This book offers insights into theoretical computer science and mathematics, distilling complex topics into manageable essays that summarize and explain key developments, historical context, and future directions of complexity, computability and algorithms.

People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck.The authors' style is characterized by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.

Unique breadth of examples from the history of computer science and mathematics Offers tips and inspiration to graduate students Authors very experienced at communicating the essence of difficult problems Includes supplementary material: sn.pub/extras

Autorentext

Richard Lipton is the Storey Professor of Computer Science at Georgia Institute of Technology. Previously he held faculty positions at Yale University, the University of California at Berkeley, and Princeton University. His research is focused primarily, but not exclusively, on theory of computation. He has made seminal contributions to many areas of computing from software engineering and program testing, to computer security and cryptography, to DNA and molecular computation, and to other areas of computer science. He is a member of The National Academy of Engineering, an ACM Fellow, and a Guggenheim fellow.

Inhalt

The Claimant, the Readers, and the Crowd.- Kenneth Iverson: Notation and Thinking.- Edmund Hillary: Proofs and Mountain Climbing.- Leonardo da Vinci: Proofs as Art.- Michael Atiyah: The Role of Proof.- Subhash Khot: Unique Games Conjecture.- Arno van den Essen: An Amazing Conjecture.- Richard Hamilton: Group Efforts.- Grigori Perelman: A New Clay Problem.- Eric Allender: Solvable Groups.- Enrico Bombieri: On Intuition.- Fred Hennie: Lower Bounds.- Volker Strassen: Amazing Results.- Adam Smith: Dumb Channels.- Georg Cantor: Diagonal Method.- Raymond Smullyan: The Reals Are Uncountable.- William Tutte: Flow Problems.- Basil Rathbone: Writing a Major Result.- Elwyn Berlekamp: Dots And Boxes.- David Johnson: Galactic Algorithms.- Warren Hirsch: Guessing The Truth.- Shimon Even: A Promise Problem.- Matei David: Improving Noam Nisan's Generator.- Ryan Williams: A New Lower Bound.- Joel Seiferas: More on the New Lower Bound.- Victor Klee: Big Results.- George Dantzig: Equations, Equations, and Equations.- Srinivasa Ramanujan: The Role of Amateurs.- John Rhodes: Approaches to Problems.- John Nash: Connections.- Chee Yap: Computing Digits of .- Henri Lebesgue: Projections Are Tricky.- Nina Balcan: A New Model of Complexity.- Sam Buss: Bounded Logic.- Anton Klyachko: Car Crashes.- Bernard Chazelle: Natural Algorithms.- Thomas Jech: The Axiom of Choice.- Alfonso Bedoya: Definitions, Definitions, and Definitions.- Hartley Rogers: Complexity Classes.- Ron Fagin: Second Order Logic.- Daniel Lokshtanov: Knapsack Problem.- Albert Einstein: Beyond Polynomial Equations.- Denis Thérien: Solvable Groups.- Andreas Björklund: Hamiltonian Cycles.- David Hilbert: The Nullstellensatz.- John Hopcroft: Thinking out of the Box.- Dick Karp: The Polynomial Hierarchy.- Nick Howgrave-Graham and Antoine Joux: Attacking the Knapsack Problem.- Hedy Lamarr: The Role of Amateurs.- Nicolas Courtois: The Linearization Method.- Neal Koblitz: Attacks on Crypto-systems.- Richard Feynman: Miracle Numbers.- Patrick Fischer: Programming Turing Machines.- Roger Apéry: Explaining Proofs.- Ron Rivest: Mathematical Gifts.- Frank Ryan: The Quarterback Teaches.- Leonard Schulman: Associativity.- Paul Seymour: Graph Minors.- Alfred Tarski: Lower Bounds on Theories.- Ken Thompson: Playing Chess.- Virginia Vassilevska: Fixing Tournaments.- Arkadev Chattopadhyay: Computing Modulo Composites.- Charles Bennett: Quantum Protocols.