In September 1984 a two-day *Symposium on Computational Mathematics–State of the Art* was held at Argonne National Laboratory in honour of James Hardy Wilkinson on his 65th birthday.

Wilkinson was one of the leading figures in 20th century numerical analysis. He developed the theory and practice of backward error analysis for floating-point computation, and developed, analyzed, and implemented in software many algorithms in numerical linear algebra. Among his many honours, Wilkinson was a Fellow of the Royal Society (elected 1969) and a winner of both the Turing Prize (1970) and the SIAM John von Neumman Lecture award (1970). His legacy endures and in 2019 we celebrated the centenary of his birth with the conference Advances in Numerical Linear Algebra.

The 1984 symposium provided “an overview of the state of the art in several of the major areas of computational mathematics” and “was particularly appropriate for this occasion in view of the many fundamental contributions in computational mathematics made by Professor Wilkinson throughout his distinguished career”.

The symposium attracted more than 260 attendees and comprised ten invited talks by distinguished researchers:

*Some Problems in the Scaling of Matrices*, G. W. Stewart*Matrix Calculations in Optimization Algorithms*, M. J. D. Powell*Numerical Solution of Differential-Algebraic Equations*, C. W. Gear*The Requirements of Interactive Data Analysis Systems*, Peter J. Huber*Linear Algebra Problems in Multivariate Approximation Theory*, C. de Boor*Computational linear Algebra in Continuation and Two Point Boundary Value Problems*, H. B. Keller*Second Thoughts on the Mathematical Software Effort: A Perspective*, W. J. Cody*Enhanced Resolution in Shock Wave Calculations*, James Glimm*Givens’ Eigenvector Recurrence Revisited*, Beresford Parlett*The State of the Art in Error Analysis*, James H. Wilkinson

Slides from the talks are available in an informal proceedings available here in PDF form and on Google Books.

Jack Dongarra has provided me with contact prints of photos taken at the workshop. I have scanned some of these and they are shown below.

One of the photos shows Jim Wilkinson with an Apple Mac that was presented to him. He used it to type up several of his later papers. Sadly, Jim died just over two years after the symposium.