The Algebraist

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Milnor has received many awards and honours for his extraordinarily important contributions. He received the National Medal of Science in 1967 and was elected a member of the National Academy of Sciences, the American Academy of Arts and Science. He is a member of the American Philosophy Society and has played a major role in the American Mathematical Society. In August 1982 Milnor received the Leroy P Steele Prize:-

The Algebraist - Iain M. Banks - Google Books The Algebraist - Iain M. Banks - Google Books

As complex, turbulent and spectacular as the gas giant on which it is set, this novel from Iain M. Banks is space opera on a truly epic scale. J Hubbard, Review: Dynamics in one complex variable, by John Willard Milnor, Bull. Amer. Math. Soc. (N.S. ) 38 (4) (2001), 495- 498. This was only one of several papers that Milnor published in 1953. The others were: The characteristics of a vector field on the two-sphere; On total curvatures of closed space curves; and (with Israel Herstein ) An axiomatic approach to measurable utility. Another paper, Link groups, was published in 1954 but it had been submitted for publication in March 1952, over a year before the first of the 1953 papers just mentioned. Milnor writes in the Introduction to Link groups:- An enormously enjoyable book, full of wonderful aliens, a sense of wonder and subtle political commentary on current events.”– Publishers Weekly(Starred Review)He began research at Princeton after graduating with his B.A. and, in 1953, before completing his doctoral studies, he was appointed to the faculty in Princeton. While undertaking research he enjoyed playing games in the common room. In particular he played Kriegspiel (a game of blindfold chess ), Go and Nash (a game invented by John Nash and now called Hex ). In fact John Nash was at Princeton during these years and Milnor and Nash often talked about game theory. Milnor's next paper, written while he was undertaking research, was Sums of positional games (1953). Milnor writes in the Introduction:- E H Spanier, Review: Characteristic classes, by John Willard Milnor and James D Stasheff, Bull. Amer. Math. Soc. 81 (5) (1975), 862- 866. In low dimensions manifolds are things that are easily visualized. A curve in space is an example of a one-dimensional manifold; the surfaces of a sphere and of a doughnut are examples of two-dimensional manifolds. But for mathematicians the dimensions one and two are just the beginning; things get more interesting in higher dimensions. Also, for physicists manifolds are very important, and it is essential for them to look at higher-dimensional examples. For example, suppose you study the motion of an airplane. To describe just the position takes three coordinates, but then you want to describe what direction it is going in, the angle of its wings, and so on. It takes three coordinates to describe the point in space where the plane is centred and three more coordinates to describe its orientation, so already you are in a six-dimensional space. As the plane is moving, you have a path in six-dimensional space, and this is only the beginning of the theory. If you study the motion of the particles in a gas, there are enormously many particles bouncing around, and each one has three coordinates describing its position and three coordinates describing its velocity, so a system of a thousand particles will have six thousand coordinates. Of course, much larger numbers occur, so mathematicians and physicists are used to working in large-dimensional spaces. He received the Wolf Prize (1989), the Leroy P Steele Prize for Mathematical Exposition (2004), the Leroy P Steele Prize for Lifetime Achievement (2011), the Abel Prize (2011) and in 2014 was made a Fellow of the American Mathematical Society.

The Algebraist by Iain M. Banks | Hachette UK

Iain Banks came to controversial public notice with the publication of his first novel, The Wasp Factory, in 1984. Consider Phlebas, his first science fiction novel, was published under the name Iain M. Banks in 1987. He is now widely acclaimed as one of the most powerful, innovative and exciting writers of his generation.E Artal Bartolo, J I Cogolludo Agustín and A Melle Hernández, John Willard Milnor, 1962 Fields Medal (Spanish ), Gac. R. Soc. Mat. Esp. 15 (3) (2012), 575- 587. H Bass, John Milnor, the algebraist, in Topological methods in modern mathematics (Houston, TX, 1993), 45- 84. E H Brown, Review: Topology from the differentiable viewpoint, by John Willard Milnor, Amer. Math. Monthly 74 (4) (1967), 461.

The Algebraist - Iain Banks - Google Books The Algebraist - Iain Banks - Google Books

The first time that I developed a particular interest in mathematics was as a freshman at Princeton University. I had been rather socially maladjusted and did not have too many friends, but when I came to Princeton, I found myself very much at home in the atmosphere of the mathematics common room. People were chatting about mathematics, playing games, and one could come by at any time and just relax. I found the lectures very interesting. I felt more at home there than I ever had before and I have stayed with mathematics ever since.J Milnor, Differential Topology Forty-six Years Later, Notices Amer. Math. Soc. 58 (6) (2011), 804- 809. J Sondow, An aroma of paradox and audacity : Milnor's work in differential topology, in Topological methods in modern mathematics (Houston, TX, 1993), 23- 30. Banks is a phenomenon…writing pure science fiction of a peculiarly gnarly energy and elegance.”–William Gibson Biography John Milnor's parents were Joseph Willard Milnor (1889- 1949) and Emily Cox (1891- 1973). Joseph Milnor, born in Williamsport, Pennsylvania, graduated from Lehigh University in 1912 with first class honours in mathematics. After serving for a year with the General Electric Company in Pittsfield, he entered the engineering department of the Western Union Telegraph Company in 1913. Nine years later he was promoted to research engineer and, in 1936, became a transmission engineer. He was appointed consulting engineer in 1943 and retired in the following year. Milnor has written eight important books: Morse theory (1963); Lectures on the h-cobordism theorem (1965); Topology from the differentiable viewpoint (1965); Singular points of complex hypersurfaces (1968); Introduction to algebraic K-theory (1971); (with Dale Husemoller ) Symmetric bilinear forms (1973); (with James D Stasheff ) Characteristic classes (1974); and Dynamics in one complex variable (1999).