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### Summary

### Summary

A celebrated mathematician traces the history of math through the lives and work of twenty-five pioneering mathematicians

In Significant Figures, acclaimed mathematician Ian Stewart explores the work of 25 of history's most important mathematicians, showing how they developed on each other's work and built the mathematics we use today.

Through these short biographies, we get acquainted with the history of mathematics from Archimedes to William Thurston, and learn about those too often left out of the cannon, such as Muhammad ibn Musa al-Khwarizmi, the creator of algebra; Ada Lovelace, the world's first computer programmer; and Emmy Noether, whose research on symmetry paved the way for modern physics.

Tracing the evolution of mathematics over the course of two millennia, Significant Figures will educate and delight aspiring mathematicians and experts alike.

### Reviews 4

### Publisher's Weekly Review

Stewart (Infinity), professor of mathematics at Warwick University, tells the history of mathematics though 25 biographies of influential mathematicians. The selections are ordered chronologically, beginning with Archimedes (third century B.C.E.) and ending with Fields Medal-winning topologist William Thurston (1946-2012). In between, the contributions of Newton, Poincaré, Gödel, and Turing, along with those of lesser-known mathematical giants, are explored. Stewart treats the spotlighted mathematics seriously and his rigorous explanations often include explanatory equations and in-depth discussions of esoteric concepts. He also strives to underscore the impact and real-world importance of each of the mathematicians' contributions. Stewart balances the demanding math with down-to-earth, even gossipy, thumbnail sketches of the mathematicians. For example, he offers that Newton may have invented the cat door; that George Boole, inventor of mathematical logic, loved his mother's gooseberry pies; and that an aging, paranoid Gödel's fear of being poisoned led him to starve himself to death. Stewart includes the mathematical accomplishments of three women, illuminating the obstacles each had to overcome to be accepted in the male-dominated field. Stewart folds into his biographies a broad swath of mathematics, including Euclidian and non-Euclidean geometries, set theory, calculus, algebra, and topology; readers with an affinity for math will find the material challenging and fun. Illus. Agent: George Lucas, Inkwell Management. (Sept.) © Copyright PWxyz, LLC. All rights reserved.

### Kirkus Review

Summarizing 2,500 years of mathematics milestones and the mathematicians who made them.Even a popularizer as skilled and prolific as Stewart (Mathematics/Univ. of Warwick; Calculating the Cosmos: How Mathematics Unveils the Universe, 2016, etc.) cannot expect general readers to fully digest his highly distilled explanations of what these significant figures did to resolve ever more complex conundrums as math advanced. The author clearly reviews Euclid and highlights the contributions of Arabic and Indian innovators in algebra and trigonometry, but things get more complicated as he turns to differential equations, three-dimensional manifolds, or multiholed tori. Thankfully, Stewart's brief but colorful sketches of the life and times of the innovators keep the pages turning. Besides well-known figures such as Archimedes, Pierre de Fermat, Isaac Newton, Alan Turing, and Kurt Gdel, the author also discusses variste Galois, the algebraist killed in a duel at age 20; Georg Cantor, who was driven to depression and breakdown by critics of his ideas of higher orders of numerical infinity; and Srinivasa Ramanujan, the self-taught Indian number theorist of phenomenal intuition. Among other biographical nuggets, we learn that Turing may not have died from self-inflicted cyanide poisoning but from inhaling fumes from other causes and that Gdel so feared being poisoned that he died of slow starvation. Stewart includes three women in his pantheon (Ada Lovelace, Sofia Kovalevskaia, and Emmy Noether) and blames centuries of cultural bias and not genes for their scant representation. In the final chapter, the author ponders what his subjects have in common. Most seem to have manifested aptitude at an early age, but otherwise, there are few shared aspects of class, character, education, or family background. One thing is certain, however: they all had a profound love for math. A text for teachers, precocious students, and intellectually curious readers unafraid to tread unfamiliar territory and learn what mad pursuits inspire mathematicians. Copyright Kirkus Reviews, used with permission.

### Booklist Review

Math is a science that has been communicated, taught, and recorded since the days of clay tablets in Babylonian times. Mathematician and prolific writer Stewart (Visions of Eternity, 2013) takes readers on a tour through the history of math from ancient Greece to China, India, Europe, and America. He also brings mathematical discoveries to life in engaging brief biographies of 25 foundational inventors of mathematical disciplines, spelling out the significance of their work. Natural patterns and cycles sparked brilliant insights about the workings of the universe in men and women whose intellect was matched by great curiosity and passion to share their ideas with others. Stewart considers just how amazing it is that concepts developed many hundreds of years ago are as accurate today as when they were first revealed and that they are still being used in cutting-edge computer programs. Part advanced math lesson and part history book, Stewart's celebration of seminal mathematicians and their findings will appeal to anyone who wants to better understand the building blocks of many of today's sciences.--Kaplan, Dan Copyright 2017 Booklist

### Choice Review

In his latest book, a collection of 25 biographies of mathematicians, Stewart (emer., Univ. of Warwick, UK) has succeeded once again in writing about mathematics for a general audience. The profiled men and women span millennia and represent diverse cultures. The book is balanced in other ways too. There is no undue emphasis placed on any particular branch of mathematics. Pure and applied math share the stage. And the mathematicians' faults are displayed along with their greatest accomplishments. These are human stories. There are not many equations to intimidate readers, yet this reviewer expects that professional mathematicians will still learn a few things, for mathematics is a very broad field and the supply of entertaining stories of its greatest stars seems to be bottomless. There is a picture in each chapter of the mathematician in question, but not many other images outside of what is required to elucidate the mathematics being described. So, while this is not a coffee-table picture book, it is an interesting read, and there are some references at the end for those who wish to delve deeper. Summing Up: Highly recommended. All levels. --Craig Bauer, York College of Pennsylvania

### Table of Contents

Introduction | p. 1 |

1 Do Not Disturb My Circles | p. 11 |

2 Master of the Way | p. 21 |

3 Dixit Algorismi | p. 28 |

4 Innovator of the Infinite | p. 37 |

5 The Gambling Astrologer | p. 45 |

6 The Last Theorem | p. 53 |

7 System of the World | p. 63 |

8 Master of Us All | p. 77 |

9 The Heat Operator | p. 87 |

10 Invisible Scaffolding | p. 96 |

11 Bending the Rules | p. 110 |

12 Radicals and Revolutionaries | p. 121 |

13 Enchantress of Number | p. 133 |

14 The Laws of Thought | p. 142 |

15 Musician of the Primes | p. 155 |

16 Cardinal of the Continuum | p. 164 |

17 The First Great Lady | p. 176 |

18 Ideas Rose in Crowds | p. 188 |

19 We Must Know, We Shall Know | p. 200 |

20 Overthrowing Academic Order | p. 210 |

21 The Formula Man | p. 221 |

22 Incomplete and Undecidable | p. 234 |

23 The Machine Stops | p. 243 |

24 Father of Fractals | p. 255 |

25 Outside In | p. 267 |

Mathematical People | p. 277 |

Notes | p. 283 |

Further Reading | p. 286 |

Index | p. 291 |