J. C. P. Miller

Jeffrey Charles Percy Miller (31 August 1906 – 24 April 1981) was an English mathematician and computing pioneer. He worked in number theory and on geometry, particularly polyhedra, where Miller's monster refers to the great dirhombicosidodecahedron.

He was an early member of the Computing Laboratory of the University of Cambridge.[1] He contributed in computation to the construction and documentation of mathematical tables,[2] and by the proposal of certain algorithms. Miller's recurrence algorithm is mentioned in the Handbook of Mathematical Functions.[3]

What Miller perceived was that in a second-order linear recurrence which has solutions sufficiently differentiated asymptotically, there is a solution that may be uniquely characterized by one initial value and a knowledge of its growth. This led to an algorithm for computing certain solutions of the equation which required only a scant knowledge of their pointwise values.[4]

As the reference says, this technique was subsequently much developed and applied, and was enunciated rather casually by Miller in a 1952 book of tables of Bessel functions.

In volume 2 of The Art of Computer Programming, Donald Knuth attributes to Miller a basic technique on formal power series, for recursive evaluation of coefficients of powers or more general functions.[5]

In the theory of stellation of polyhedra, he made some influential suggestions to H. S. M. Coxeter. These became known as Miller's rules. The 1938 book on the fifty-nine icosahedra resulted, written by Coxeter and Patrick du Val.[6] In the 1930s, Coxeter and Miller found 12 new uniform polyhedra, a step in the process of their complete classification in the 1950s.[7] Miller also made an early investigation into what is now known as the Rule 90 cellular automaton.[8]

Dr Miller was married to Germaine Miller (née Gough) in 1934 and had three children (David, Alison and Jane). Germaine died in Cambridge in her 100th year in March 2010 and is buried at St Andrew's Church, Chesterton, Cambridge.

Notes

1. A brief informal history of the Computer Laboratory
2. A. Fletcher, J. C. P. Miller and L. Rosenhead, An index of mathematical tables; this work is mentioned in Diana H. Hook, Jeremy M. Norman, Michael R. Williams, Origins of Cyberspace: A Library on the History of Computing, Networking, and Telecommunications (2002), p. 362, as compiled in 1943, and remaining useful until the 1960s.
3. Milton Abramowitz, Irene A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (1965), p. xiii.
4. Wimp, Jet (1984). Computation with recurrence relations. Pitman. p. 162. ISBN 978-0273085089.
5. Knuth, Donald E. (1981). The Art of Computer Programming, Volume 2: Seminumerical Algorithms (2nd ed.). Addison Wesley. p. 507. ISBN 9780201038224.
6. Stellation and facetting - a brief history
7. Peter R. Cromwell, Polyhedra: "One of the Most Charming Chapters of Geometry" (1999), p. 178.
8. Miller, J. C. P. (1970), "Periodic forests of stunted trees", Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, 266 (1172): 63–111, Bibcode:1970RSPTA.266...63M, doi:10.1098/rsta.1970.0003, JSTOR 73779.

Further reading

• Doron Zeilberger,The J. C. P. Miller recurrence for exponentiating a polynomial, and its q-analog, Journal of Difference Equations and Applications, Volume 1, Issue 1 1995, pages 57 – 60.