Bridges to Infinity: The Human Side of Mathematics

by Michael Guillen

Explains important mathematical concepts, such as probability and statistics, set theory, paradoxes, symmetries, dimensions, game theory, randomness, and irrational numbers

Genres: Science, Mathematics, Nonfiction

204 pages, Hardcover

First published November 1, 1983

About the author

Dr. Guillen taught physics at Harvard, was ABC News' Science Editor, is a three-time Emmy winner, a TV host, movie producer, speaker, bestselling author, and host of the internationally popular podcast "Science+God."

Reviews

[عبدالرحمن عقاب · Rating 4 out of 5]

كتاب جميل رائق؛ عن الرياضيات، في أعظم تمثلاتها، وهو ما وصفه المؤلف بحاسة التصور والخيال الرياضي. والتي جعل منها حاسة سادسة، يستخدمها الرياضي في تشييد عوالمه وبناء معادلاته. يسبق بها زمانه، ويتجاوز معطياته. 

لكنه -أعني المؤلف- كتب عما أصاب الرياضيات من سهام في لبها، في تباهيها باليقين القائم على المنطق. وما واجهه هذا اليقين من هزات عنيفة، حين اكتشف علماء الرياضيات تناقضات وفجوات قاد إليها المنطق المتين ذاته! 

وحدثنا عن تنازلات قدمها الرياضيون في سبيل ردم هذه الفجوات، وعن آمال استجدت لإعادة تشكيل المنطق وإن اختلف، وتلك الثقة وإن اهتزت. 

صيغ الكتاب بلغة سلسلة شائقة، وبأمثلة واضحة، وجاءت ترجمته بديعة منسابة. 

[David Windsor · Rating 5 out of 5]

Book is a deceptive description. This work reads like a selection of scholarly articles chosen for their approachability by the non initiated in mathematics. It broaches advances subjects like non-euclidean geometry and set theory. Finishing the book gives you hope and appeal for math that Most college level classes (Calculus, Trig and Linear Algebra) rob from us.

Bridges to infinity shows us that math can be about creativity and ntot just rote memorization.

[Ann · Rating 4 out of 5]

I really enjoyed this book - thanks to Amy for recommending it. It makes me want to read Godel Escher Bach, which I have always wanted to read but never felt brave enough.

I loved the actual mathematical core of each essay - the concepts were very clearly explained and even I, with my less-than-adequate spatial imagination, was able to visualize the abstract mathematical constructs Guillen described. I finally "get" non-Euclidean geometry, irrational numbers and topology, at least well enough for my purposes.

I'd love it if he wrote a new edition - it was written in 1985 and I'm sure many advances have been made in math theory and application since then. For example, the last chapter on combinatorial problems (e.g. airline routing) hinges on the idea that no computer current (in 1985) or in the "foreseeable future" would have the power to completely solve these complex problems. I wonder if this is still the case.

There was one really dated and infuriating reference in the chapter on Godel, where Guillen uses as an example of an unproveable verity "a seductive question" psed by a man to a woman in a TV ad: "Is it true when you say no, you really mean yes?". Argh!

The reason the book got only 4 stars is that each chapter ended with a paragraph or two, trying to tie the math to some aspect of human philosophy, psychology or social theory. Those paragraphs seemed very weak to me, and by half-way through the book, I found myself just skimming them, and turning the page quickly to get to the next substantive bit of writing. I was surprised, because I generally love books that tie ideas together from diverse fields, but these connections just didn't work for me.

I think I'll end up re-reading several of the essays in this book every year or so, to really lock in the math concepts.

[Aathavan · Rating 5 out of 5]

this is one of the best books that I have read. It provides a birds eye view of the development of mathematics as a science covering everything from geometry to game theory and how they all relate to life. was particularly taken by the essay on the role of faith in mathematics and the consequence of Gödel's result onlimitations of logic.

I think this will be one book that I would like to return to from time to time

[Flora · Rating 2 out of 5]

It would be more interesting if it wasn't so confusing

[Justin Ritter · Rating 5 out of 5]

Good expose on various topics that are focused on non-technical explanations.

[Kathy Nealen · Rating 4 out of 5]

A set of essays that introduce complex math topics without the rigorous mathematical language.
Favorite quote: Related to topology (believe it or not!) "What is it about us individually that survives a lifetime of aging? And what is it about us collectively that might survive the millions of years of future evolutionary changes - if we are, in fact, evolving? Those unresolved questions bear on the larger questions of our uniqueness and how we think of ourselves as fitting into the scheme of things; they also bear on how we can recognize old friends at reunions without resorting to name badges."

[ddjiii · Rating 5 out of 5]

I read this set of essays(I think I actually bought it myself) when it was first published. It does a remarkable job at laying out the ideas behind very challenging mathematical ideas - comparative infinities, non-euclidian geometries, etc. - in a form that any interested person can understand. There are almost no equations. It also gets at the mathematician's idea of beauty, and the motivation for why some of these ideas were pursued. The gulf between science and humanities is rarely bridged, and this book does one of the best jobs of it I know.

[RA · Rating 4 out of 5]

Irrational numbers, infinity, asymptotic limits, Euclidean geometry, non-Euclidean geometry, set theory, combinatorics, catastrophe theory, topological equivalence, game theory; and the ultimate in math anxiety: mathematician Leonhard Euler confronted French scholar and atheist Denis Diderot with the following, "Monsieur, (a + b^n )/n = X, therefore God exists; respond!" Diderot was speechless.

[Kitty · Rating 4 out of 5]

Guillen does a great job in this introduction to mathematics aimed at those who suffer from math-anxiety. Bridges of Infinity brings the wonder and intrigue of the math world into clear focus without the use of a single equation. I recommend this book to anyone who is curious about why mathematicians are often so passionate about their work.

[Tue Le · Rating 4 out of 5]

Depending on who you are, certain chapters may seem intimidating or simplistic. Nevertheless, it is fine book introducing various topics in mathematics. I recommend it to everyone who is at least somewhat curious about what modern mathematics is like.

[Amy · Rating 5 out of 5]

The best book about math for non-math people (like me) I've ever read.

[Paul · Rating 3 out of 5]

Like a lot of similar math books, very good but loses steam towards the end

[Kevin Lin · Rating 4 out of 5]

A math book that the masses can enjoy. Michael Guillen shines in breaking down many complex fields of mathematics to simple categories that everyone can understand.

[Randy Ades · Rating 5 out of 5]

great book!

[J.R. Barnes · Rating 5 out of 5]

Loved the book. How anyone could read this book and not fall in love with mathematics is beyond me.