seamus dubhghaill

Promoting Irish Culture and History from Little Rock, Arkansas, USA

Tag Archives: Geometrical Optics


by Leave a comment

Birth of John Lighton Synge, Mathematician & Physicist

John Lighton Synge FRSC FRS, mathematician and physicist, whose seven-decade career includes significant periods in Ireland, Canada, and the United States, is born in Dublin on March 23, 1897. He is a prolific author and influential mentor and is credited with the introduction of a new geometrical approach to the theory of relativity.

Synge is born into a prominent Church of Ireland family. His uncle, John Millington Synge, is a famous playwright. He is more distantly related to the winner of the 1952 Nobel Prize in Chemistry, Richard Laurence Millington Synge. He is a great-great-great-grandson of the mathematician and bishop Hugh Hamilton.

Synge attends St. Andrew’s College, Dublin and in 1915 enters Trinity College Dublin (TCD). He is elected a Foundation Scholar his first year, which is unusual as it is normally won by more advanced students. While an undergraduate at TCD, he spots a non-trivial error in Analytical Dynamics of Particles and Rigid Bodies, a textbook by E. T. Whittaker, who had recently taught there, and notifies Whittaker of the error. In 1919 he is awarded a BA in Mathematics and Experimental Physics, and also a gold medal for outstanding merit. In 1922 he is awarded an MA, and in 1926 a Sc.D., the latter upon submission of his published papers up to then.

In 1918, Synge marries Elizabeth Eleanor Mabel Allen. She is also a student at TCD, first of mathematics, then of history, but family finances forced her to leave without graduating. Their daughters Margaret (Pegeen), Cathleen and Isabel are born in 1921, 1923 and 1930 respectively. The middle girl grows up to become the distinguished Canadian mathematician Cathleen Synge Morawetz.

Synge is appointed to the position of lecturer at Trinity College, and then accepts a position at the University of Toronto in 1920, where he is an assistant professor of mathematics until 1925. There he attends 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.

Synge returns to Trinity College Dublin, in 1925, where he is elected to a fellowship and is appointed the University Professor of Natural Philosophy (later to be known as “physics”). He is a member of the American Mathematical Society and the London Mathematical Society. He is treasurer of the Royal Irish Academy in 1929. He goes back to Toronto in 1930, where he is appointed Professor of Applied Mathematics and becomes Head of the Department of Applied Mathematics. In 1940, he supervises three Chinese students, Guo Yonghuai, Qian Weichang and Chia-Chiao Lin, who later become leading applied mathematicians in China and the United States.

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

Synge returns 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, a contributor to quantum mechanics, who is also a Senior Professor.

Synge makes 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 Albert Einstein‘s theory of relativity. He studies an extensive range of mathematical physics problems, but his best-known work revolves around using geometrical methods in general relativity.

Synge is one of the first physicists to seriously study the interior of a black hole, and his early work is cited by both Martin David Kruskal and George Szekeres in their independent discoveries of the true structure of the Schwarzschild black hole. Synge’s later derivation of the Szekeres-Kruskal metric solution, which is motivated by a desire to avoid “using ‘bad’ coordinates to obtain ‘good’ coordinates,” has been generally under-appreciated in the literature, but is adopted by Chandrasekhar in his black hole monograph.

In pure mathematics, Synge is perhaps best known for Synge’s theorem, which concerns the topology of closed orientable Riemannian manifold of positive sectional curvature. When such a space is even-dimensional and orientable, the theorem says it must be simply connected. In odd dimensions, it instead says that such a space is necessarily orientable.

Synge also creates the game of Vish in which players compete to find circularity (vicious circles) in dictionary definitions.

Synge retires in 1972. He receives many honours for his works. He is elected as a fellow of the Royal Society of London in 1943. He is elected as a fellow of the Royal Society of Canada, and in 1943 is 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. In 1954 he is elected an honorary fellow of Trinity College Dublin. He is president of the Royal Irish Academy from 1961 until 1964. The Royal Society of Canada establishes the John L. Synge Award in his honour in 1986.

Synge dies on March 30, 1995, in Dublin, exactly one week after his ninety-eighth birthday.


by 2 Comments

Death of Mathematician Sir William Rowan Hamilton

Sir William Rowan Hamilton, Irish mathematician, Andrews Professor of Astronomy at Trinity College, Dublin, and Royal Astronomer of Ireland, who makes important contributions to classical mechanics, optics, and algebra, dies in Dublin on September 2, 1865, following a severe attack of gout.

Hamilton is born in Dublin on August 4, 1805, the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819). He is part of a small but well-regarded school of mathematicians associated with Trinity College, Dublin, which he enters at age eighteen. He is said to have shown immense talent at a very early age. Astronomer Bishop Dr. John Brinkley remarks of the 18-year-old Hamilton, “This young man, I do not say will be, but is, the first mathematician of his age.”

Trinity College awards him two Optimes, or off-the-chart grades. He studies both classics and mathematics and is appointed Professor of Astronomy just prior to his graduation. He then takes up residence at Dunsink Observatory where he spends the rest of his life.

Although Hamilton regards himself as a pure mathematician rather than a physicist, his work is of major importance to physics, particularly his reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In pure mathematics, he is best known as the inventor of quaternions.

Hamilton’s scientific career includes the study of geometrical optics, classical mechanics, adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions, solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions, linear operators on quaternions and proving a result for linear operators on the space of quaternions, which is a special case of the general theorem which today is known as the Cayley–Hamilton theorem. He also invents Icosian calculus, which he uses to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.

Hamilton retains his faculties unimpaired to the very last, and steadily continues the task of finishing the Elements of Quaternions which occupies the last six years of his life. He dies in Dublin on September 2, 1865, following a severe attack of gout precipitated by excessive drinking and overeating. He is buried in Mount Jerome Cemetery in Dublin.


by Leave a comment

Birth of Mathematician William Rowan Hamilton

william-rowan-hamilton

Sir William Rowan Hamilton, Irish mathematician who makes important contributions to classical mechanics, optics, and algebra, is born in Dublin on August 4, 1805.

Hamilton is the fourth of nine children born to Sarah Hutton (1780–1817) and Archibald Hamilton (1778–1819). He is part of a small but well-regarded school of mathematicians associated with Trinity College, Dublin, which he enters at age eighteen. He is said to have shown immense talent at a very early age. Astronomer Bishop Dr. John Brinkley remarks of the 18-year-old Hamilton, “This young man, I do not say will be, but is, the first mathematician of his age.”

Trinity College awards him two Optimes, or off-the-chart grades. He studies both classics and mathematics, and is appointed Professor of Astronomy just prior to his graduation. He then takes up residence at Dunsink Observatory where he spends the rest of his life.

Although Hamilton regards himself as a pure mathematician rather than a physicist, his work is of major importance to physics, particularly his reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In pure mathematics, he is best known as the inventor of quaternions.

Hamilton’s scientific career includes the study of geometrical optics, classical mechanics, adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions, solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions, linear operators on quaternions and proving a result for linear operators on the space of quaternions, which is a special case of the general theorem which today is known as the Cayley–Hamilton theorem. He also invents Icosian calculus, which he uses to investigate closed edge paths on a dodecahedron that visit each vertex exactly once.

Hamilton retains his faculties unimpaired to the very last, and steadily continues the task of finishing the Elements of Quaternions which occupies the last six years of his life. He dies on September 2, 1865, following a severe attack of gout precipitated by excessive drinking and overeating. He is buried in Mount Jerome Cemetery in Dublin.