# John Lighton Synge

**John Lighton Synge** (/sɪŋ/; 23 March 1897 – 30 March 1995)^{[1]} was an Irish mathematician and physicist.

## Background

Synge was born 1897 in Dublin, Ireland, in a Protestant family and educated at St. Andrew's College, Dublin. He entered Trinity College, Dublin in 1915. He won a Foundation Scholarship in his first year, which was remarkable because it was normally won by third year students. While an undergraduate he spotted a non-trivial error in a leading textbook in advanced mathematical analysis, written by E. T. Whittaker, and notified Whittaker of the error.^{[2]} In 1919 he was awarded an M.A. in both Mathematics and Experimental Physics, and also a gold medal for outstanding merit.

He married Eleanor Mabel Allen in 1918. Their daughters Margaret (Pegeen), Cathleen and Isabel were born in 1921, 1923 and 1930 respectively. Synge's daughter Cathleen Synge Morawetz went on to become a distinguished mathematician too. Synge's uncle John Millington Synge was a famous playwright, and Synge is more distantly related to the 1952 Nobel prizewinner in chemistry Richard Laurence Millington Synge. His older brother, Edward Hutchinson Synge, also won a Foundation Scholarship in Trinity for Mathematics, and while his achievements are often overshadowed by his more famous brother, he is known for his pioneering work in optics, particularly in near field optical imaging.

He died on 30 March 1995 in Dublin.

## Career in mathematics and physics

Synge was appointed to the position of lecturer at Trinity College, and then accepted a position at the University of Toronto in 1920. From 1920 until 1925, Synge was an assistant professor of mathematics at the University of Toronto. There he attended lectures by Ludwik Silberstein on the theory of relativity, stimulating him to contribute "A system of space-time co-ordinates", a letter in *Nature* in 1921.^{[3]}^{[4]}

Synge returned to Trinity College, Dublin, in 1925, where he was elected to a fellowship and was appointed the University Professor of Natural Philosophy^{[5]} (the old name for physics). He was a member of the American Mathematical Society and the London Mathematical Society. He was treasurer of the Royal Irish Academy in 1929. He went back to Toronto in 1930. He was appointed Professor of Applied Mathematics and became Head of the Department of Applied Mathematics. In 1940, he supervised three Chinese students, Guo Yonghuai, Chien Wei-zang and Chia-Chiao Lin, who later became leading applied mathematicians in China and the United States.

He spent some of 1939 at Princeton University, and in 1941, he was a visiting professor at Brown University. In 1943 he was appointed as Chairman of the Mathematics Department of Ohio State University. Three years later he became Head of the Mathematics Department of the Carnegie Institute of Technology in Pittsburgh, where John Nash was one of his students. He spent a short time as a ballistic mathematician in the US Air Force between 1944 and 1945.

He returned to Ireland in 1948, accepting the position of Senior Professor in the School of Theoretical Physics at the Dublin Institute for Advanced Studies. This school had been set up in 1940, and had several outstanding members, including Erwin Schrödinger (who contributed to quantum mechanics), who was also a Senior Professor.

## His contributions

Synge made outstanding contributions to different fields of work including classical mechanics, general mechanics and geometrical optics, gas dynamics, hydrodynamics, elasticity, electrical networks, mathematical methods, differential geometry, and Einstein's theory of relativity. He studied an extensive range of mathematical physics problems, but his best known work revolved around using geometrical methods in general relativity.

He was one of the first physicists to seriously study the interior of a black hole, and is sometimes credited with anticipating the discovery of the structure of the Schwarzschild vacuum (a black hole).

He also created the game of Vish in which players compete to find circularity (vicious circles) in dictionary definitions.^{[6]}

## Honours

Synge received many honours for his works. He was elected as a fellow of the Royal Society of London in 1943. He was elected as a fellow of the Royal Society of Canada, and in 1943 was the first recipient of the society's Henry Marshall Tory Medal, as one of the first mathematicians working in Canada to be internationally recognised for his research in mathematics. He was president of the Royal Irish Academy from 1961 until 1964. The Royal Society of Canada established the John L. Synge Award in his honour in 1986.

John Lighton Synge retired in 1972. During his time at the Dublin Institute for Advanced Studies, about 12% of all workers in the relativity theory studied there. Professor Hermann Bondi, who gave the first J. L. Synge Public Lecture in 1992, had this to say: "Every one of the other 88% has been deeply influenced by his geometric vision and the clarity of his expression". He was awarded the Boyle Medal by the Royal Dublin Society in 1972.^{[7]}

During his long scientific career, Synge published over 200 papers and 11 books. He proved the result now known as Synge's theorem.

## Selected publications

- "Principal Directions in a Riemann Surface".
*Proc Natl Acad Sci U S A*.**8**(7): 198–203. 1922. Bibcode:1922PNAS....8..198S. doi:10.1073/pnas.8.7.198. PMC 1085093. PMID 16586876. - "Principal Directions in the Einstein Solar Field".
*Proc Natl Acad Sci U S A*.**8**(7): 204–207. 1922. Bibcode:1922PNAS....8..204S. doi:10.1073/pnas.8.7.204. PMC 1085094. PMID 16586877. - "A generalisation of the Riemannian line-element".
*Trans. Amer. Math. Soc*.**27**(1): 61–67. 1925. doi:10.1090/s0002-9947-1925-1501298-7. MR 1501298. - "The apsides of general dynamical systems".
*Trans. Amer. Math. Soc*.**34**(3): 481–522. 1932. doi:10.1090/s0002-9947-1932-1501649-7. MR 1501649. - "On the Expansion or Contraction of a Symmetrical Cloud under the Influence of Gravity".
*Proc Natl Acad Sci U S A*.**20**(12): 635–640. 1934. Bibcode:1934PNAS...20..635S. doi:10.1073/pnas.20.12.635. PMC 1076503. PMID 16587921. *Geometrical optics – an introduction to Hamilton's method.*Cambridge 1937.- "The absolute optical instrument".
*Trans. Amer. Math. Soc*.**44**(1): 32–46. 1938. doi:10.1090/s0002-9947-1938-1501960-5. MR 1501960. - with Byron Griffith:
*Principles of Mechanics.*McGraw Hill 1942, 3rd edn. 1959. *The hypercircle in mathematical physics – a method for the solution of boundary value problems.*Cambridge 1957.^{[8]}*Classical dynamics.*In: Siegfried Flügge (ed.):*Handbuch der Physik – Prinzipien der klassischen Dynamik und Feldtheorie.*1960.*Relativity – the General Theory.*North Holland 1960.^{[9]}*General Relativity.*In: DeWitt (ed.):*Relativity, Groups and Topology.*Les Houches Lectures 1963.- with Alfred Schild:
*Tensor Calculus.*University of Toronto Press, 1949,^{[10]}rev. edn. 1956, 1964, corr. printing 1969, 1981; Dover, 1978, 2009. *Relativity: The Special Theory.*North Holland, 1956,^{[11]}2nd edn. 1965, 1972.*Talking about relativity.*North Holland 1970.

## Notes

- ↑ Florides, P. S. (2008). "John Lighton Synge. 23 March 1897 -- 30 March 1995".
*Biographical Memoirs of Fellows of the Royal Society*.**54**: 401–424. doi:10.1098/rsbm.2007.0040. - ↑ McCartney and Whitaker, p. 212.
- ↑ E. Riehm & F. Hoffman (2011)
*Turbulent times in Mathematics*, p. 80, American Mathematical Society ISBN 978-0-8218-6914-7 - ↑ Synge, J. L. (27 October 1921). "A System of Space-Time Co-ordinates".
*Nature*.**108**: 275. Bibcode:1921Natur.108..275S. doi:10.1038/108275a0. - ↑ Spearman, T.D. (1992). "400 years of mathematics: The eighteenth century". Trinity College Dublin. Retrieved 17 September 2016.
- ↑ Synge,
*Science: Sense and Nonsense*, p. 23-24, p. 32. - ↑ "John L. Synge". Royal Dublin Society. Retrieved 11 February 2013.
- ↑ Diaz, J. B. (1959). "Review:
*The hypercircle method in mathematical physics*, by J. L. Synge".*Bull. Amer. Math. Soc*.**65**(2): 103–108. doi:10.1090/s0002-9904-1959-10301-3. - ↑ Schild, Alfred (1962). "Review:
*Relativity: The general theory*, by J. L. Synge".*Bull. Amer. Math. Soc*.**68**(3): 167–169. doi:10.1090/s0002-9904-1962-10729-0. - ↑ De Cicco, John (1951). "Review:
*Tensor calculus*, by J. L. Synge and A. Schild".*Bull. Amer. Math. Soc*.**57**(6): 500–502. doi:10.1090/S0002-9904-1951-09556-7. - ↑ Taub, A. H. (1956). "Review:
*Relativity: The special theory*, by J. L. Synge".*Bull. Amer. Math. Soc*.**62**(4): 420–423. doi:10.1090/s0002-9904-1956-10057-8.

## References

- McCartney, Mark; Andrew Whitaker (2003).
*Physicists of Ireland: Passion and Precision*. Bristol and Philadelphia: Institute of Physics Pub. ISBN 0-7503-0866-4. - Synge, J. L. (1951).
*Science: Sense and Nonsense*. London: Cape. ISBN 0-8369-7332-1. (worldcat) - Synge, J. L. (1957).
*Kandelman's Krim; A Realistic Fantasy*. London: Cape. (worldcat)

## External links

- John Lighton Synge at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "John Lighton Synge",
*MacTutor History of Mathematics archive*, University of St Andrews.