Joseph Henry Maclagan Wedderburn

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and letters, judged to be "eminently distinguished in their subject". This soci ...

FRS (2 February 1882 – 9 October 1948) was a Scottish mathematician, who taught at

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ...

for most of his career. A significant algebraist, he proved that a finite

division algebra In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible. Definitions Formally, we start with a non-zero algebra ''D'' over a fie ...

is a field, and part of the Artin–Wedderburn theorem on

simple algebra In abstract algebra, a branch of mathematics, a simple ring is a non-zero ring that has no two-sided ideal besides the zero ideal and itself. In particular, a commutative ring is a simple ring if and only if it is a field. The center of a sim ...

s. He also worked on

group theory In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen ...

and

matrix algebra In abstract algebra, a matrix ring is a set of matrices with entries in a ring ''R'' that form a ring under matrix addition and matrix multiplication . The set of all matrices with entries in ''R'' is a matrix ring denoted M''n''(''R'')Lang, '' ...

. His younger brother was the lawyer

Ernest Wedderburn Sir Ernest MacLagan Wedderburn (3 February 1884 – 3 June 1958) was a Scottish lawyer, and a significant figure both in the civic life of Edinburgh and in the legal establishment. He held the posts of Professor of Conveyancing in the Univers ...

Life

Joseph Wedderburn was the tenth of fourteen children of Alexander Wedderburn of Pearsie, a physician, and Anne Ogilvie. He was educated at Forfar Academy then in 1895 his parents sent Joseph and his younger brother

Ernest Ernest is a given name derived from Germanic word ''ernst'', meaning "serious". Notable people and fictional characters with the name include: People *Archduke Ernest of Austria (1553–1595), son of Maximilian II, Holy Roman Emperor * Ernest, ...

to live in

Edinburgh Edinburgh ( ; gd, Dùn Èideann ) is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. Historically part of the county of Midlothian (interchangeably Edinburghshire before 1921), it is located in Lothian ...

with their paternal uncle, J R Maclagan Wedderburn, allowing them to attend

George Watson's College George Watson's College is a co-educational independent day school in Scotland, situated on Colinton Road, in the Merchiston area of Edinburgh. It was first established as a hospital school in 1741, became a day school in 1871, and was m ...

. This house was at 3 Glencairn Crescent in the West End of the city. In 1898 Joseph entered the

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 1 ...

. In 1903, he published his first three papers, worked as an assistant in the Physical Laboratory of the University, obtained an MA degree with

First Class Honours The British undergraduate degree classification system is a grading structure for undergraduate degrees or bachelor's degrees and integrated master's degrees in the United Kingdom. The system has been applied (sometimes with significant variati ...

in mathematics, and was elected a Fellow of the

Royal Society of Edinburgh The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

, upon the proposal of

George Chrystal George Chrystal FRSE FRS (8 March 1851 – 3 November 1911) was a Scottish mathematician. He is primarily know for his books on algebra and his studies of seiches (wave patterns in large inland bodies of water) which earned him a Gold Meda ...

, James Gordon MacGregor,

Cargill Gilston Knott Cargill Gilston Knott FRS, FRSE LLD (30 June 1856 – 26 October 1922) was a Scottish physicist and mathematician who was a pioneer in seismological research. He spent his early career in Japan. He later became a Fellow of the Royal Society, ...

and William Peddie. Aged only 21 he remains one of the youngest Fellows ever. He then studied briefly at the

University of Leipzig Leipzig University (german: Universität Leipzig), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December ...

and the

University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative ...

, where he met the algebraists Frobenius and Schur. A

Carnegie Scholarship Carnegie may refer to: People *Carnegie (surname), including a list of people with the name *Clan Carnegie, a lowland Scottish clan Institutions Named for Andrew Carnegie * Carnegie Building (Troy, New York), on the campus of Rensselaer Polyte ...

allowed him to spend the 1904–1905 academic year at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

where he worked with

Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this wa ...

, E. H. Moore, and most importantly,

Leonard Dickson Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also reme ...

, who was to become the most important American algebraist of his day. Returning to Scotland in 1905, Wedderburn worked for four years at the

as an assistant to

, who supervised his

D.Sc Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used f ...

, awarded in 1908 for a thesis titled ''On Hypercomplex Numbers''. He gained a PhD in algebra from the University of Edinburgh in 1908. From 1906 to 1908, Wedderburn edited the ''

Proceedings of the Edinburgh Mathematical Society In academia and librarianship, conference proceedings is a collection of academic papers published in the context of an academic conference or workshop. Conference proceedings typically contain the contributions made by researchers at the conferen ...

''. In 1909, he returned to the United States to become a Preceptor in Mathematics at

; his colleagues included Luther P. Eisenhart,

Gilbert Ames Bliss Gilbert Ames Bliss, (9 May 1876 – 8 May 1951), was an American mathematician, known for his work on the calculus of variations. Life Bliss grew up in a Chicago family that eventually became affluent; in 1907, his father became president of the ...

, and George Birkhoff. Upon the outbreak of the

First World War World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...

, Wedderburn enlisted in the British Army as a private. He was the first person at Princeton to volunteer for that war, and had the longest war service of anyone on the staff. He served with the

Seaforth Highlanders The Seaforth Highlanders (Ross-shire Buffs, The Duke of Albany's) was a line infantry regiment of the British Army, mainly associated with large areas of the northern Highlands of Scotland. The regiment existed from 1881 to 1961, and saw service ...

in France, as

Lieutenant A lieutenant ( , ; abbreviated Lt., Lt, LT, Lieut and similar) is a commissioned officer rank in the armed forces of many nations. The meaning of lieutenant differs in different militaries (see comparative military ranks), but it is often ...

(1914), then as

Captain Captain is a title, an appellative for the commanding officer of a military unit; the supreme leader of a navy ship, merchant ship, aeroplane, spacecraft, or other vessel; or the commander of a port, fire or police department, election precinct, e ...

of the 10th Battalion (1915–18). While a Captain in the Fourth Field Survey Battalion of the

Royal Engineers The Corps of Royal Engineers, usually called the Royal Engineers (RE), and commonly known as the ''Sappers'', is a corps of the British Army. It provides military engineering and other technical support to the British Armed Forces and is head ...

in France, he devised sound-ranging equipment to locate enemy artillery. He returned to Princeton after the war, becoming Associate Professor in 1921 and editing the ''

Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as th ...

'' until 1928. While at Princeton, he supervised only three PhDs, one of them being

Nathan Jacobson Nathan Jacobson (October 5, 1910 – December 5, 1999) was an American mathematician. Biography Born Nachman Arbiser in Warsaw, Jacobson emigrated to America with his family in 1918. He graduated from the University of Alabama in 1930 and was awar ...

. In his later years, Wedderburn became an increasingly solitary figure and may even have suffered from depression. His isolation after his 1945 early retirement was such that his death from a heart attack was not noticed for several days. His

Nachlass ''Nachlass'' (, older spelling ''Nachlaß'') is a German word, used in academia to describe the collection of manuscripts, notes, correspondence, and so on left behind when a scholar dies. The word is a compound in German: ''nach'' means "after ...

was destroyed, as per his instructions. Wedderburn received the MacDougall-Brisbane Gold Medal and Prize from the

in 1921, and was elected to the

Royal Society of London 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, r ...

in 1933.

Work

In all, Wedderburn published about 40 books and papers, making important advances in the theory of rings, algebras and matrix theory. In 1905, Wedderburn published a paper that included three claimed proofs of a theorem stating that a noncommutative

finite Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...

division ring In algebra, a division ring, also called a skew field, is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial ring in which every nonzero element has a multiplicative inverse, that is, an element ...

could not exist. The proofs all made clever use of the interplay between the additive group of a finite

''A'', and the

multiplicative group In mathematics and group theory, the term multiplicative group refers to one of the following concepts: *the group under multiplication of the invertible elements of a field, ring, or other structure for which one of its operations is referre ...

''A''* = ''A''-. Parshall (1983) notes that the first of these three proofs had a gap not noticed at the time. Meanwhile, Wedderburn's Chicago colleague Dickson also found a proof of this result but, believing Wedderburn's first proof to be correct, Dickson acknowledged Wedderburn's priority. But Dickson also noted that Wedderburn constructed his second and third proofs only after having seen Dickson's proof. Parshall concludes that Dickson should be credited with the first correct proof. This theorem yields insights into the structure of

projective geometries. In their paper on "Non-Desarguesian and non-Pascalian geometries" in the 1907 ''

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...

'', Wedderburn and Veblen showed that in these geometries,

Pascal's theorem In projective geometry, Pascal's theorem (also known as the ''hexagrammum mysticum theorem'') states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined ...

is a consequence of

Desargues' theorem In projective geometry, Desargues's theorem, named after Girard Desargues, states: :Two triangles are in perspective ''axially'' if and only if they are in perspective ''centrally''. Denote the three vertices of one triangle by and , and ...

. They also constructed finite projective geometries which are neither "Desarguesian" nor "Pascalian" (the terminology is

Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many ...

's). Wedderburn's best-known paper was his sole-authored "On hypercomplex numbers," published in the 1907

Proceedings of the London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

, and for which he was awarded the D.Sc. the following year. This paper gives a complete classification of

simple Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by Johnn ...

and

semisimple algebra In ring theory, a branch of mathematics, a semisimple algebra is an associative artinian algebra over a field which has trivial Jacobson radical (only the zero element of the algebra is in the Jacobson radical). If the algebra is finite-dimen ...

s. He then showed that every finite-dimensional

can be constructed as a direct sum of

s and that every

isomorphic In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word i ...

to a

for some

. The Artin–Wedderburn theorem generalises this result, with the ascending chain condition. His best known book is his
Lectures on Matrices
' (1934), which Jacobson praised as follows: About Wedderburn's teaching:

Life

Work

See also

References

Further reading