Who Was Nicholas Higham? A Mathematician, Royal Society Research Professor and a SIAM President

The world of mathematics has lost one of its brightest stars. Nicholas ‘Nick’ Higham, a Royal Society Research Professor and Richardson Professor of Applied Mathematics at the University of Manchester, passed away on January 20, 2024, after a courageous 18-month battle with cancer. He was 60 years old.

Higham was a leading figure in the field of numerical analysis, the study of algorithms for solving mathematical problems with computers. He was widely respected for his work on the accuracy and stability of numerical algorithms, which are essential for applications ranging from scientific computing to machine learning. He authored over 140 publications and several books, including the highly acclaimed “Accuracy and Stability of Numerical Algorithms.”

Higham was also a dedicated teacher and mentor, who inspired and supported many students and colleagues throughout his career. He was known for his passion, enthusiasm, and generosity, as well as his excellent communication skills. He contributed to many journals, conferences, and societies, including the Society for Industrial and Applied Mathematics (SIAM), where he served as President from 2017 to 2018.

Nicholas Higham’s achievements and contributions were recognized by many honors and awards, such as the Alston S. Householder Award, the Leslie Fox Prize, the IMA Gold Medal, the SIAM George Pólya Prize, and the election to the Fellowship of the Royal Society, the ACM, and the Royal Academy of Engineering.

Higham’s passing is a tremendous loss to the academic and scientific community, as well as to his family, friends, and admirers. He will be remembered not only for his brilliant and influential research, but also for his kindness, humility, and integrity. He leaves behind a rich legacy that will continue to inspire and benefit future generations of mathematicians and scientists.

A Life of Excellence and Innovation

Nicholas John Higham was born on December 25, 1963, in Eccles, Greater Manchester, England. He attended Eccles Grammar School and Eccles College, where he developed a keen interest in mathematics and computing. He then went on to study at the University of Manchester, where he obtained his B.Sc. in mathematics in 1982, his M.Sc. in numerical analysis and computing in 1983, and his Ph.D. in numerical analysis in 1985, under the supervision of Professor George Hall.

Our professors Nicholas Higham and William Parnell have been awarded prizes from @LondMathSoc!

Read more below:
: https://t.co/wqtcQ5irQq pic.twitter.com/esxwQHipSY
— University of Manchester Department of Mathematics (@ManUniMaths) July 1, 2019

Higham’s doctoral thesis, titled “Nearness Problems in Numerical Linear Algebra,” laid the foundation for his future research on the accuracy and stability of numerical algorithms. He devised new methods and techniques for solving problems such as matrix nearness, matrix approximation, matrix scaling, matrix sign function, and matrix square root. He also introduced the concept of the matrix condition number, which measures how sensitive a matrix problem is to perturbations.

After completing his Ph.D., Higham joined the Department of Mathematics at the University of Manchester as a lecturer in 1985. He was promoted to senior lecturer in 1991, reader in 1993, and professor in 1998. He held the Richardson Chair of Applied Mathematics since 2002, and was appointed as a Royal Society Research Professor in 2007, a prestigious position that allowed him to devote his time to research.

Nicholas spent a year as a visiting assistant professor at Cornell University from 1988 to 1989, where he collaborated with Professor Charles Van Loan, a renowned expert in numerical linear algebra. He also visited and worked with many other eminent researchers and institutions around the world, such as Professor Gene Golub at Stanford University, Professor Roger Horn at the University of Utah, Professor Alan Edelman at MIT, Professor Nick Trefethen at Oxford University, and Professor Cleve Moler at MathWorks, the company behind MATLAB.

Higham’s research spanned a wide range of topics in numerical analysis, such as matrix functions, matrix equations, matrix polynomials, matrix factorizations, matrix norms, matrix perturbation theory, rounding error analysis, floating-point arithmetic, eigenvalue problems, singular value problems, linear systems, nonlinear systems, optimization problems, and polynomial approximation. He developed and analyzed many novel and efficient algorithms for solving these problems, and provided software implementations for them in MATLAB, LAPACK, and the NAG Library.

Higham’s research had a significant impact on both theory and practice. He advanced the understanding of the mathematical properties and computational aspects of numerical algorithms, and provided rigorous error bounds and stability results for them. He also demonstrated the usefulness and applicability of his algorithms to various fields and disciplines, such as control theory, signal processing, image processing, data analysis, machine learning, network science, quantum computing, and computational biology.

Nicholas was a prolific and influential writer, who authored over 140 journal articles, 15 book chapters, and 4 books. His articles appeared in many prestigious journals, such as SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, Numerische Mathematik, Linear Algebra and its Applications, and BIT Numerical Mathematics. His books were published by SIAM, Oxford University Press, and Cambridge University Press, and received high praise and acclaim from the mathematical community.

Higham’s first book, “Accuracy and Stability of Numerical Algorithms,” published in 1996, is widely regarded as a classic and authoritative reference in the field. It covers the theory and practice of numerical algorithms, with an emphasis on the effects of rounding errors and the methods for controlling them. It contains a comprehensive and systematic treatment of topics such as floating-point arithmetic, matrix norms, condition numbers, backward error analysis, forward error analysis, stability, accuracy, and mixed precision. It also provides many examples, exercises, and MATLAB codes to illustrate and implement the concepts and techniques.

Higham’s second book, “Functions of Matrices: Theory and Computation,” published in 2008, is the first book devoted to the subject of matrix functions, which are functions of square matrices that generalize the notion of scalar functions. It presents the theory and computation of matrix functions, such as matrix exponential, matrix logarithm, matrix square root, matrix sign function, and matrix cosine. It also explores the applications of matrix functions to problems such as differential equations, dynamical systems, graph theory, and quantum mechanics.

Higham’s third book, “Handbook of Writing for the Mathematical Sciences,” published in 1998, is a practical and comprehensive guide for writing mathematical papers and books. It covers topics such as style, grammar, punctuation, notation, terminology, structure, organization, presentation, references, citations, and LaTeX. It also provides advice on how to write for different audiences, purposes, and formats, such as journals, books, conferences, lectures, and reviews.

Nicholas Higham’s fourth book, “The Princeton Companion to Applied Mathematics,” published in 2015, is a monumental and encyclopedic work that showcases the diversity and richness of applied mathematics. It contains over 200 entries written by leading experts in the field, covering topics such as mathematical modeling, numerical analysis, scientific computing, optimization, differential equations, dynamical systems, discrete mathematics, geometry, algebra, analysis, probability, statistics, and applications to various areas of science and engineering. It also features biographies of prominent applied mathematicians, historical accounts, and essays on current trends and challenges.

Higham’s books have been translated into several languages, such as Chinese, Japanese, Korean, and Russian. They have been widely adopted and used by students, researchers, and practitioners around the world. They have also received many positive reviews and endorsements from eminent mathematicians, such as Gilbert Strang, Lloyd N. Trefethen, William J. Cook, and Cleve Moler.

A Legacy of Service and Leadership

Higham was not only a distinguished researcher and writer, but also a devoted teacher and mentor, who shared his knowledge and passion with many students and colleagues. He taught various undergraduate and postgraduate courses at the University of Manchester, such as numerical analysis, numerical linear algebra, matrix computations, and scientific computing. He supervised 30 Ph.D. students and 12 postdoctoral researchers, many of whom have become successful and influential academics and professionals in their own right.

Nicholas Higham was also a generous and active contributor to the mathematical community, who took on many roles and responsibilities in various journals, conferences, and societies. He served as an editor or associate editor for several journals, such as SIAM Review, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Scientific Computing, Numerical Algorithms, and Foundations of Computational Mathematics. He also served as a guest editor for special issues of journals, such as Linear Algebra and its Applications, BIT Numerical Mathematics, and Numerical Linear Algebra with Applications.

Higham organized and participated in many conferences and workshops, both nationally and internationally. He was a member of the steering committee for the Householder Symposia on Numerical Linear Algebra, and the program committee for the SIAM Conferences on Applied Linear Algebra. He also chaired or co-chaired several conferences, such as the SIAM-UKIE Annual Meeting, the IMA Conference on Numerical Linear Algebra and Optimization, and the Manchester SIAM Student Chapter Conference.