Trefethen obtained his bachelor's degree from Harvard University in 1977 and his master's from Stanford University in 1980. His PhD was on *Wave Propagation and Stability for Finite Difference Schemes* supervised by Joseph E. Oliger at Stanford University.

Following his PhD, Trefethen went on to work at the Courant Institute of Mathematical Sciences in New York, Massachusetts Institute of Technology, and Cornell University, before being appointed to a chair at the University of Oxford and a Fellowship of Balliol College, Oxford.

As of 2009, he has published around 125 journal papers spanning a wide range of areas within numerical analysis and applied mathematics, including non-normal eigenvalue problems and applications, spectral methods for differential equations, numerical linear algebra, fluid mechanics, computational complex analysis, 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. Trefethen is currently an ISI highly cited researcher.

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 has recently been heavily involved in the creation and development of the MATLAB-based Chebfun software project.

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

B
M
I
=
1.3
w
e
i
g
h
t
/
h
e
i
g
h
t
2.5

(International System of Units)

*Numerical Linear Algebra* (1997) with David Bau
*Spectral Methods in Matlab* (2000)
"Hydrodynamic stability without eigenvalues" with Anne Trefethen, Satish Reddy, and Tobin Driscoll
"Pseudospectra of linear operators" *SIAM Review* (1997)
Trefethen was the first winner of the Leslie Fox Prize for Numerical Analysis. He is a fellow of the American Mathematical Society, and a member of the National Academy of Engineering in the United States. Trefethen was elected a Fellow of the Royal Society (FRS) in 2005, his certificate of election reads:

In 2013 Trefethen was awarded the Naylor Prize and lectureship in Applied Mathematics from the London Mathematical Society

Trefethen has one son and one daughter from his first marriage to Anne Elizabeth Trefethen (née Daman).