(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can't succeed in 4, burn 3. This I do often."
Marshall was elected in 1865 to a fellowship at St John's College at Cambridge, and became lecturer in the moral sciences in 1868. In 1885 he became professor of political economy at Cambridge, where he remained until his retirement in 1908. Over the years he interacted with many British thinkers including Henry Sidgwick, W.K. Clifford, Benjamin Jowett, william Stanley Jevons, Francis Ysidro Edgeworth, John Neville Keynes and John Maynard Keynes. Marshall founded the "Cambridge School" which paid special attention to increasing returns, the theory of the firm, and welfare economics; after his retirement leaderships passed to Arthur Cecil Pigou and John Maynard Keynes.
Marshall desired to improve the mathematical rigour of economics and transform it into a more scientific profession. In the 1870s he wrote a small number of tracts on international trade and the problems of protectionism. In 1879, many of these works were compiled into a work entitled The Theory of Foreign Trade: The Pure Theory of Domestic Values. In the same year (1879) he published The Economics of Industry with his wife Mary Paley.
Marshall had been Mary Paley's professor of political economy at Cambridge and the two were married in 1877, forcing Marshall to leave his position as a Fellow of St John's College, Cambridge to comply with celibacy rules at the university. He became the first principal at University College, Bristol, which was the institution that later became the University of Bristol, again lecturing on political economy and economics. He perfected his Economics of Industry while at Bristol, and published it more widely in England as an economic curriculum; its simple form stood upon sophisticated theoretical foundations. Marshall achieved a measure of fame from this work, and upon the death of william Jevons in 1882, Marshall became the leading British Economist of the scientific school of his time.
His health problems had gradually grown worse since the 1880s, and in 1908 he retired from the university. He hoped to continue work on his Principles but his health continued to deteriorate and the project had continued to grow with each further investigation. The outbreak of the First World War in 1914 prompted him to revise his examinations of the international economy and in 1919 he published Industry and Trade at the age of 77. This work was a more empirical treatise than the largely theoretical Principles, and for that reason it failed to attract as much acclaim from theoretical economists. In 1923, he published Money, Credit, and Commerce, a broad amalgam of previous economic ideas, published and unpublished, stretching back a half-century.
Marshall began his economic work, the Principles of Economics, in 1881, and spent much of the next decade at work on the treatise. His plan for the work gradually extended to a two-volume compilation on the whole of economic thought. The first volume was published in 1890 to worldwide acclaim, establishing him as one of the leading economists of his time. The second volume, which was to address foreign trade, money, trade fluctuations, taxation, and collectivism, was never published.
Marshall returned to Cambridge, via a brief period at Balliol College, Oxford during 1883–4, to take the seat as Professor of Political Economy in 1884 on the death of Henry Fawcett. At Cambridge he endeavoured to create a new tripos for economics, a goal which he would only achieve in 1903. Until that time, economics was taught under the Historical and Moral Sciences Triposes which failed to provide Marshall the kind of energetic and specialised students he desired.
Marshall served as President of the first day of the 1889 Co-operative Congress.
From 1890 to 1924 he was the respected father of the economic profession and to most economists for the half-century after his death, the venerable grandfather. He had shied away from controversy during his life in a way that previous Leaders of the profession had not, although his even-handedness drew great respect and even reverence from fellow economists, and his home at Balliol Croft in Cambridge had no shortage of distinguished guests. His students at Cambridge became leading figures in economics, including John Maynard Keynes and Arthur Cecil Pigou. His most important legacy was creating a respected, academic, scientifically founded profession for economists in the Future that set the tone of the field for the remainder of the 20th century.
Gary Becker (1930-2014), the 1992 Nobel prize winner in economics, has mentioned that Milton Friedman and Alfred Marshall were the two greatest influences on his work.
Alfred Marshall's wife was Mary Paley, co-founder of Newnham College; she continued to live in Balliol Croft until her death in 1944; her ashes were scattered in the garden.
His home, Balliol Croft, was renamed Marshall House in 1991 in his honour when it was bought by Lucy Cavendish College, Cambridge.
Over the next two decades he worked to complete the second volume of his Principles, but his unyielding attention to detail and ambition for completeness prevented him from mastering the work's breadth. The work was never finished and many other, lesser works he had begun work on – a memorandum on trade policy for the Chancellor of the Exchequer in the 1890s, for instance – were left incomplete for the same reasons.