Taming the Infinite by Ian Stewart (PDF)

Description

From ancient Babylon to the last great unsolved problems, Ian Stewart brings us his definitive history of mathematics. In his famous straightforward style, Professor Stewart explains each major development–from the first number systems to chaos theory–and considers how each affected society and changed everyday life forever.Maintaining a personal touch, he introduces all of the outstanding mathematicians of history, from the key Babylonians, Greeks and Egyptians, via Newton and Descartes, to Fermat, Babbage and Godel, and demystifies math’s key concepts without recourse to complicated formulae. Written to provide a captivating historic narrative for the non-mathematician, Taming the Infinite is packed with fascinating nuggets and quirky asides, and contains 100 illustrations and diagrams to illuminate and aid understanding of a subject many dread, but which has made our world what it is today.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent writing. Other than brief mentions of global warming and mocking it’s critics, it’s excellent. The climate change is a bit preachy and condescending in all his books, unfortunately. But overall, worth the read for the mathematics.

⭐this is a well written history but an advanced knowledge of mathematics will be useful as the author presents formulas and theorums beyond day to day usage.however it is possible to skip the hard corp math concepts and just enjoy the historical presentation itself.

⭐One of the reasons I read TAMING THE INFINITE because I am a science teacher. Since being a teacher entails helping students understand the sources, tools, and limits of knowledge, I have made it a point to read books on math to help me better understand these things myself. Stewart’s book is excellent for that purpose. Though I use simple algebra, trigonometry, and calculus regularly, my knowledge never extended beyond sophomore-level math, and I’ve forgotten most of that, so much of this book was well over my head. However, any reader should be able to get the gist of the historical development of mathematics, as well as its importance in the development and maintenance of the modern world. Stewart includes little blurbs throughout the text explaining what the various branches of mathematics did for people in the time that it was developed, and what it continues to do for us in the present time.There are still some points upon which I’m not altogether clear. When preparing to teach IB Theory of Knowledge, we were told that mathematics is an axiomatic system, with each set of axioms being logically consistent, but completely independent of each other. However, when Andrew Wiles solved Fermat’s Last Theorem that solution enabled the mapping of the axioms, theorems, and so on from one to the other. And Felix Klein “in his Erlangen programme of 1872 unified almost all known types of geometry, and clarified links between them, by considering geometry as the invariants of a transformation group. (Whatever that might mean). Geometry thereby became a branch of group theory (p.250).” So I wonder if all “realms” of mathematics might be unified in this way.I am also not completely clear on whether or not chaos theory is deterministic. Stewart writes: “The determinacy of the laws of physics follows from a simple mathematical fact: there is at most one solution to a differential equation.” He then quotes Laplace’s mathematical view of determinism, in which Laplace states that an intellect capable of knowing all of the forces and positions of all the particles comprising the universe “for such an intellect nothing could be uncertain, and the future just like the past would be present before its eyes (p.358).” Stewart later states that though chaos is “irregular, unpredictable, and highly sensitive to small disturbances . . . chaos is based on deterministic laws (p.372).” Unpredictable in practice does not mean impossible to predict in principle. So would a hypothetical intelligence having all necessary information on all particles be able to predict the future? Or is their more than one possible solution? If so, then what does deterministic mean here? It is now commonly accepted that quantum events are nondeterministic — although Bertrand Russell (and I think David Bohm) believe that these are also deterministic by forces hidden to us — but chaos theory deals with macroscopic events. Do macroscopic events have a completely nondeterministic bifurcation point or not? I am currently under the impression that they do not, except as they might be influenced by quantum events.For that matter, in mathematics the notion of strange attractors, “a mathematical system that a system inevitably homes in on,” is logical enough (since mathematicians say so); but I don’t get how they make sense in the physical world. Why are the particles caught up in a typhoon not breaking the law of inertia?One of the other issues we discussed in TOK was whether mathematics is created or discovered. I think Stewart says that it’s a little of both. On the other hand, in an article of his I read many years ago — and can’t recall the title — he ridiculed the belief that mathematics existed as an archetype in a collective unconscious, as the psychoanalyst Carl Jung maintained. However, there might be some evidence that mathematics exists in the mind independent of invention. In THE SELFISH GENE, Richard Dawkins explains that catching a ball in flight requires being able to unconsciously solve quadratic functions. If this is true for people, then it must also be true for toads that catch flies in flight, and hawks that catch sparrows. Idiot savants, and some people who have sustained head injuries, are able to perform complicated calculations that they were clearly never taught, nor consciously invented by themselves. Henri Poincaré tried to describe the process by which his subliminal mind arrived at the correct solution to complicated theorems in his essay MATHEMATICAL DISCOVERY. He described the subliminal mind functioning like a machine, testing combination after combination, but the criteria by which it recognizes the correct solution is that it is the one which is beautiful. It seems rather far-fetched to insist that the appreciation of mathematical beauty arose from the adaptation to the physical environment.Stewart maintains that the universe is merelyphysical, and that life and consciousness arose by happenstance. And yet he writes: “Complex systems support the view that on a lifeless planet with sufficiently complex chemistry, life is likely to arise spontaneously and to organize itself into ever more complex and sophisticated forms. What remains to be understood is what kinds of rules lead to the spontaneous emergence of self-replicating configurations in our own universe — in short, what kind of physical laws make this first crucial step towards life not only possible but inevitable (p.371).” Must we seriously take it for granted that these physical laws “just happen” to exist, and that one cannot even suggest — without being subjected to angry insults and ridicule — that the existence of these laws might mean that both life and consciousness are intrinsic qualities of existence?

⭐Ian Stewart’s book is a good history of mathematics from the earliest times in Babylon to the present. It is fairly short, but covers the topic quite well. I think the book is particularly useful for non-math people who would like to have a general understanding of the history and development of the subject. Of particular value are the short bios of the leading figures in math. It also explains what each math discipline is and what it is useful for.

⭐Another gem by Stewart with delightful examples, a breathtaking perspective, and thoughtful considerations on where we have been, where we are, and where we may be going. This book should be read by anyone involved in the teaching or practice of mathematics and is a handy companion to James D. Bailey’s equally thoughtful Mapematics [sic] books, which deal with infinitesimals: non-computational solution generators such as neural nets, computer learning by genetic algorithm recombination, and the solution of non-biological problems using protein folding techniques. Bailey’s should also be read by anyone interested in the teaching of mathematics or in the design of mathematical curricula at any level from elementary school to graduate school.

⭐This is a super book which gives a fascinating history of maths and its characters, including their rivalries, and puts many of the concepts in a context both historical and scientific.The majority of the book is readily accessible to anyone who passed a good O level, but the important concepts beyond that level are well introduced, and if some people don’t get the full maths impact, then it should still give them an idea of the impact of maths on our lives.That I see as the point of this book; in a country (writing in the UK) where people seem to be proud of innumeracy and mathematical ignorance, a book such as this shows how everything that happens can be described by maths, and everything we have and make depends upon maths.It is a great shame that the spectacular failure-even sabotage- of our education system over the last few decades makes this book less attractive and accessible to people than it should be.If you’re not afraid to look at maths, then even if the concepts are more than you really want to follow, the book will still take you on a journey of understanding.Another excellent piece of work by Ian Stewart, one of our great teachers and communicators.

⭐A very well presented book which you can follow without being an engineer or a maths nerd

⭐Great value – entertaining

⭐Stewart è la versione internazionale del nostro Odifreddi: scrive tanti libri, ma, a differenza dell’italiano, qui c’èmeno fumo e più arrosto. Non si addentra in formule e dimostrazioni, ma cerca di comunicare lo spirito dei ragionamenti.Buon libro, ma non esaustivo, e neppure esauriente. Col tempo è migliorata la parte tecnica (ricordo una disastrosa 3° edizione sulla teoria di Galois, con una erratissima formula sulla risoluzione delle equazioni algebriche di 3^ grado).

⭐

⭐Excellent book on mathematics. Recommended for anyone who is interested in the evolution and history of mathematics and the many great people, cultures and civilizations that contributed to it’s development and widespread application.

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