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 university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
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
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
, and part of the
Artin–Wedderburn theorem on
simple algebras. 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'')Lang, ''U ...
.
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 Universi ...
.
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
Forfar Academy is a comprehensive school serving the community in and around the market town of Forfar, Angus, Scotland.
In 2019, Forfar Academy was ranked 251 out of 339 secondary schools in Scotland for pupils achieving 5 highers or more.
Nota ...
then in 1895 his parents sent Joseph and his younger brother
Ernest
Ernest is a given name derived from Germanic languages, 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 ...
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 school (United Kingdom), independent day school in Scotland, situated on Colinton Road, in the Merchiston area of Edinburgh. It was first established as a Scottish education in the eight ...
. 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 15 ...
. 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
James Gordon MacGregor, FRS FRSE LLD (31 March 1852 in Halifax, Canada – 21 May 1913 in Edinburgh) was a Canadian physicist. He was described as "brilliant, energetic, nervous, impatient", and not suffering fools gladly.
Life
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
250px, William Peddie (ca 1910)
William Peddie FRSE LLD (31 May 1861 – 2 June 1946) was a Scottish physicist and applied mathematician, known for his research on colour vision and molecular magnetism.
Life
He was born in Papa Westray in Orkney ...
. 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 Decemb ...
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 o ...
, 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 was lon ...
,
E. H. Moore
Eliakim Hastings Moore (; January 26, 1862 – December 30, 1932), usually cited as E. H. Moore or E. Hastings Moore, was an American mathematician.
Life
Moore, the son of a Methodist minister and grandson of US Congressman Eliakim H. Moore, di ...
, 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
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 15 ...
as an assistant to
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 ...
, 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
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
; his colleagues included
Luther P. Eisenhart,
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 lon ...
,
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 one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
, 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 servic ...
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 sub ...
(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 heade ...
in France, he devised
sound-ranging
In land warfare, artillery sound ranging is a method of determining the coordinates of a hostile battery using data derived from the sound of its guns (or mortar or rockets) firing. The same methods can also be used to direct artillery fire at ...
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 the ...
'' 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
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 ...
from 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 ...
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, re ...
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
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 structures ...
of 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 ...
''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
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 ...
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 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, 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
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 ...
can be constructed as a direct sum of
simple algebras and that every
simple algebra is
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 is ...
to a
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, ''U ...
for some
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 ...
. 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:
See also
*
Hypercomplex number
In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers.
The study of hypercomplex numbers in the late 19th century forms the basis of modern group represent ...
s
*
Wedderburn–Etherington number The Wedderburn–Etherington numbers are an integer sequence named for Ivor Malcolm Haddon Etherington.. and Joseph Wedderburn. that can be used to count certain kinds of binary trees. The first few numbers in the sequence are
:0, 1, 1, 1, 2, 3, 6, ...
*
Wedderburn's little theorem In mathematics, Wedderburn's little theorem states that every finite domain is a field. In other words, for finite rings, there is no distinction between domains, division rings and fields.
The Artin–Zorn theorem generalizes the theorem to al ...
*
Wedderburn's theorem (division ring)
*
Wedderburn's theorem (simple ring)
*
Artin–Wedderburn theorem
References
Further reading
*
*Robert Hooke (1984
Recollections of Princeton, 1939–1941*
Karen Parshall
Karen Hunger Parshall (born 1955, Virginia; ''née'' Karen Virginia Hunger) is an American historian of mathematics. She is the Commonwealth Professor of History and Mathematics at the University of Virginia with a joint appointment in the Corco ...
(1983) "In pursuit of the finite division algebra theorem and beyond: Joseph H M Wedderburn,
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 ...
, and
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 lon ...
," ''Archives of International History of Science 33'': 274–99.
* Karen Parshall (1985) "Joseph H. M. Wedderburn and the structure theory of algebras," ''Archive for History of Exact Sciences 32'': 223–349.
* Karen Parshall (1992) "New Light on the Life and Work of Joseph Henry Maclagan Wedderburn (1882–1948)," in Menso Folkerts ''et al.'' (eds.): ''Amphora: Festschrift für
Hans Wußing zu seinem 65. Geburtstag'', Birkhäuser Verlag, 523–537.
{{DEFAULTSORT:Wedderburn, Joseph
1882 births
1948 deaths
20th-century American mathematicians
People from Forfar
People educated at Forfar Academy
People educated at George Watson's College
Alumni of the University of Edinburgh
Leipzig University alumni
Humboldt University of Berlin alumni
University of Chicago alumni
Academics of the University of Edinburgh
Princeton University faculty
Fellows of the Royal Society of Edinburgh
Fellows of the Royal Society
Seaforth Highlanders officers
Royal Engineers officers
Algebraists
British Army personnel of World War I
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