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 Literature, letters, judged to be "eminently distinguished in their subject". ...

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

Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...

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 ( Wedderburn's little theorem), 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 group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

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'') (alterna ...

. His younger brother was the lawyer Ernest Wedderburn.

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 the Germanic languages, Germanic word ''ernst'', meaning "serious", often shortened to Ernie. Notable people and fictional characters with the name include: People *Archduke Ernest of Austria (1553–1595), ...

to live in

Edinburgh Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh ...

with their paternal uncle, J. R. Maclagan Wedderburn, allowing them to attend George Watson's College. 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 (, ; abbreviated as ''Edin.'' in Post-nominal letters, post-nominals) is a Public university, public research university based in Edinburgh, Scotland. Founded by the City of Edinburgh Council, town council under th ...

. 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 used for undergraduate degrees or bachelor's degrees and integrated master's degrees in the United Kingdom. The system has been applied, sometimes with significant var ...

in mathematics, and was elected a Fellow of the

Royal Society of Edinburgh The Royal Society of Edinburgh (RSE) 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 establis ...

, upon the proposal of

George Chrystal George Chrystal FRSE FRS (8 March 1851 – 3 November 1911) was a Scottish mathematician. He is primarily known 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 and William Peddie. Aged 21 on election he remains one of the youngest Fellows ever. He then studied briefly at the

University of Leipzig Leipzig University (), 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 1409 by Frederick I, Electo ...

and the

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

, where he met the algebraists

Frobenius Frobenius is a surname. Notable people with the surname include: * Ferdinand Georg Frobenius (1849–1917), mathematician ** Frobenius algebra ** Frobenius endomorphism ** Frobenius inner product ** Frobenius norm ** Frobenius method ** Frobenius g ...

and Schur. A Carnegie Scholarship allowed him to spend the 1904–1905 academic year at the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

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 was lo ...

, E. H. Moore, and most importantly, Leonard Dickson, 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, 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 1909, he returned to the United States to become a Preceptor in Mathematics at

; his colleagues included Luther P. Eisenhart,

, Gilbert Ames Bliss, and

George Birkhoff George David Birkhoff (March21, 1884November12, 1944) was one of the top American mathematicians of his generation. He made valuable contributions to the theory of differential equations, dynamical systems, the four-color problem, the three-bo ...

. Upon the outbreak of the

First World War World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

, 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 Junior officer, junior commissioned officer rank in the armed forces of many nations, as well as fire services, emergency medical services, Security agency, security services ...

(1914), then as

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

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 the engineering arm of the British Army. It provides military engineering and other technical support to the British Armed Forces ...

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 t ...

'' until 1928. While at Princeton, he supervised only three PhDs, one of them being Nathan Jacobson. 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 language, 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 word, compound in ...

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

division ring In algebra, a division ring, also called a skew field (or, occasionally, a sfield), 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 multiplicativ ...

could not exist. The proofs all made clever use of the interplay between the

additive group An additive group is a group of which the group operation is to be thought of as ''addition'' in some sense. It is usually abelian, and typically written using the symbol + for its binary operation. This terminology is widely used with structu ...

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 finite 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 pure and applied mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must ...

'', Wedderburn and Veblen showed that in these geometries, Pascal's theorem 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 tho ...

. 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 and philosophy of mathematics, philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad ...

'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 John ...

and semisimple algebras. He then showed that every finite-dimensional semisimple algebra can be constructed as a direct sum of

s and that every

isomorphic In mathematics, an isomorphism is a structure-preserving mapping or morphism 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 the ...

to a

for some

. The Artin–Wedderburn theorem generalises these results to algebras with the descending 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