A History of Mathematics at Cambridge from the early days to the present

The University of Cambridge has taught and hosted some of the most influential mathematicians throughout history. An extraordinary number of pioneering thinkers from Cambridge have produced work that continues to influence mathematical research and many other areas of human endeavour, and many of our current mathematicians continue in this tradition. These include:

James Maxwell (1831–1879) Robert Recorde (c.1512-1558) Mathematician who carried out Welsh physician and mathematician revolutionary work on electricity and credited with inventing the equals magnetism and on the kinetic theory of (=) sign. gases. Formulated ‘Maxwell’s Equations’, a major breakthrough in the field of electrodynamics. Isaac Newton (1643-1727) Lord Rayleigh (1842-1919) Mathematician and physicist who Physicist who co-discovered Argon, continues to be recognised as one of for which he won the Nobel Prize the most influential scientists of all time. for physics in 1904, and discovered a Formulated the laws of motion and phenomenon now named Rayleigh made significant contributions to optics. scattering, which explains why the sky is blue. Brook Taylor (1685-1731) Discovered what came to be known Philippa Fawcett (1868-1948) as Taylor’s Theorem and the Taylor Mathematician and educationalist who Series, which approximates any n-times conducted research in fluid dynamics. differentiable function by a nth-order In 1890 she became the first woman to obtain the highest score in the polynomial. Mathematical Tripos exams. She was the daughter of suffragist Millicent Fawcett. Charles Babbage (1791-1871) Created the ‘difference engine’ to Bertrand Russell (1872-1970) perform mathematical calculations, With A. N. Whitehead he wrote and later the ‘analytical engine’, which Principia Mathematica, an attempt provided the foundations for many of to create a logical foundation for the fundamental ideas behind today’s mathematics, and one of the most computers. He famously worked with famous texts ever written on the Ada Lovelace, the first programmer. foundations of mathematics. As well as a mathematician, he was a philosopher, George Green (1793-1841) historian and political activist. Developed the famous Green’s Theorem, relating line integrals to Srinivasa Ramanujan (1887-1920) double integrals over a region. A self- A self-taught Indian mathematician, he taught mathematician, he was the made extraordinary contributions to son of a baker and worked as a miller many areas of pure mathematics, in spite until he became an undergraduate at of having almost no formal education. Cambridge at the age of 40. Among his many discoveries are the Lord Kelvin (1824-1907) Ramanujan prime and the Ramanujan Mathematical physicist and engineer theta function. whose triumphs included the first Mary Cartwright (1900-1998) practical trans-Atlantic cable, a First female mathematician to be tidal prediction machine and the elected to the Royal Society. With J.E. standard marine compass. His Littlewood she was the first to analyse a pioneering thermodynamics work dynamical system with chaos. is commemorated in the absolte temperature scale of degreed Kelvin. www.maths.cam.ac.uk/undergraduate-admissions Paul Dirac (1902-1984) Steven Hawking (1942-2018) Creator of the complete theoretical One of the most well-known present-day formulation of quantum mechanics. mathematicians, his work focused mainly Among his many achievements was on cosmology. He predicted that black the prediction of the positron. His holes emit radiation and proposed a contributions to quantum mechanics theory that could unify general relativity won him the Nobel prize in Physics. and quantum mechanics. He published many popular science books, including ‘A Brief History of Time’. Alan Turing (1912-1954) Mathematician, wartime code-breaker, Anne Davis (1951- ) and computer science pioneer. Works in the field of theoretical and Reformulated Gödel’s results on particularly modified gravity theory. decidability, creating what is now She has been one of the leading known as Turing Machines, which are proponents of the chameleon particle capable of simulating the logic of any theory that potentially accounts for the computer algorithm. observed acceleration of the universe which presents a major cosmological puzzle. Abdus Salam (1926-1996) Pioneered the mathematics behind David Spiegelhalter (1953- ) the first Grand Unified Theory of Statistician and Winton Professor of physics, using Lie Algebras. In 1979 the Public Understanding of Risk. His he won the Nobel prize in physics for research includes the Bayesian his contribution to the electroweak approach to clinical trials and unification. Many of his theories have epidemiology. His blog, ‘Understanding been proven by experiments conducted Uncertainty’, explains statistics to a in the Large Hadron Collider. general audience

James Lighthill (1924-1998) His pioneering work in fluid dynamics Frances Kirwan (1959- ) and noise reduction was used in the Her work in algebraic and symplectic design of Concorde. He founded geometry has earned her the Senior Whitehead Prize, and has advanced nonlinear acoustics, and showed the understanding of the structure of that the same nonlinear equations geometric objects by investigating could model waves in rivers and road their algebraic and topological traffic flow. He also helped develop properties. She was the second communication satellites, and applied youngest President of the London fluid mechanics to understanding blood Mathematical Society. flow and breathing.

James Ezeilo (1930-2013) Tim Gowers (1963- ) Often referred to as the father of His early work on Banach spaces mathematics in Nigeria, his work earned him the Junior Whitehead included pioneering use of Leray- Prize. He specialises in combinatorics Schauder degree theory. As a PhD and combinatorial number theory, student of Mary Cartwright in among other fields, and was Cambridge he advanced the theory of awarded the Fields Medal for his non-linear differential equations of the many mathematical achievements. third order. Pioneered internet-based “massively collaborative mathematics”.

Come and join one of the best Mathematics Faculties in the world. Some of the new Cambridge mathematicians of today will shape the future of mathematical research and use mathematical theories and equations to advance fields as diverse as medical diagnostics, cryptography and internet security, the behaviour of avalanches, epidemiology, the prediction of financial markets, climate change, linguistics, art restoration, communication networks, from the nervous system to the internet, and many more. Be one of them! www.maths.cam.ac.uk/undergraduate-admissions