Thomas John I'Anson Bromwich (8 February 1875 – 24 August 1929) was an English

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, mathematical structure, structure, space, Mathematica ...

, and a fellow of the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

Life

Thomas John I'Anson Bromwich was born on 8 February 1875, in

Wolverhampton Wolverhampton ( ) is a city and metropolitan borough in the West Midlands (county), West Midlands of England. Located around 12 miles (20 km) north of Birmingham, it forms the northwestern part of the West Midlands conurbation, with the towns of ...

, England. He was descended from Bryan I'Anson, of Ashby St Ledgers, Sheriff of London and father of the 17th century 1st Baronet Sir Bryan I'Anson of Bassetsbury. His parents emigrated to

South Africa South Africa, officially the Republic of South Africa (RSA), is the Southern Africa, southernmost country in Africa. Its Provinces of South Africa, nine provinces are bounded to the south by of coastline that stretches along the Atlantic O ...

, where in 1892 he graduated from high school. He attended

St John's College, Cambridge St John's College, formally the College of St John the Evangelist in the University of Cambridge, is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, founded by the House of Tudor, Tudor matriarch L ...

, where in 1895 he became

Senior Wrangler The Senior Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain". Specifically, it is the person who achiev ...

. In 1897, he became a lecturer at St. John's. From 1902 to 1907, he was a professor of mathematics at

Queen's College, Galway The University of Galway () is a public research university located in the city of Galway, Ireland. The university was founded in 1845 as "Queen's College, Galway". It was known as "University College, Galway" (UCG) () from 1908 to 1997 and as ...

. In 1906, he was elected a

fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

. In 1907, he returned to Cambridge and again became a fellow and lecturer at St. John's. He was a vice president of the Royal Society in 1919 and 1920. He died in

Northampton Northampton ( ) is a town and civil parish in Northamptonshire, England. It is the county town of Northamptonshire and the administrative centre of the Unitary authorities of England, unitary authority of West Northamptonshire. The town is sit ...

on 24 August 1929, hanging himself in his bedroom.

Work

Bromwich worked in both

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

and

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

G. H. Hardy Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...

called him "The best pure mathematician among the applied mathematicians at Cambridge, and the best applied mathematician among the pure mathematicians". Today, Bromwich is perhaps best known for justifying

Oliver Heaviside Oliver Heaviside ( ; 18 May 1850 – 3 February 1925) was an English mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, an ...

's operator calculus. Part of this involved using a

contour integral In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration is closely related to the calculus of residues, a method of complex analysis. ...

to do an

inverse Laplace transform In mathematics, the inverse Laplace transform of a function F(s) is a real function f(t) that is piecewise- continuous, exponentially-restricted (that is, , f(t), \leq Me^ \forall t \geq 0 for some constants M > 0 and \alpha \in \mathbb) and h ...

. This particular contour integral is now often called the ''Bromwich integral'', although it is also called by other names. Other topics Bromwich investigated include solutions of the

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, Electrical network, electr ...

, and the scattering of electromagnetic

plane wave In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of ...

s by spheres. He also investigated, and wrote a book on, the theory of

quadratic form In mathematics, a quadratic form is a polynomial with terms all of degree two (" form" is another name for a homogeneous polynomial). For example, 4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong t ...

s. In 1906 he derived Bromwich inequality in the field of

matrices Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the ...

which gives narrower bounds to characteristic roots than those given by Bendixson's inequality. In 1908 he wrote ''An introduction to the theory of infinite series''. A second edition appeared in 1926. G. H. Hardy praised the book highly, while criticizing the way in which it was laid out. The book is still in print. Here is th
publisher's description
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Notes

External links

* {{DEFAULTSORT:Bromwich, Thomas John I'Anson Fellows of the Royal Society Alumni of St John's College, Cambridge Fellows of St John's College, Cambridge 20th-century English mathematicians People from Wolverhampton Senior Wranglers 1875 births 1929 deaths Suicides by hanging in England 1929 suicides