Jeffrey Charles Percy Miller (31 August 1906 – 24 April 1981) was an English mathematician and

computing pioneer This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do. Pioneers ~ Items marked with a tilde are circa dates. See also * Computer Pioneer Award * IEEE John von N ...

. He worked in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and on

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, particularly

polyhedra In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary su ...

, where Miller's monster is a nickname of the

great dirhombicosidodecahedron In geometry, the great dirhombicosidodecahedron (or great snub disicosidisdodecahedron) is a nonconvex uniform polyhedron, indexed last as . It has 124 faces (40 Triangle, triangles, 60 Square, squares, and 24 Pentagram, pentagrams), 240 Edge (g ...

Early life and education

Miller was born at

Isleworth Isleworth ( ) is a suburban town in the London Borough of Hounslow, West London, England. It lies immediately east of Hounslow and west of the River Thames and its tributary the River Crane, London, River Crane. Isleworth's original area of ...

Middlesex Middlesex (; abbreviation: Middx) is a Historic counties of England, former county in South East England, now mainly within Greater London. Its boundaries largely followed three rivers: the River Thames, Thames in the south, the River Lea, Le ...

(now

West London West London is the western part of London, England, north of the River Thames, west of the City of London, and extending to the Greater London boundary. The term is used to differentiate the area from the other parts of London: Central London, N ...

), and educated at

St Paul's School, London St Paul's School is a Selective school, selective Private schools in the United Kingdom, independent day school (with limited boarding school, boarding) for boys aged 13–18, founded in 1509 by John Colet and located on a 43-acre site by Rive ...

and

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

(BA 1928, MA 1931, PhD 1933).

Career

He was an early member of the Computing Laboratory of the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

. He contributed in computation to the construction and documentation of

mathematical tables Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely us ...

, and by the proposal of certain

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

Miller's recurrence algorithm Miller's recurrence algorithm is a procedure for the backward calculation of a rapidly decreasing solution of a three-term recurrence relation developed by J. C. P. Miller. It was originally developed to compute tables of the modified Bessel funct ...

is mentioned in the '' Handbook of Mathematical Functions''. In volume 2 of ''

The Art of Computer Programming ''The Art of Computer Programming'' (''TAOCP'') is a comprehensive multi-volume monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. it consists of published volumes 1, 2, 3, 4A, and 4 ...

'',

Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of comp ...

attributes to Miller a basic technique on

formal power series In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual algebraic operations on series (addition, subtraction, multiplication, division, partial su ...

, for recursive evaluation of coefficients of powers or more general functions. In the theory of

stellation In geometry, stellation is the process of extending a polygon in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific ...

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 ''The Fifty-Nine Icosahedra'' is a book written and illustrated by Harold Scott MacDonald Coxeter, H. S. M. Coxeter, Patrick du Val, P. Du Val, H. T. Flather and J. F. Petrie. It enumerates certain stellations of the regular convex or Platonic re ...

resulted, written by Coxeter and

Patrick du Val Patrick du Val (March 26, 1903 – January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named af ...

. In the 1930s, Coxeter and Miller found 12 new

uniform polyhedra In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent. Uniform polyhedra may be regular (if also fac ...

, a step in the process of their complete classification in the 1950s. Miller also made an early investigation into what is now known as the

Rule 90 In the mathematics, mathematical study of cellular automaton, cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function. It consists of a one-dimensional array of cells, each of which can hold either a 0 or ...

cellular automaton A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessel ...

. Miller was a Fellow of the

Royal Astronomical Society The Royal Astronomical Society (RAS) is a learned society and charitable organisation, charity that encourages and promotes the study of astronomy, planetary science, solar-system science, geophysics and closely related branches of science. Its ...

from 1929; his obituary in the Society's journal noted his early interest and work in astronomy – including papers on the effect of distribution of density on the period of pulsation in a star, and on the effect of opacity in the point-source stellar model – and observed that, "but for a serious illness that interrupted his university postgraduate years, there is little doubt that ewould have continued to work in the field of astronomy and would have made notable contributions to it."

Personal life

In 1934, Miller married Germaine Gough. They 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 St Andrew's Church, Chesterton is a Church of England parish church in Chesterton, Cambridge. It is a Grade I listed building. A church was first recorded on this site around 1200. The church was presented in 1217 to the papal legate, Cardinal G ...

, Cambridge.

Early life and education

Career

Personal life

Notes

References

Further reading