Cambridge Philosophical Society

The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of theology and medicine. The society was granted a royal charter by William IV in 1832.

The society has published several scientific journals, including Biological Reviews (established 1926) and Mathematical Proceedings of the Cambridge Philosophical Society (formerly entitled Proceedings of the Cambridge Philosophical Society, published since 1843). Transactions of the Cambridge Philosophical Society was published between 1821–1928, but was then discontinued.

Cambridge Philosophical Society
TypeScientific Society
Legal statusRoyal Charter, granted by King William IV in 1832
Focusfor the purpose of promoting scientific inquiry
HeadquartersCambridge, CB21RX
United Kingdom United Kingdom
Honorary Members and Fellows
Professor S Conway Morris
Main organ
The Council


As Cambridge's oldest scientific society founded in 1819, the society was founded by Adam Sedgwick and John Stevens Henslow. Its prime purpose is to "keep alive the spirit of inquiry". For almost 200 years, this spirit has been kept alive by its members and its activities. The society is independent of the University of Cambridge, although it is located within the Cambridge compound. The Society has provided an open forum and played a key role in raising the profile of the sciences to the public.

Fellow of the Cambridge Philosophical Society (F.C.P.S.)

Members of the Society are called Fellows and are permitted to use the 'FCPS' post-nominal title. Fellows are usually academics or graduate students involved in mathematical or scientific research within the University. A Fellow must be recommended in writing by both a Fellow of the Society who has been a member for at least three years and a person of appropriate standing, who knows the candidate in a professional capacity. Approved candidates are elected at open meetings of the Society following proposal at Council Meetings.[1]

The equivalent organisation for philosophers is the Cambridge Moral Sciences Club.


The society publishes one of the oldest mathematical journals in history, including the "Mathematical Proceedings" (1843) [2]. It also publishes the "Biological Reviews" since 1926.


The society organizes lectures given by prominent scientists and mathematicians[3]. The lectures are free and open to all who are interested to attend.


  1. ^ "Membership". cambridge philosophical society.
  2. ^
  3. ^

Further reading

  • A. Rupert Hall (1969). The Cambridge Philosophical Society: A History 1819-1969. Cambridge Philosophical Society. ISBN 0-9500348-1-9.
  • Susannah Gibson (2019). The Spirit of Inquiry: How One Extraordinary Society Shaped Modern Science. Oxford University Press. ISBN 9780198833376

External links

A Mathematical Theory of Natural and Artificial Selection

A Mathematical Theory of Natural and Artificial Selection is the title of a series of scientific papers by the British population geneticist J.B.S. Haldane, published between 1924 and 1934. Haldane outlines the first mathematical models for many cases of evolution due to selection, an important concept in the modern synthesis of Darwin's theory with Mendelian genetics.

Anil Kumar Gain

Anil Kumar Gain (1 February 1919 – 7 February 1978) (also spelt Anil Kumar Gayen) was an Indian mathematician and statistician best known for his works on the Pearson product-moment correlation coefficient in the field of applied statistics, with his colleague Ronald Fisher. He received his Ph.D. from the University of Cambridge under the supervision of Henry Ellis Daniels, who was the then President of the Royal Statistical Society. He was honoured as a Fellow of the Royal Statistical Society and the Cambridge Philosophical Society.Gain was the president of the statistics section of the Indian Science Congress Association, as well as the head of the Department of Mathematics at the Indian Institute of Technology Kharagpur. He later went on to found Vidyasagar University, naming it after the famous social reformer of the Bengali renaissance, Ishwar Chandra Vidyasagar.

Du Val singularity

In algebraic geometry, a Du Val singularity, also called simple surface singularity, Kleinian singularity, or rational double point, is an isolated singularity of a complex surface which is modeled on a double branched cover of the plane, with minimal resolution obtained by replacing the singular point with a tree of smooth rational curves, with intersection pattern dual to a Dynkin diagram of A-D-E singularity type. They are the canonical singularities (or, equivalently, rational Gorenstein singularities) in dimension 2. They were studied by Patrick Du Val (1934a, 1934b, 1934c) and Felix Klein.

The Du Val singularities also appear as quotients of C2 by a finite subgroup of SL2(C); equivalently, a finite subgroup of SU(2), which are known as binary polyhedral groups. The rings of invariant polynomials of these finite group actions were computed by Klein, and are essentially the coordinate rings of the singularities; this is a classic result in invariant theory.

Extracts from Letters to Henslow

Extracts from Letters to Henslow is an 1835 pamphlet published by John Stevens Henslow at his own expense of extracts from ten letters Charles Darwin sent him while on HMS Beagle. This pamphlet helped to establish Darwin's reputation amongst renowned scientific publications. However, upon learning of this pamphlet's publication Darwin was "a good deal horrified" at Henslow making public "what had been written without care or accuracy".

Francisco Javier González-Acuña

Francisco Javier González-Acuña (nickname "Fico") is a mathematician in the UNAM's institute of mathematics and CIMAT, specializing in low-dimensional topology.

He did his graduate studies at Princeton University, obtaining his Ph.D. in 1970. His thesis, written under the supervision of Ralph Fox, was titled On homology spheres.

An early result of González-Acuña is that a group G is the homomorphic image of some knot group if and only if G is finitely generated and has weight at most one. This result (a "remarkable theorem", as Lee Neuwirth called it in his review),

was published in 1975 in the highly respected journal, Annals of Mathematics. In 1978, together with José María Montesinos, he answered a question posed by Fox, proving the existence of 2-knots whose groups have infinitely many ends.

With Hamish Short, González-Acuña proposed and worked on the cabling conjecture: the only knots in the 3-sphere which admit a reducible Dehn surgery, i.e. a surgery which results in a reducible 3-manifold, are the cable knots. This conjecture is one of the most relevant, unresolved questions in the theory of Dehn surgery on knots in the 3-sphere.

González-Acuña has made other significant contributions, which have been published in journals such as Transactions of the American Mathematical Society, Topology and Mathematical Proceedings of the Cambridge Philosophical Society.

G/G/1 queue

In queueing theory, a discipline within the mathematical theory of probability, the G/G/1 queue represents the queue length in a system with a single server where interarrival times have a general (meaning arbitrary) distribution and service times have a (different) general distribution. The evolution of the queue can be described by the Lindley equation.The system is described in Kendall's notation where the G denotes a general distribution for both interarrival times and service times and the 1 that the model has a single server. Different interarrival and service times are considered to be independent, and sometimes the model is denoted GI/GI/1 to emphasise this.

Gabriel Paternain

Gabriel Pedro Paternain is a Uruguayan mathematician. He is Professor of Mathematics in DPMMS at the University of Cambridge, and a fellow of Trinity College. He obtained his Licenciatura from Universidad de la Republica in Uruguay in 1987, and his PhD from the State University of New York at Stony Brook in 1991. He has lectured several undergraduate and graduate courses and has gained widespread popularity due to his entertaining and informal lecturing style, which has been recognised by the university in the past for its high calibre. He was managing editor of the mathematical journal Mathematical Proceedings of the Cambridge Philosophical Society for the period 2006-2011.

He is known for his work on dynamical and geometrical aspects of Hamiltonian systems, in particular magnetic and geodesic flows. His recent

research focuses on geometric inverse problems and his collaboration with Mikko Salo and Gunther Uhlmann yielded solutions to several inverse problems in two dimensions, including the tensor tomography problem and the proof of spectral rigidity of an Anosov surface.

In his spare time he partakes in a wide variety of sports, notably football.

George Green (mathematician)

George Green (14 July 1793 – 31 May 1841) was a British mathematical physicist who wrote An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (Green, 1828). The essay introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in physics, and the concept of what are now called Green's functions. Green was the first person to create a mathematical theory of electricity and magnetism and his theory formed the foundation for the work of other scientists such as James Clerk Maxwell, William Thomson, and others. His work on potential theory ran parallel to that of Carl Friedrich Gauss.

Green's life story is remarkable in that he was almost entirely self-taught. He received only about one year of formal schooling as a child, between the ages of 8 and 9.

Mathematical Proceedings of the Cambridge Philosophical Society

Mathematical Proceedings of the Cambridge Philosophical Society is a mathematical journal published by Cambridge University Press for the Cambridge Philosophical Society. It aims to publish original research papers from a wide range of pure and applied mathematics. The journal, formerly titled Proceedings of the Cambridge Philosophical Society, has been published since 1843.

On Physical Lines of Force

"On Physical Lines of Force" is a famous four-part paper written by James Clerk Maxwell published between 1861 and 1862. In it, Maxwell derived the equations of electromagnetism in conjunction with a "sea" of "molecular vortices" which he used to model Faraday's lines of force. Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/6 when "On Faraday's Lines of Force" was read to the Cambridge Philosophical Society. Maxwell made an analogy between the density of this medium and the magnetic permeability, as well as an analogy between the transverse elasticity and the dielectric constant, and using the results of a prior experiment by Wilhelm Eduard Weber and Rudolf Kohlrausch performed in 1856, he established a connection between the speed of light and the speed of propagation of waves in this medium.

The paper ushered in a new era of classical electrodynamics and catalyzed further progress in the mathematical field of vector calculus. Because of this, it is considered one of the most historically significant publications in the field of physics and of science in general, comparable with Einstein's Annus Mirabilis papers and Newton's Principia Mathematica.

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 after him.


Pliosauridae is a family of plesiosaurian marine reptiles from the Earliest Jurassic to the early Late Cretaceous (Hettangian to Turonian stages) of Australia, Europe, North America and South America. Past the Turonian, they may have been replaced by the mosasaurs. It was formally named by Harry G. Seeley in 1874.


Procolophonomorpha is an order or clade of early reptiles that appeared during the Middle Permian. It constitutes a diverse assemblage that includes a number of lizard-like forms, as well as more diverse types such as the pareiasaurs. The most important subclade, Procolophonia, is traditionally thought to be ancestral to (and hence to include) turtles. Lee 1995, 1996, 1997 argues that turtles evolved from pareiasaurs, but this view is by no means held unanimously. Rieppel and deBraga 1996 and deBraga and Rieppel, 1997 argue that turtles evolved from sauropterygians.

Robert Peirson

Robert Peirson (2 June 1821 – 15 June 1891) was an English astronomer and theoretical physicist.Born into a wealthy family at their residence at No. 5, Barnsbury Park, Islington, Middlesex, Robert Peirson lived his life there except during his residence at Cambridge.

He was admitted a Foundation Scholar in 1842, and took his degree as Third Wrangler in 1845, the year of Dr Parkinson and Sir William Thomson (now Lord Kelvin). He was admitted a Fellow of the College in 1849 in succession to Mr Blick, who had accepted the living of Brandesburton; and kept his Fellowship till 1855. He does not appear to have held any College office. In 1850 he was awarded the first Adams Prize, founded in 1848, for an essay on The Theory of the Long Inequality of Uranus and Neptune, which was printed in vol. ix of the Transactions of the Cambridge Philosophical Society.

After leaving Cambridge he lived a reclusive life and occupied himself with the study of astronomy and optics. In 1858 he purchased several acres of land in Wimbledon Park, Surrey, and arranged the construction there during 1859 to 1861 of a stately residence, which he named Devonshire Lodge. However, he suffered a severe financial reverse shortly before he could move there. Consequently, he had to sell Devonshire Lodge and remain at his Barnsbury residence.

He never married. His posthumous papers were examined by Alfred William Flux, Fellow of St John's College, Cambridge, with a view to the publication of some portion of them. In 1893, St. John's College Library acquired the manuscript papers and a few notebooks. The material is contained in 50 boxes, and the majority relates to astronomy and optics, dating from 1854 to 1890.

Sir George Stokes, 1st Baronet

Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Anglo-Irish physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Lucasian Professor of Mathematics from 1849 until his death in 1903. As a physicist, Stokes made seminal contributions to fluid dynamics, including the Navier-Stokes equation, and to physical optics, with notable works on polarization and fluorescence. As a mathematician, he popularised "Stokes' theorem" in vector calculus and contributed to the theory of asymptotic expansions.

Stokes was made a baronet (hereditary knight) by the British monarch in 1889. In 1893 he received the Royal Society's Copley Medal, then the most prestigious scientific prize in the world, "for his researches and discoveries in physical science". He represented Cambridge University in the British House of Commons from 1887 to 1892, sitting as a Tory. Stokes also served as president of the Royal Society from 1885 to 1890 and was briefly the Master of Pembroke College, Cambridge.

Ursell number

In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953.

The Ursell number is derived from the Stokes wave expansion, a perturbation series for nonlinear periodic waves, in the long-wave limit of shallow water – when the wavelength is much larger than the water depth. Then the Ursell number U is defined as:

which is, apart from a constant 3 / (32 π2), the ratio of the amplitudes of the second-order to the first-order term in the free surface elevation. The used parameters are:

So the Ursell parameter U is the relative wave height H / h times the relative wavelength λ / h squared.

For long waves (λh) with small Ursell number, U ≪ 32 π2 / 3 ≈ 100, linear wave theory is applicable. Otherwise (and most often) a non-linear theory for fairly long waves (λ > 7 h) – like the Korteweg–de Vries equation or Boussinesq equations – has to be used. The parameter, with different normalisation, was already introduced by George Gabriel Stokes in his historical paper on surface gravity waves of 1847.

Valentine Joseph

Valentine Joseph (27 January 1929 – 15 March 2017) was a Sri Lankan Tamil mathematician, noted for his contributions to education.

William Bate Hardy Prize

The William Bate Hardy Prize is awarded by the Cambridge Philosophical Society. It is awarded once in three years “for the best original memoir, investigation or discovery by a member of the University of Cambridge in connection with Biological Science that may have been published during the three years immediately preceding”.

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