The Algebraist

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An enormously enjoyable book, full of wonderful aliens, a sense of wonder and subtle political commentary on current events.”– Publishers Weekly(Starred Review) 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. The book is largely about Fassin's adventures to find the Dweller List, as he goes from planet to planet, system to system, encountering various species and entities.

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

For a good overview of Milnor's mathematics, see the citations for the various prizes which he has won at THIS LINK.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. The references [ 4 ] to [ 18 ] give a good indication of the wide influence of Milnor's work up to 1992 (when these articles were written ). The article [ 4 ] is a survey of Milnor's work in algebra, particularly in algebraic K K K-theory, where his work continues to have important influences. The article [ 17 ] looks at nine papers which Milnor had written on differential geometry. It discusses Milnor's theorem, which shows that the total curvature of a knot is at least 4. Among other results discussed are Milnor's result showing that we cannot necessarily "hear the shape" of a 16-dimensional torus, and another result giving upper and lower bounds on the number of distinct words of a given length in a finitely generated subgroup of the fundamental group. E H Brown, Review: Topology from the differentiable viewpoint, by John Willard Milnor, Amer. Math. Monthly 74 (4) (1967), 461.

The Algebraist by Iain M. Banks | Hachette Book Group

I enjoyed the book for its setting and world-building. The idea that religious extremists hunted down all AIs to execute them was fascinating.It is 4034 AD. Humanity has made it to the stars. Fassin Taak, a Slow Seer at the Court of the Nasqueron Dwellers, will be fortunate if he makes it to the end of the year.

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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. The book, for those not familiar with it, is about a far future where all intergalactic civilization is connected via wormholes. Large gas giants are occupied by Dwellers, ancient non-humanoid aliens whose history spans millennia. Seers seek to gain knowledge from these Dwellers by spending time among the aliens. One Seer, Fassin Taak, stumbles upon a Dweller List, which can has drastic implications for all galactic civilization. Meanwhile, an extremist religious leader organizes an assault on Fassin's home system to obtain the Dweller List.For those not acquainted with large-scale SF, The Algebraist is a perfect place to have your mind blown to smithereens with all that its vast canvas delivers. In particular, if you're used to the less ambitious and necessarily less physically astonishing pleasures of contemporary fiction, you might want to take out insurance on the integrity of your skull. He was promoted to professor in 1960 then, in 1962, Milnor was appointed to the Henry Putman chair.

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It is evident now that low-dimensional dynamics, to a large extent initiated by Milnor's work, is a fundamental part of general dynamical systems theory. Milnor cast his eye on dynamical systems theory in the mid- 1970s. By that time the Smale program in dynamics had been completed. Milnor's approach was to start over from the very beginning, looking at the simplest nontrivial families of maps. The first choice, one-dimensional dynamics, became the subject of his joint paper with Thurston. Even the case of a unimodal map, that is, one with a single critical point, turns out to be extremely rich. This work may be compared with Poincaré's work on circle diffeomorphisms, which 100 years before had inaugurated the qualitative theory of dynamical systems. Milnor's work has opened several new directions in this field, and has given us many basic concepts, challenging problems and nice theorems. N H Kuiper, Review: Morse theory, by John Willard Milnor, Bull. Amer. Math. Soc. 71 (1) (1965), 136- 137. Banks is a phenomenon…writing pure science fiction of a peculiarly gnarly energy and elegance.”–William Gibson Imagine that he is hugely enthusiastic and charming, and that his thoughtful analyses of contemporary human politics range from the individual to the mass, from theory to action, from ideology to consequence.E H Spanier, Review: Characteristic classes, by John Willard Milnor and James D Stasheff, Bull. Amer. Math. Soc. 81 (5) (1975), 862- 866. H Bass, John Milnor, the algebraist, in Topological methods in modern mathematics (Houston, TX, 1993), 45- 84. verifyErrors }}{{ message }}{{ /verifyErrors }}{{ Imagine that the storyteller has a well-educated and thoughtful mind with which he fills you in on all the details of these new worlds and peculiar personalities, and that he has the skill to paint in words the most breathtaking portraits of our universe on levels from the chemical to the personal. 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.