approximation Practice'' (SIAM, 2013 and 2020) * ''Exploring ODEs'' (SIAM, 2018) with Á. Birkisson and T. A. Driscoll * ''An Applied Mathematician’s Apology'' (SIAM, 2022)

Awards and honours

Trefethen was the first winner of the Leslie Fox Prize for Numerical Analysis. In 1998 he was an Invited Speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

in Berlin. He is a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, and a member of the

National Academy of Engineering The National Academy of Engineering (NAE) is an American Nonprofit organization, nonprofit, NGO, non-governmental organization. It is part of the National Academies of Sciences, Engineering, and Medicine (NASEM), along with the National Academ ...

in the United States. Trefethen was elected a Fellow of the Royal Society (FRS) in 2005, and his certificate of election reads: In 2010 Trefethen was awarded the

Gold Medal A gold medal is a medal awarded for highest achievement in a non-military field. Its name derives from the use of at least a fraction of gold in form of plating or alloying in its manufacture. Since the eighteenth century, gold medals have b ...

of the

Institute of Mathematics and its Applications The Institute of Mathematics and its Applications (IMA) is the UK's chartered professional body for mathematicians and one of the UK's learned societies for mathematics (another being the London Mathematical Society). The IMA aims to advance ...

in recognition of his "outstanding contributions to mathematics and its applications over a period of years". In 2013 Trefethen was awarded the Naylor Prize and lectureship in Applied Mathematics from the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

. He was awarded the George Pólya Prize for Mathematical Exposition in 2017 and the John von Neumann Prize in 2020 by SIAM.

Personal life

Trefethen has one son and one daughter from his first marriage to Anne Elizabeth Trefethen (née Daman). He is currently married to Kate McLoughlin, a professor of English Literature at Oxford.

References

External links

Personal website
at Oxford University
Chebfun
project website * * * {{DEFAULTSORT:Trefethen, Lloyd Nicholas Fellows of the Royal Society Numerical analysts 20th-century British mathematicians 21st-century British mathematicians Living people Harvard University alumni Stanford University alumni 1955 births Fellows of the American Mathematical Society Fellows of Balliol College, Oxford Fellows of the Society for Industrial and Applied Mathematics Members of the United States National Academy of Engineering Presidents of the Society for Industrial and Applied Mathematics Courant Institute of Mathematical Sciences faculty

Nick Nick may refer to: People and fictional characters * Nick (given name), a list of people and fictional characters * Désirée Nick, German actress and writer Places * Nick, Hungary, a village * Nick, Warmian-Masurian Voivodeship, Poland, a ...

Members of the United States National Academy of Sciences