**Ian R. Porteous** was a mathematician at the University of Liverpool, a known as a pioneer of Clifford Algebra, and an educator on the Merseyside. He is best known for three books on geometry and modern algebra. In Liverpool he and Peter Giblin are known for their registered charity *Mathematical Education on Merseyside* which promotes enthusiasm for mathematics through sponsorship of an annual competition. He served on the International Advisory Board of the triannual International Conferences on Clifford Algebras and their Applications.

Porteous wrote his thesis *Algebraic Geometry* under W. V. D. Hodge and Michael Atiyah at University of Cambridge in 1961. In 1971 his article “The normal singularities of a submanifold” was published in Journal of Differential Geometry 5:543–64. It was concerned with the smooth embeddings of an *m*-manifold in R^{n}.

In 1969 Porteous published *Topological Geometry* with Van Nostrand Reinhold and Company. It was reviewed in Mathematical Reviews by J. Eells, who interpreted it as a three-term textbook for a sequence in abstract algebra, geometric algebra, and differential calculus in Euclidean and Banach spaces and on manifolds. Eells says “Surely this book is the product of substantial thought and care, both from the standpoints of consistent mathematical presentation and of student’s pedagogical requirements.” In 1981 a 2nd ed. was published with Cambridge University Press.

In 1995 he published *Clifford Algebras and the Classical Groups*, Peter R. Law reviewed it: “Porteous’ presentation of the subject matter sets a standard by which others may be judged.” The book has 24 chapters including 8:quaternions, 13:The classical groups, 15:Clifford algebras, 16:Spin groups, 17:Conjugation, 20:Topological spaces, 21:Manifolds, 22:Lie groups. Porteous acknowledged the contribution of his student Tony Hampson and anticipatory work by Terry Wall.

Porteous maintained his interest in singularity theory, and in 1994 published *Geometric Differentiation*. The subtitle, “for the intelligence of curves and surfaces” refers to the phrase “for the intelligence of curved lines” appearing in a calculus text of 1696. The review by J. D. Chillingworth says it is “aimed at advanced undergraduates or beginning graduate students in mathematics … a peculiar feature of the book is its use of compact notation for differentiation using numerical subscripts that allow tidy presentation of calculations.” Furthermore, it has “connections to optics, kinematics and architecture as well as (more recently) geology, tomography, computer vision and face-recognition.” The underlying theme of the study are critical points of appropriate distance-squared functions. 2nd ed. 2001, adding some material from a work of Vladimir Arnold on spherical curves.

Ian Porteous’ commitment to mathematics education can be seen through the work of his charity “Mathematical Education on Merseyside”. As recounted in the book *Challenging Mathematics*, in 1978 Giblin and Porteous began to organize a CHALLENGE competition for first and second formers in secondary school. By 1989 they were drawing 3500 participants each year. Held over two weekends in the Spring Term, students consider six questions each round. Marking was arranged through the Mathematics Department of Liverpool University, and prizes were awarded at “an evening of mathematical recreation”. Broad participation was encouraged by making half the problems widely accessible. Solutions to the problems appear in their book.

Ian Porteous passed away suddenly of a heart attack on the afternoon of the 30th January 2011. He was in the company of his wife Shiona.

## References

- Vladimir Arnold (1995) “The geometry of spherical curves and the algebra of quaternions”, translated by Ian Porteous,
*Russian Mathematical Surveys*50:1–68. - JD Chillingsworth Review of
*Geometric Differentiation* - Giblin, P. J.; Porteus, I. R. (1990),
*Challenging Mathematics*, Oxford University Press, ISBN0199143617 - Peter R. Law Review of
*Clifford Algebras and the Classical Groups*. - Ian Porteous (2005) Mathematical Education on Merseyside.
- Ian Porteous corrections to
*Clifford Algebras and the Classical Groups* - Ian R. Porteous at the Mathematics Genealogy Project.

*Source: *Email from W.R. Rodrigues, Jr., received 01 February 2011. Biographical information adapted from Wikipedia. http://euklid.bauing.uni-weimar.de/ICCA9