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

English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...

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, structure, space, models, and change. History O ...

, 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, metropolitan borough and administrative centre in the West Midlands, England. The population size has increased by 5.7%, from around 249,500 in 2011 to 263,700 in 2021. People from the city are called "Wulfrunian ...

, 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. It is bounded to the south by of coastline that stretch along the Atlantic Ocean, South Atlantic and Indian Oceans; to the ...

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

St John's College, Cambridge St John's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge founded by the House of Tudor, Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corpo ...

, where in 1895 he became

Senior Wrangler The Senior Frog 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 ...

. 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. 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 judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemati ...

. 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 market town and civil parish in the East Midlands of England, on the River Nene, north-west of London and south-east of Birmingham. The county town of Northamptonshire, Northampton is one of the largest towns in England ...

on 24 August 1929, a suicide.

Work

Bromwich worked in both

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

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 (3 ...

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 FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vec ...

'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 the piecewise-continuous and exponentially-restricted real function ''f''(''t'') which has the property: :\mathcal\(s) = \mathcal\(s) = F(s), where \mathcal denotes the ...

. 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, and electric circuits. ...

, and the scattering of electromagnetic

plane wave In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, th ...

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 most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

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 in England 1929 suicides