The Magical Maze
Royal Institution Christmas Lectures 1997 Now available online from the Royal Institution 
The Royal Institution's free online archive of videos of past Christmas Lectures now includes the five lectures I gave in 1997:
• Sunflowers and snowflakes • The pattern of tiny feet • Outrageous fortune • Chaos and cauliflowers • Fearful symmetry (with the tiger!) 
A new edition will be published by Cambridge University Press on 23 August 2018. 
This new edition of a classic textbook develops complex analysis from the established theory of real analysis by emphasising the differences that arise from the richer geometry of the complex plane. Key features are the use of simple topological ideas to translate visual intuition to rigorous proof, and, in this edition, addressing the conceptual conflicts between pure and applied approaches headon. The first edition has been clarified and corrected. Three new chapters discuss infinitesimals, homology, and preview advanced topics.

Significant Figures Lives and Works of Trailblazing Mathematicians Succinct summaries of twentyfive of the most influential mathematicians of all time, from Archimedes to modern day giant William Thurston... With short descriptions of their most significant works, the book provides a concise overview of what has been hot in math at different times in the discipline's history. Keith Devlin 
Ingredients
Rock Star — a planetless blue giant orbited by hundreds of millions of rocks forming a single vast asteroid field, subtly disobeying human laws of gravity and dynamics. An enigma concealing the greatest threat that humanity has ever encountered. Old Earth — polluted, damaged, all ice melted, ecosystems slowly dying. Most of its people live in the polar regions, in floating cities, or in undersea domes. Kept alive by external aid, imported down three closely guarded beanstalks. The Concordat — a looseknit federation of former Old Earth colony worlds and their own colonies, wealthy beyond measure. Imposed Quarantine on the birth world of humanity 1700 years ago, denying it access to the stars, except for carefully vetted colonists. Its ultimate power is a monopoly on the means of interstellar travel. Ira da Terra — a person and a liberation movement. Terraists will stop at nothing to free Earth from Concordat dominion and repression, and open the path to the Galaxy. 
Church of Cthulhu — surviving in the remnants of drowned Manhattan, waiting for their souls to be eaten when the stars are right.
Qish — a lost colony, rediscovered in Living Labyrinth, which has lost most human science but developed tech based on syntei. Syntei — matter transmitters that grow on trees. Reaching the Concordat, syntelics threaten its very basis … even as it faces the danger from Rock Star. Nazg — a system with twentythree inhabited worlds and innumerable artificial habitats. Home to Salim Sisters, the Concordat’s most advanced hitech corporation. Valkyrie — an obsolete Da Silva caltrop, used to train candidates for Galactic citizenship, twice destroyed. Its impossibly resurrected crew must work with the Syntelic League to save the human race from annihilation. Recipe Mix thoroughly and simmer over relentlessly increasing heat. 
BREAKING NEWS
Fejes Tóth's Zone Conjecture New Record for the Largest Prime When was Zero Invented? Maybe Dark Matter Doesn't Exist 61Sphere's Unique Smooth Structure AI Plays Superhuman Go How zebrafish use Stokes' theorem Best of all possible ribosomes Topological quantum chemistry Formal proof of Kepler conjecture Maryam Mirzakhani How the lizard got its spots Seismology proof found As difficult as ABC? Boolean Pythagorean triples 
Now available in paperback as well as kindle eBook.
Who were the mysterious PAXIAL? What were the enigmatic prisms that they left on a thousand worlds? Billy the Joat needs to find out, because the PAXIAL prisms are the key to finding his father, who disappeared on a covert mission when the Joat was a child. His taste for practical jokes keeps getting him into trouble with authority; his ability to solve impossible problems for the Quaternity, keeps getting him out of it. His investigations home in on the Etonians, an enormously powerful human family. The quest leads the Joat deep into Sharraby Breach, a forbidden region of distorted spacetime... and what he finds there threatens not just his own future, but that of the entire human race. 
New edition of What Shape is a Snowflake?
with updated text and many new images Think of a zebra’s stripes, the complexities of a spider’s web, the uniformity of desert dunes, or the spirals in a sunflower head … think of a snowflake. The Beauty of Numbers in Nature shows how life on Earth follows the principles of mathematics. Each chapter looks at a different kind of patterning system and the mathematics that underlies it. Elegantly illustrated, the book is an illuminating and engaging vision of how mathematics finds expression in the beauty of nature.

UK edition in print now

US edition coming soon

Infinity has connections to religion, philosophy, metaphysics, logic, physics, and mathematics. The infinitely large is intimately related to the infinitely small (infinitesimal). Cosmologists wonder whether space and time are infinite. Philosophers and mathematicians from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Infinity is a concept with important practical applications. Mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite. 
Science fiction novel written with Jack Cohen.
eBook now available from ReAnimus Press. Paperback and eBook from amazon. A (slightly) revised edition of the 2000 novel. 
In the year 2270 strange wheeled artifacts—wheelers—are found buried beneath the icy surface of Callisto. No one knows what they were used for and who left them there. At the same time, it is discovered that the moons of Jupiter have moved . An expedition finds that Jupiter is inhabited by a race of balloonlike aliens, who defend their world against comet strikes by moving their moons. This time they are aiming an incoming comet directly at Earth! An Earth child with an intuitive understanding of animal behavior becomes the key to contacting them—and joining forces with them to save the world.

Sam, Jane, Felix, Elzabet (Lady Elzabet of Quynt), Tinka, and Marco have just been brought together — a mismatched bunch overqualified and highlyskilled trainees from all corners of the Concordat, assembled on a small moon, taking their first steps toward Starhome and qualification as galactic citizens. If they survive. Their first training mission: An extended voyage to the boondocks, out in space where all they can damage is themselves (and a very expensive Da Silva starship). Everything starts out normally, quantum jumping through spacetime congruences as the Da Silva drive does... until it's very much not normal, and they find themselves in a very strange place indeed. As they explore their new environment, they become aware of a dramatic secret which, if they can report it to the Concordat, will change everything...


NOW IN PAPERBACK
An uptotheminute guide to the cosmos. The formation of the Earth and its Moon, the planets and asteroids of the solar system, the Galaxy and the universe. Describes the architecture of space and time, dark matter and dark energy, how galaxies, stars and planets form, why stars implode, how everything began, and how it’s all going to end. Parallel universes, finetuning of the cosmos for life, what forms alien life might take, and the likelihood of life on Earth being snuffed out by an asteroid. Explains the fundamentals of gravity, relativity, quantum theory, and how they relate to each other.

Mathematics has been the driving force in astronomy and cosmology since the ancient
Babylonians. Kepler’s work on the orbits of the planets led Newton to formulate his theory of gravity. Two centuries later tiny irregularities in the motion of Mars inspired Einstein to devise his theory of General Relativity. Eighty years ago ago the discovery that the universe is expanding led to the Big Bang theory of its origins. This in turn led cosmologists to add new features, such as inflation, dark matter, and dark energy. But does inflation explain the structure of today’s universe? Does dark matter exist? Could a scientific revolution be on the way that will challenge the longheld scientific orthodoxy and once again transform our understanding of the universe? 
AUTHOR PAGE ON AMAZON
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MANIFOLD magazine
All twenty issues of this cult student mathematical fanzine from the 1960s and 70s are now free online on this site. 