Steve Vickers (born c. 1953) is 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, structure, space, models, and change.
History
O ...
and
computer scientist
A computer scientist is a person who is trained in the academic study of computer science.
Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (a ...
. In the early 1980s, he wrote
ROM
Rom, or ROM may refer to:
Biomechanics and medicine
* Risk of mortality, a medical classification to estimate the likelihood of death for a patient
* Rupture of membranes, a term used during pregnancy to describe a rupture of the amniotic sac
* R ...
firmware
In computing, firmware is a specific class of computer software that provides the low-level control for a device's specific hardware. Firmware, such as the BIOS of a personal computer, may contain basic functions of a device, and may provide h ...
and manuals for three
home computers, the
ZX81
The ZX81 is a home computer that was produced by Sinclair Research and manufactured in Dundee, Scotland, by Timex Corporation. It was launched in the United Kingdom in March 1981 as the successor to Sinclair's ZX80 and designed to be a low-cost ...
,
ZX Spectrum
The ZX Spectrum () is an 8-bit home computer that was developed by Sinclair Research. It was released in the United Kingdom on 23 April 1982, and became Britain's best-selling microcomputer.
Referred to during development as the ''ZX81 Colour ...
, and
Jupiter Ace
The Jupiter Ace by Jupiter Cantab was a British home computer of the early 1980s. The Ace differed from other microcomputers of the time in that its programming environment used Forth instead of the more popular BASIC.
After Jupiter Cantab ce ...
.
The latter was produced by
Jupiter Cantab, a short-lived company Vickers formed together with
Richard Altwasser, after the two had left
Sinclair Research
Sinclair Research Ltd is a British consumer electronics company founded by Clive Sinclair in Cambridge. It was originally incorporated in 1973 as Westminster Mail Order Ltd, renamed Sinclair Instrument Ltd, then Science of Cambridge Ltd, then ...
. Since the late 1980s, Vickers has been an academic in the field of geometric logic, writing over 30 papers in scholarly journals on mathematical aspects of computer science. His book ''Topology via Logic'' has been influential over a range of fields (extending even to
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimen ...
, where
Christopher Isham
Christopher Isham (; born 28 April 1944), usually cited as Chris J. Isham, is a theoretical physicist at Imperial College London.
Research
Isham's main research interests are quantum gravity and foundational studies in quantum theory. He was ...
of
Imperial College London
Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
has cited Vickers as an early influence on his work on
topoi
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion ...
and
quantum gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...
). In October 2018, he retired as senior lecturer at the
University of Birmingham
, mottoeng = Through efforts to heights
, established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univer ...
. As announced on his university homepage, he continues to supervise PhD students at the university and focus on his research.
Education
Vickers graduated from
King's College, Cambridge
King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the cit ...
with a degree in mathematics and completed a PhD at
Leeds University
, mottoeng = And knowledge will be increased
, established = 1831 – Leeds School of Medicine1874 – Yorkshire College of Science1884 - Yorkshire College1887 – affiliated to the federal Victoria University1904 – University of Leeds
, t ...
, also in mathematics.
Sinclair Research
In 1980 he started working for Nine Tiles, which had previously written the
Sinclair BASIC
Sinclair BASIC is a dialect of the programming language BASIC used in the 8-bit home computers from Sinclair Research and Timex Sinclair. The Sinclair BASIC interpreter was made by Nine Tiles Networks Ltd.
History
Sinclair BASIC was orig ...
for the
ZX80
The Sinclair ZX80 is a home computer launched on 29 January 1980 by Science of Cambridge Ltd. (later to be better known as Sinclair Research). It is notable for being one of the first computers available in the United Kingdom for less than a h ...
. He was responsible for the adaptation of the 4K
ZX80
The Sinclair ZX80 is a home computer launched on 29 January 1980 by Science of Cambridge Ltd. (later to be better known as Sinclair Research). It is notable for being one of the first computers available in the United Kingdom for less than a h ...
ROM into the 8K ROM used in the
ZX81
The ZX81 is a home computer that was produced by Sinclair Research and manufactured in Dundee, Scotland, by Timex Corporation. It was launched in the United Kingdom in March 1981 as the successor to Sinclair's ZX80 and designed to be a low-cost ...
and also wrote the ZX81 manual. He then wrote most of the ZX Spectrum ROM, and assisted with the user documentation.
Vickers left in 1982 to form "Rainbow Computing Co." with
Richard Altwasser. The company became
Jupiter Cantab and they were together responsible for the development of the commercially unsuccessful
Jupiter ACE
The Jupiter Ace by Jupiter Cantab was a British home computer of the early 1980s. The Ace differed from other microcomputers of the time in that its programming environment used Forth instead of the more popular BASIC.
After Jupiter Cantab ce ...
, a competitor to the similar
ZX Spectrum
The ZX Spectrum () is an 8-bit home computer that was developed by Sinclair Research. It was released in the United Kingdom on 23 April 1982, and became Britain's best-selling microcomputer.
Referred to during development as the ''ZX81 Colour ...
.
Academia
Originally at the
Department of Computing at
Imperial College London
Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
, Vickers later joined the Department of Pure Mathematics at the
Open University
The Open University (OU) is a British Public university, public research university and the largest university in the United Kingdom by List of universities in the United Kingdom by enrolment, number of students. The majority of the OU's underg ...
before moving to the School of
Computer Science at the
University of Birmingham
, mottoeng = Through efforts to heights
, established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univer ...
, where he is currently a senior lecturer and the research student tutor of the School of Computer Science.
Research
Vickers' main interest lies within geometric logic. His book ''Topology via Logic'' introduces
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing h ...
from the point of view of some computational insights developed by
Samson Abramsky
Samson Abramsky (born 12 March 1953) is Professor of Computer Science at University College London. He was previously the Christopher Strachey Professor of Computing at the University of Oxford, from 2000 to 2021.
He has made contributions to t ...
and Mike Smyth. It stresses the
point-free approach and can be understood as dealing with theories in the so-called geometric logic, which was already known from
topos
In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notio ...
theory and is a more stringent form of
intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems o ...
. However, the book was written in the language of
classical mathematics In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive ...
.
Extending the ideas to toposes (as generalised spaces) he found himself channelled into
constructive mathematics
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove th ...
in a geometric form and in ''Topical Categories of Domains'' he set out a geometrisation programme of, where possible, using this geometric mathematics as a tool for treating point-free spaces (and toposes) as though they had "enough points". Much of his subsequent work has been in case studies to show that, with suitable techniques, it was indeed possible to do useful mathematics geometrically. In particular, a notion of "geometric transformation of points to spaces" gives a natural fibrewise treatment of topological bundles. A recent project of his has been to connect this with the topos approaches to physics as developed by
Chris Isham and others (see Doering and Isham's ''What is a Thing? Topos Theory in the Foundations of Physics'') at
Imperial College
Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
, and Klaas Landsman's group at
Radboud University Nijmegen
Radboud University (abbreviated as RU, nl, Radboud Universiteit , formerly ''Katholieke Universiteit Nijmegen'') is a public research university located in Nijmegen, the Netherlands. The university bears the name of Saint Radboud, a 9th century ...
(see Heunen, Landsman and Spitters' ''A Topos for Algebraic Quantum Theory'').
Bibliography
* Steven Vickers, "An induction principle for consequence in arithmetic universes", Journal of Pure and Applied Algebra 216 (8–9), ISSN 0022-4049, pp. 1705 – 2068, 2012.
* Jung, Achim and Moshier, M. Andrew and Vickers, Steven, "Presenting dcpos and dcpo algebras", in Bauer, A. and Mislove, M., Proceedings of the 24th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIV), pp. 209–229, Electronic Notes in Theoretical Computer Science, Elsevier, 2008.
* Steven Vickers, "Cosheaves and connectedness in formal topology", Annals of Pure and Applied Logic, ISSN 0168-0072, 2009.
* Steven Vickers, "A localic theory of lower and upper integrals", Mathematical Logic Quarterly, 54 (1), pp. 109–103, 2008.
* Steven Vickers, "Locales and toposes as spaces", in Aiello, Marco and Pratt-Hartmann, Ian E. and van Benthem, Johan F.A.K., Springer, Handbook of Spatial Logics, Springer, 2007, , Chapter 8, pp. 429–496.
* Palmgren, Erik and Vickers, Steven, "Partial Horn logic and cartesian categories", Annals of Pure and Applied Logic, 145 (3), pp. 314–353, ISSN 0168-0072, 2007.
* Steven Vickers, "Localic completion of generalized metric spaces I, Theory and Applications of Categories", ISSN 1201-561X, 14, pp. 328–356, 2005.
* Steven Vickers, "Localic completion of generalized metric spaces II: Powerlocales, Journal of Logic and Analysis", ISSN 1759-9008, 1 (11), pp. 1–48, 2009.
* Steven Vickers, "The double powerlocale and exponentiation: a case study in geometric logic", Theoretical Computer Science, ISSN 0304-3975, vol. 316, pp. 297–321, 2004.
* Steven Vickers, "Topical Categories of Domains", in Winskel, Proceedings of the CLICS workshop, Aarhus, Computer Science Department, Aarhus University, 1992.
* Vickers, S. J., "Topology via Constructive Logic", in Moss and Ginzburg and de Rijke, Logic, Language and Computation Vol II, Proceedings of conference on Information-Theoretic Approaches to Logic, Language, and Computation, 1996, , 157586181X, CSLI Publications, Stanford, pp. 336–345, 1999.
* Vickers, S. J., "Toposes pour les vraiment nuls", in Edalat, A. and Jourdan, S. and McCusker, G., Advances in Theory and Formal Methods of Computing 1996, , Imperial College Press, London, pp. 1–12, 1996.
* Vickers, S. J., "Toposes pour les nuls", Techreport Doc96/4,
Department of Computing,
Imperial College London
Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
, (first published in Semantics Society Newsletter no. 4).
* Broda, K. and Eisenbach, S. and Khoshnevisan, H. and Vickers, S.J., "Reasoned Programming", , Prentice Hall, International Series in Computer Science, 1994.
*
Johnstone, P. T. and Vickers, S. J., "Preframe Presentations Present", in Carboni, A. and Pedicchio, M.C. and Rosolini, G., Category Theory – Proceedings, Como 1990, , 0-387-54706-1, Lecture Notes in Mathematics, 1488, Springer-Verlag, 1991.
* Steven Vickers, "Topology Via Logic", Cambridge University Press, , 1996.
* Doring, Andreas and Isham, Chris, "What is a Thing?: Topos Theory in the Foundations of Physics", in Bob Coecke, New Structures in Physics, Chapter 13, pp. 753–940, Lecture Notes in Physics, 813, Springer, 2011, , (also see arXiv:0803.0417v1.)
* Heunen, Chris and Landsman, Nicolaas P. and Spitters, Bas, A Topos for Algebraic Quantum Theory, 2009, Communications in Mathematical Physics, 291 (1), pp. 63–110, ISSN 0010-3616 (Print) 1432-0916 (Online).
References
External links
Steve Vickers' homepageat the University of Birmingham
with Richard Altwasser and Steven Vickers
{{DEFAULTSORT:Vickers, Steve
Year of birth missing (living people)
Living people
Alumni of King's College, Cambridge
Alumni of the University of Leeds
British computer programmers
British technology writers
Sinclair Research
Academics of Imperial College London
Academics of the Open University
Academics of the University of Birmingham