**Max Newman**'s father, Herman Alexander Neumann, was German and Max had the family name of Neumann until he changed it in 1916. Herman Neumann worked in England as the secretary to a company. Herman had married Sarah Pike who was the daughter of a leather dresser, and came from a farming family, but had become a primary school teacher.

Max attended the City of London School, entering in 1908. From there he gained a scholarship to St John's College, Cambridge, which he entered in 1915. Of course World War I had already begun when he entered university and as a consequence, after obtaining First Class in Part 1 of the Mathematical Tripos, he interrupted his studies. As we mentioned above, it was at this time that he changed his name by deed poll from Neumann to Newman. From 1916 until 1919 Newman undertook work related to the war, doing various jobs such as army paymaster and schoolmaster. He returned to Cambridge after his war related duties ended in 1919, graduated in 1921, and then became a Fellow of St John's College in 1923.

During a visit to Vienna in session 1922-23 he was strongly influenced by Reidemeister. From 1927 he was a lecturer at Cambridge in addition to his holding his Fellowship. Newman visited Princeton in 1928-9 during which time he was a Rockefeller Research Fellow working closely with Alexander. Newman married Lyn Irvine in 1934. She was the daughter of John Irvine, a Church of Scotland minister, and she was an accomplished author. They had two sons.

While at Cambridge Newman taught a course on the foundations of mathematics. It was these lectures which introduced Turing to the concept of 'decidability' that in turn inspired Turing's famous paper, *On Computable Numbers, with an application to the Entscheidungsproblem*. which was published with considerable help from Newman. Without Newman's encouragement, Turing might not have done this work and got drawn into codebreaking.

Newman returned to Princeton for a second visit in 1937-8. In 1939 he was elected a Fellow of the Royal Society. He was later (1958) to receive the Sylvester medal from the Royal Society:-

In 1942 he joined the Government Code and Cipher School at Bletchley Park and worked there on Colossus with J H C Whitehead and Bill Tutte. His important contribution is described in [2] and in [1]:-... in recognition of his distinguished contributions to combinatory topology, Boolean algebras and mathematical logic.

At the end of the War Newman was appointed to a chair to succeed Mordell as Fielden Professor of Mathematics at Manchester and, three years later, he appointed Turing to the post of Reader in Mathematics in his Department. He made other fine appointments such as Bernhard Neumann and Cassels. Along with Hodge and Henry Whitehead, Newman set up the British Mathematical Colloquium.The work to which Newman contributed, though distinct from that on "Enigma", has been described as being of comparable importance. He devised a way of carrying forward the work of Tiltman and Tutte by the use of specially designed machines and for this purpose was given charge of a section, commonly called "Newmanry".

He ran this section admirably. He soon became involved in designing a much more advanced machine, which many think has a place in the early history of digital computers. The design brought into play his knowledge of formal logic. All this gave him an insight into what could be done by electronic means, and convinced him that general purpose digital computers could and should be built.

His mathematical work was in the field of combinatorial topology where he greatly influenced his friend Henry Whitehead. A series of papers by Newman on this topic between 1926 and 1932 revolutionised the field. He achieved this by giving a totally new definition of combinatory equivalence based on three elementary moves, rather than on the notion of subdivision which had previously been used. This allowed him to recast the subject avoiding the difficulties which had previously arisen.

Newman also wrote an important paper on theoretical computer science, produced a topological counter-example of major significance in collaboration with Henry Whitehead, and wrote an outstanding paper on periodic transformations in abelian topological groups. He only wrote one book *Elements of the topology of plane sets of points* (1939). Writing in [4], Peter Hilton claims that:-

In 1962 Newman was presented with the De Morgan Medal from the London Mathematical Society. The President of the Society, Mary Cartwright, gave a tribute to Newman's work which is reported in [3]:-... this is the only text in general topology which can be wholeheartedly recommended without qualification. It is beautifully written in the limpid style one would expect of one who combined clarity of thought, breadth of view, depth of understanding and mastery of language. Newman saw, and presented, topology as part of the whole of mathematics, not as an isolated discipline: and many must wish he had written more.

In 1964 Newman retired from his Manchester chair but he most certainly did not give up mathematics. He taught a course at the University of Warwick and at this time I [EFR] was a research student there and met him and attended lectures he gave. He was an outstanding teacher, clearly giving much attention to the organisation of his material. Retirement was also an opportunity for Newman to relaunch his research career which he did with the vigour of a young academic. He published a highly significant paper in 1966 which proved the Poincaré Conjecture for topological manifolds of dimension greater than 4.His early work on Combinatory Topology has exercised a decisive influence on the development of that subject. At a time when the study of manifolds was based on a number of different combinatory concepts, he established a simple combinatory system of simplicial complexes with an equivalence relation based on elementary moves. ... He has proved two important results about fixed points. The first was an early inroad on Hilbert's Fifth Problem, in which he proved that abelian continuous groups do not have arbitrarily small subgroups, the second was a simplified proof of a difficult fixed point theorem of Cartwright and Littlewood arising in the study of differential equations. ...

Lynn Newman died in 1973, and later in the same year he married Margaret Penrose, the daughter of a professor of physiology, who was the widow of the physician Professor Lionel Sharples Penrose.

Wylie, writing in the *Dictionary of National Biography*, gives an indication of Newman's interests outside mathematics:-

Newman was a very gifted pianist and a strong chess player. He also enjoyed reading ... At first contact perhaps austere, he was in fact a splendid companion, with a great sense of humour and a quite delightful turn of phrase.

**Article by:** *J J O'Connor* and *E F Robertson*

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