John Wishart's father was John Wishart (born in Montrose, Forfarshire about 1867) who was a 'boot cutter and closer'. His mother was Elizabeth Wishart (born in Edinburgh about 1866). He had an older brother Scott (born about 1897) and a younger brother James (born about 1900).
Wishart's family moved from Montrose to Perth in Scotland when John was two years old. He attended Perth Academy and then, in 1916, entered the University of Edinburgh. There he was taught mathematics by E T Whittaker.
World War I meant that Wishart's university career was disrupted. He spent two years from 1917 to 1919 in the Black Watch regiment and served in France in 1918. He completed his university course in 1922, graduating with a First Class degree in mathematics and physics. He had taken a teacher training course at Moray House as part of his degree and, after graduating, he moved to Leeds accepting a post as mathematics teacher at West Leeds High School.
In 1924, after a recommendation from Whittaker, Wishart was offered a post in University College, London, as assistant to Pearson. Pearson had a project for Wishart to work on and, given that Whittaker had set up his mathematical laboratory in Edinburgh, it was clear why Whittaker's advice on a possible assistant had been sought. Pearson had published his Tables of the Incomplete Gamma Function in 1922 and now he was looking for computational help in his next 'tables' project Tables of the Incomplete Beta Function.
Wishart learned a great deal of statistics during his three years with Pearson. He attended Pearson's lectures and learnt how to go about statistical research. After a few months as a Mathematical Demonstrator at Imperial College, Wishart accepted an offer from R A Fisher to be his statistical assistant at Rothamsted.
When Yule left his Cambridge lectureship in Statistics in 1931 there was a reorganisation of statistics teaching at Cambridge. A Readership in Statistics was created in the Faculty of Agriculture to teach courses in that Faculty and courses in Mathematics. A separate lectureship in Economic Statistics was also created. Wishart was appointed to the Readership in the Faculty of Agriculture.
A laboratory was set up by Wishart at Cambridge for his postgraduate students. Cochran was one of these postgraduates and he described his time studying with Wishart:-
In those days he believed in his students keeping office hours. When he assigned me a desk in the Laboratory, he told me that he expected me to be sitting at the desk most of the day when not in class. He instructed me to do three hours computing a day on a table of the 1% level of z to 7 decimal places ... Having anticipated a free and easy life as a graduate student, punctuated of course by periods of esoteric thinking when the spirit moved me, I didn't much like either the office hours or the computing, but I don't think they did me any harm.
There were two aspects to Wishart's teaching at Cambridge since he taught both mathematics students and agriculture students. This suited him well since he had both a flair for mathematical statistics and a flair for very practical applications of experimental design. The arrangement did not suit other academics at Cambridge, however, and Wishart had to fight many academic battles.
The problem that Wishart's position caused at Cambridge was that he was too high powered a statistician for those in Agriculture but the mathematicians were also unhappy to send their students to the Faculty of Agriculture for statistics courses, and they would have much preferred to have statistics completely within Mathematics.
If World War II had not come along it is unclear how the problems would have resolved themselves. As it was, Wishart worked in army Intelligence from 1940 to 1942 and then on statistical work for the Admiralty from 1942 to 1946. The problems he had been having at Cambridge before the War made him think long and hard about whether to return, but his love of teaching, more than anything else, took him back.
At Cambridge more statisticians were taken on within Mathematics and a Statistical Laboratory was set up within the Mathematics Faculty in 1949. Wishart became Head of the Statistical Laboratory in 1953.
In  Wishart's international connections are summed up:-
There are probably few statisticians who have had more friends scattered across the world that had John Wishart. Many of these friendships were made in the course of his work as a teacher of statistical method to practical agriculturists overseas. ... A pioneering visit to Nanking University in 1934 had been followed after the war by visits to Spain in 1947, to the United States in 1949, to India in 1954 and then, in his last year, to Mexico, where he was taking a leading part in the work of the Training Centre in Experimental Design arranged by the United Nations Food and Agricultural Organisation.
Some of Wishart's most important publications were in the 1928-32 period before he became so involved with teaching at Cambridge. In 1928 he derived the generalised product-moment distribution which is now named the Wishart distribution. This distribution is described in  as:-
... fundamental to multivariate statistical analysis ...
and is fully described on pages 154 to 163 of . As well as further papers on the Wishart distribution, he also studied properties of the distribution of the multiple correlation coefficient which Fisher had considered earlier. In addition he wrote many papers on agricultural applications of statistics such as fertiliser trials, sugar beet experiments, crop experimentation and pig nutrition.
Wishart was also much involved with the work of the Royal Statistical Society. He was one of the Fellows who formed the organising committee of the Agriculture research section in 1933. In 1945 he became chairman of the Royal Statistical Society's Research Section. He also sat on two committees of the Royal Statistical Society on the Teaching of Statistics: the reports of these committees appearing in the Journal of the Royal Statistical Society in 1948 and 1955.
One other service that Wishart performed for statistics was his editorial work for Biometrika. He served as Assistant editor from 1937 and Associate Editor from 1948.
Wishart died in a bathing accident in Acapulco, Mexico, which he was visiting as a representative of the United Nations Food and Agriculture Organisation to arrange setting up a research centre to apply statistical techniques in agricultural research.
Article by: J J O'Connor and E F Robertson