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, with travel to the nearby planets well established, a bizarre discovery is made on Callisto, the eighth moon of Jupiter. Dozens upon dozens of strange wheeled artifacts—wheelers—are found buried beneath the icy surface. No one knows what they were used for and who left them in our solar system. At the same time, it is discovered that the moons of Jupiter have moved from their ageold positions. A quickly formed expedition finds that Jupiter is inhabited by a race of balloonlike aliens, who defend their world against comet strikes by moving their moons using gravitational technology. This time, though, their redirection is aiming an incoming comet directly at Earth! Communication at first proves impossible, but an Earth child who has an intuitive understanding of animal behavior becomes the key to contacting them—and joining forces with them to save the world. 
THE FOURTH LAW OF HUMANICS
New SF story in Nature's "Futures" section. PLUS a blog on the thinking behind it. 
Science fiction novel written with Tim Poston.
eBook now available from ReAnimus Press. Paperback and eBook from amazon. 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...
Living Labyrinth wrings out every angle of a plausible scientific idea all inside a great story. For MORE, and a spoiler warning, visit the book's website, where you will find maps, history, ecology, games, a Galactic gazetteer, details of the complications of interstellar travel, and much else. [Website is still at beta stage and subject to further revision.] IN FINAL STAGES OF PREPARATION: The sequel, Rock Star. 
In 2012 the Japanese mathematician Shinichi Mochizuki published a 500page proof, online, of the ABC conjecture. This is one of the most important unsolved problems in number theory, and a correct proof would be revolutionary. However, Mochizuki's methods are very technical, and so radical that it has taken the mathematical community four years to start to come to grips with them — and only after that can the proof's correctness be judged. Optimism is now growing that the proof is right. The conjecture relates the prime factors of three numbers a, b, c such that a + b = c. This looks very simple, but the consequences of the relationship are deep and powerful. Moreover, Mochizuki's new “InterUniversal Teichmüller Theory” could lead to other farreaching new results.
Three computer scientists have announced a computerassisted proof of the Boolean Pythagorean Triples Problem, involving 200 terabytes of data. MORE...
New from Profile
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? 
BREAKING NEWS
Boolean Pythagorean Triples Problem Elliptic curves and banking security Where the brain stores words Dynamics from noisy data The Chameleon's Tongue The real butterfly effect 8 and 24dimensional sphere packing Andrew Wiles gets Abel prize How snakes slither 
PUBLISHED March 1 2017
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. 
AUTHOR PAGE ON AMAZON
Books, photos, twitter feed, and more 
MANIFOLD magazine
All twenty issues of this cult student mathematical fanzine from the 1960s and 70s are now free online on this site. 