John Michael Hammersley, (21 March 1920 – 2 May 2004) was a British
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
best known for his foundational work in the theory of
self-avoiding walks
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (group), lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theory, graph theoretical notion of a Path ( ...
and
percolation theory
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected ...
.
Early life and education
Hammersley was born in
Helensburgh
Helensburgh ( ; ) is a town on the north side of the Firth of Clyde in Scotland, situated at the mouth of the Gareloch. Historically in Dunbartonshire, it became part of Argyll and Bute following local government reorganisation in 1996.
Histo ...
in
Dunbartonshire
Dunbartonshire () or the County of Dumbarton is a Shires of Scotland, historic county, lieutenancy areas of Scotland, lieutenancy area and registration county in the west central Lowlands of Scotland lying to the north of the River Clyde. Dunbar ...
, and educated at
Sedbergh School
Sedbergh School is a Public school (United Kingdom), public school (English Private schools in the United Kingdom, private boarding school, boarding and day school, day school) in the town of Sedbergh in Cumbria, North West England. It comprise ...
. He started reading
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
at
Emmanuel College, Cambridge
Emmanuel College is a constituent college of the University of Cambridge. The college was founded in 1584 by Sir Walter Mildmay, Chancellor of the Exchequer to Elizabeth I. The site on which the college sits was once a priory for Dominican mo ...
but was called up to join the
Royal Artillery
The Royal Regiment of Artillery, commonly referred to as the Royal Artillery (RA) and colloquially known as "The Gunners", is one of two regiments that make up the artillery arm of the British Army. The Royal Regiment of Artillery comprises t ...
in 1941. During his time in the army he worked on
ballistics
Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially weapon munitions such as bullets, unguided bombs, rockets and the like; the science or art of designing and acceler ...
. He graduated in mathematics in 1948. He never studied for a PhD but was awarded an ScD by Cambridge University and a DSc by Oxford University in 1959.
Academic career
With
Jillian Beardwood and J.H. Halton, Hammersley is known for the Beardwood-Halton-Hammersley Theorem. Published by the
Cambridge Philosophical Society in a 1959 article entitled “The Shortest Path Through Many Points,” the theorem provides a practical solution to the “
traveling salesman problem
In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exac ...
.”
He held a number of positions, both in and outside academia. His book ''Monte Carlo Methods'' with David Handscomb was published in 1964. He is known for devising an early solution to the
moving sofa problem in 1968.
He was an advocate of
problem solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business an ...
, and an opponent of abstraction in mathematics, taking part in the
New Math debate.
He was a fellow (later professorial fellow) of
Trinity College, Oxford
Trinity College (full name: The College of the Holy and Undivided Trinity in the University of Oxford, of the foundation of Sir Thomas Pope (Knight)) is a Colleges of the University of Oxford, constituent college of the University of Oxford in E ...
, from 1961,
reader in mathematical statistics at
Oxford University
The University of Oxford is a collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the second-oldest continuously operating u ...
from 1969, and elected
Fellow of the Royal Society
Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...
(FRS) in 1976.
See also
*
Hammersley set
*
Hammersley-Clifford theorem
*
Low-discrepancy sequence
In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x_1, \ldots, x_N has a low discrepancy of a sequence, discrepancy.
Roughly speaking, the discrepancy of a sequence is low if the p ...
References
1920 births
2004 deaths
Alumni of Emmanuel College, Cambridge
People educated at Sedbergh School
Fellows of the Royal Society
Probability theorists
British Army personnel of World War II
Royal Artillery officers
{{UK-mathematician-stub