From Here to Infinity (book)

From Here to Infinity: A Guide to Today's Mathematics, a 1996 book by mathematician and science popularizer Ian Stewart, is a guide to modern mathematics for the general reader. It aims to answer questions such as "What is mathematics?", "What is it for " and "What are mathematicians doing nowadays?". Author Simon Singh describes it as "An interesting and accessible account of current mathematical topics".^[1]

Summary

After an introductory chapter The Nature of Mathematics, Stewart devotes each of the following 18 chapters to an exposition of a particular problem that has given rise to new mathematics or an area of research in modern mathematics.

• Chapter 2 - The Price of Primality - primality tests and integer factorisation
• Chapter 3 - Marginal Interest - Fermat's last theorem
• Chapter 4 - Parallel Thinking - non-Euclidean geometry
• Chapter 5 - The Miraculous Jar - Cantor's theorem and cardinal numbers
• Chapter 6 - Ghosts of Departed Quantities - calculus and non-standard analysis
• Chapter 7 - The Duellist and the Monster - the classification of finite simple groups
• Chapter 8 - The Purple Wallflower - the four colour theorem
• Chapter 9 - Much Ado About Knotting - topology and the Poincaré conjecture
• Chapter 10 - More Ado About Knotting - knot polynomials
• Chapter 11 - Squarerooting the Unsquarerootable - complex numbers and the Riemann hypothesis
• Chapter 12 - Squaring the Unsquarable - the Banach-Tarski paradox
• Chapter 13 - Strumpet Fortune - probability and random walks
• Chapter 14 - The Mathematics of Nature - the stability of the Solar System
• Chapter 15 - The Patterns of Chaos - chaos theory and strange attractors
• Chapter 16 - The Two-and-a-halfth Dimension - fractals
• Chapter 17 - Dixit Algorizmi - algorithms and NP-complete problems
• Chapter 18 - The Limits of Computability - Turing machines and computable numbers
• Chapter 19 - The Ultimate in Technology Transfer - experimental mathematics and the relationship between mathematics and science

Editions

• 1st edition (1987): published under the title The Problems of Mathematics
• 2nd edition (1992)
• retitled/revised edition (1996)

References

1. ↑ My Favourite Mathematics Books, Simon Singh