Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge.

In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.

“Vero, you remember you once said there were people who would follow me to the gates of hell?” “A figure of speech.” “We’d better find them. That’s where we’re going.” After the defeat of the evil Dominion forces at Farholme, Commander Merral D’Avanos prepares a task force to rescue thirty hostages captured by the fleeing Margrave Lezaroth. Merral’s only hope is that he can get to the hostages before they’re taken to Lord-Emperor Nezhuala at the Blade of Night—the nexus of the Dominion’s power. But in order to get there, Merral and his crew will have to survive a perilous trip through Below Space. Meanwhile, news of the Dominion’s defeat at Farholme reaches Ancient Earth but is tempered by the sobering truth of the enemy’s growth and strength. It is now clear that an attack on the Assembly is imminent, but how far should the Assembly go to stop it? And does the real danger lie in the Dominion or in the subtle evil that has arrived at the heart of the Assembly itself? The Infinite Day is the thrilling conclusion to the epic Lamb among the Stars series that has readers and critics raving.

A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."

The Aravind Eye Care System, based in India, is the world's largest provider of high-quality eye care. It is also one of the world's most incredible and revolutionary organizations. This is the first book to explore Aravind's history and the distinctive philosophies, practices, and commitments that are the keys to its success.