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Biologists have long dismissed mathematics as being unable to meaningfully contribute to our understanding of living beings. Within the past ten years, however, mathematicians have proven that they hold the key to unlocking the mysteries of our world--and ourselves.
In The Mathematics of Life, Ian Stewart provides a fascinating overview of the vital but little-recognized role mathematics has played in pulling back the curtain on the hidden complexities of the natural world--and how its contribution will be even more vital in the years ahead. In his characteristically clear and entertaining fashion, Stewart explains how mathematicians and biologists have come to work together on some of the most difficult scientific problems that the human race has ever tackled, including the nature and origin of life itself.
- Sales Rank: #994940 in Books
- Published on: 2011-06-07
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.19" w x 6.13" l, 1.30 pounds
- Binding: Hardcover
- 368 pages
Review
Kirkus
“An ingenious overview of biology with emphasis on mathematical ideas – stimulating.”
New Scientist
“Stewart flexes his mathematical muscles when he explores concepts like symmetrical viruses and puzzle-solving slime moulds. As always, he explains complicated mathematical ideas brilliantly.”
The Guardian
“A timely account of why biologists and mathematicians are hooking up at last…Stewart is Britain's most brilliant and prolific populariser of mathematics…Mathematics of Life is dense with information, written with Stewart's characteristic lightness of touch and will please the dedicated maths reader…. [T]he book is a testament to the versatility of maths and how it is shaping our understanding of the world.”
Discover
“It is difficult to find many biologists who enjoy math, or vice versa, but British number cruncher Ian Stewart successfully crosses over. Here he argues that solving some of the biggest scientific mysteries, including life’s origins and prevalence in the universe, hinges on a union of these fields. He skillfully recasts the history of biology within a mathematical context…then applies his left-brained perspective to the hot new field of astrobiology. Bio majors: Try the book, then bite the bullet and enroll in Math 101.”
“The Mathematics of Life is at its best in discussing the role that the discipline has played in our understanding of viruses…. Mr. Stewart’s discussion of the intersection of viruses and geometry, and other topics, is absorbing.” Boston Globe
“Stewart revels in intellectual wanderlust, taking us from explanations of why Fibonnaci’s sequence shows up so often in nature to rather in-depth treatments of evolutionary theory to number-crunching the possibilities of life on other planets…. Stewart is great at communicating wonder, but it’s often his skepticism that makes The Mathematics of Life such an enjoyable read – you get the sense that as a man who fully grasps numbers, he doesn’t take kindly to how frequently they are abused in mainstream treatments of science.” Science News
“In this engaging overview, a mathematician describes how the field of biomathematics is answering key questions about the natural world and the origins of life.”
Choice “The hallmark traits of clarity and though-provoking content are as evident in The Mathematics of Life as in the author’s other writings, but the added bonus of the interrelationship with biology makes this book all the more noteworthy…. Interested readers who are not mathematics devotees will still find the book highly informative and readable, given that the work avoids formulas while illustrating math’s emerging role in the field of biology…. Highly recommended.”
About the Author
Ian Stewart is Emeritus Professor of Mathematics and an active researcher at Warwick University in England. His writing has appeared in New Scientist, Discover, Scientific American, and many newspapers in the United Kingdom and United States. He lives in Warwick, England.
Most helpful customer reviews
90 of 94 people found the following review helpful.
New Math and New Applications
By Rob Hardy
There is a famous joke, an oldie, about the farmer who hired mathematicians to help him increase his milk yield. He got their report back, and read its initial sentence: "Consider a spherical cow..." Ian Stewart quotes the joke in _The Mathematics of Life_ (Basic Books) because it illustrates how mathematicians in their ivory towers can be far removed from the world of practical and messy living stuff. Mathematics was great for chemistry, and engineering, and physics, but if you studied biology, you could get by without being adept in math. Stewart, an emeritus professor of mathematics who has written many popular books about his field of expertise, says that not only has the divide between the two fields begun to shrink, but also that the driving force for the mathematics of the next century will be biology. His book is an agreeable introduction to this new arena for mathematics, and explains, without too many scary equations or too many spherical cows, the recent biological applications of topology, knot theory, game theory, multi-dimensional geometries, and more. Of course, biologists have always used mathematics to tally up population sizes or average heights, but that is arithmetic, and as important as arithmetic is, mathematics is more than numbers - it applies to shapes, processes, structures, and patterns, the very sorts of stuff that make up biology. Stewart is a clear writer, and there is plenty of biology he has explained here, along with examples, none too deep or daunting, of how the math promotes understanding of living stuff.
Stewart begins with a wonderful example of this sort of the importance of context with an examination of the Fibonacci sequence found in plants. The sequence is easily derived; start with a 1 and then another 1; every succeeding number is just the sum of the two immediately preceding numbers, as in 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... Since we have a notion that "genes do everything," there isn't any reason that genes could not code for marigolds that had something other than 13 petals, or asters something other than 21 petals, or pineapples or pine cones with spirals that come in something other than 5 or 8 or 13. Those numbers, and the others in the series, show up repeatedly nonetheless. The answer is that the genes don't code for such patterns at all; they code for growth at the tip of a stem, and the buds of growth there push themselves around in arrangements that reflect an angular version of phi, the Golden Ratio, a ratio reflected in successive numbers of the Fibonacci sequence. Botanists knew in the 1850s that these numbers showed up all over in the plant world, but doing the counting and showing the numbers was all that could be done at the time; the mathematics of the growing stem tip could only be seen once its processes had been microscopically observed. Then, too, different mathematical models showed that if the packing numbers were slightly different, if the angles were a little more or less than phi, then the buds (or spirals or seeds) don't pack nearly so close together.
The chapters, always clear and crammed with biology as well as mathematics, take in biological problems ranging from the tiny (knot theory as applied to strands of DNA) to calculations of the possibilities of life elsewhere in the cosmos. Game theory is used to help explain how lizards compete for mates and also the possible mechanics of one species splitting into two new ones. Stewart mentions the input of game designers for the mathematical program Foldit, in which players hunt for the right way to fold a given protein, something that our cells do every microsecond but which is fiendishly difficult for computers to model. The construction of viruses is best understood by looking at them in the fourth or higher dimension, and Stewart does a fine job of explaining to us stuck in the third what those higher dimensions mean. The "reaction-diffusion" equations invented by the computer pioneer Alan Turing tell us lots about animal stripes and spots. Animal gaits can be easily modeled and reflect a simple neuronal circuit called a central pattern generator (this is an area of Stewart's own research). There's an old puzzle, which it seems to me is far from ever being solved: just why is it that math so beautifully models and promotes understanding of so many aspects of our world? The examples here immeasurably deepen the question.
58 of 68 people found the following review helpful.
This book hurts
By S. Matthews
Prof. Ian Stewart FRS is clever and well-regarded. For a long time, his book on Galois theory was on my to-read list. This book was a major disappointment. It started off, in prospect, as a possible five stars, but it rapidly slid down to two.
What are the problems? Too many to list, but here are some.
First, there is actually precious little mathematics here, esp. in the first hundred pages or so. Then the text is littered with statements that were almost literally painful to read. At one point, he observes that the number of bits required to encode the human genome is approximately the same as the capacity of a CD - thus 'we are roughly as complex as Seargent Peppers Lonely Hearts Club Band'. This is a _completely_ content free remark, for reasons that I am sure Prof. Stewart is aware of, when he is making any effort at all. He implies that we didn't 'really' know that a reef-knot cannot be untied, until topologists managed to prove it in this century. This is a serious confusion of models and reality. It is more accurate to say that we have known, _with absolute certainty_ that you cannot untie a reef-knot with fixed ends, we juat haven't bothered to shoe-horn that knowledge into the language of algebraic topology. Presumably we didn't know until this century either (because mathematics tells us that you can) that you could take a sphere the size of a football apart, and put it together as a sphere the size of the sun? This chapter ends up in a discussion of protein structure that I expected to build to some interesting mathematical theory for solving the protein folding problem (more a statistial physics problem than a mathematics problem, per se, I would have thought), but that ends up by saying nothing more than that there is surely some metric under which there is a continuously descending path in the potential space for a protein, because otherwise it wouldn't reliably fold (you don't say) but we don't know what that metric looks like - in the meantime some people have made the problem into a video game, and it turns out that there are people who are good at solving the problem. Cool! (I don't really think so, more sunday supplement cute, actually. What has that got to do with mathematics, or science, really?
He has a discussion of the structure of viruses that tells us (and not a lot of people know this) that some viruses have a structure that is found in 3d cross-sections of 4d lattices - I expected him at this point to provide a causal explanation of why this might be so, but the chapter just stops at this point.
There are various remarks about data analytics (e.g. clustering, classification tree construction) that avoid all concrete detail and look to be just plain misleading about computational complexity.
I could go on(really? you ask), but this review is already too long.
In 1968, J. Maynard Smith published a perfect little classic of a book, 'Mathematical Ideas in Biology' (CUP, 130pp in my copy). It is long out of print, but surely easy to track down. Stewart isn't in competition.
17 of 19 people found the following review helpful.
The seeds of a sunflower show consistent mathematical patterns that scientists have been striving to understand
By Didaskalex
*****
"Though a complete understanding of how mathematics pries secrets out of nature requires long and rigorous study, Stewart conveys to general readers the fundamental axioms with lucidly accessible writing, supplemented with helpful charts and illustrations.... A rewarding adventure for the armchair scientist." -- Booklist
The versatility of mathematical approach has proven ideal, as a vital tool, to find an intuitive solution just about every problem. Mathematics quantitatively describe everything from the shape of viruses to the structure and function of DNA, and helps to explain the evolutionary games that led to the diversity of life on Earth. Mathematics is one of the fastest propellers for advancing science, and is considered "one of the greatest creations of mankind."
Ian Stewart, Britain's most prolific popularizer of mathematics could be introducing us to a revolutionary approach to an array of bioscience subjects that may have been traditionally considered descriptive, qualitative, and dull. Through a fascinating account on the historical exploration of biology, he portrays mathematics as the 'essential tension' promising new revolutionary perspective that will advance our understanding of the mysteries of life. Such mathematical approach determine all, from the shape of a flower to symmetrical viruses. Stewart leads us to believe that nature is a lot more interesting than most people ever imagined, telling us how biology is fun, and that Japanese researchers claimed an Ig Nobel Prize for demonstrating that slime molds can solve puzzles!
Stewart, like MIT Thomas Kuhn, perceives the advances of life science as leaps caused by revolutions in approach, and proposes its five tension points were the invention of the microscope, the systematic classification of the living creatures, evolution, detection of genes, and discovery of the DNA structure. But he strongly believes that truly fundamental changes to the way we thought about biology will be advanced by looking through the lens of Mathematics. The recent celebration of the human genome project's tenth anniversary, disappointingly ended. Scientists and the press are both blamed for creating false hopes for genomic research in human health. As the DNA era is running out of heat, biology is in desperate need of a fresh mathematical approach. While the work of biological scientists is basic to the future leap forward of biological and medical sciences, any breakthrough that has been expected, could not possibly deliver the awaited personalized drugs, and mass cure miracles, without the help of mathematical tools.
After reading "The Mathematics of Life," you can look at the world through a mathematical lens and see the beauty and meaning that is revealed. Julie Rehmeyer, a math columnist for Science News, summarizes Stewart findings, "A surprising number of plants have spiral patterns in which each leaf, seed, or other structure follows the next at a particular angle called the golden angle. The golden angle is closely related to the celebrated golden ratio, which the ancient Greeks and others believed to have divine and mystical properties. Leonardo da Vinci believed that the human form displays the golden ratio. Scientists were puzzled over this pattern of plant growth for hundreds of years. Even though these numbers were introduced in 1202, Fibonacci numbers and the Fibonacci sequence are prime examples of "how mathematics is connected to seemingly unrelated things."
Why would plants 'prefer' the golden angle to any other?
How can plants possibly 'know' anything about Fibonacci numbers?
I was eager to know about the golden angle, and find out how math could give a hint, just to offer the reader an advance appetizer. Initially, researchers thought these patterns might provide an evolutionary advantage by somehow promoting plants' survival. The golden angle is about 137.5ยบ. Two radii of a circle C form the golden angle, if they divide the circle into two areas A and B, so that A/B = B/C. But recently, they have come to believe that the answer lies in the biochemistry of plants as they develop new leaves, flowers, or other structures. Scientists have not entirely solved the mystery, but a basic understanding of the process seems to be emerging. And the answers are sending botanists back to their electron microscopes to re-examine plants they thought they had already understood.
"The seeds of a sunflower, the spines of a cactus, and the bracts of a pine cone, all grow in whirling spiral patterns. Remarkable for their complexity and beauty, they also show consistent mathematical patterns that scientists have been striving to understand." -- Julie Rehmeyer
The Golden Ratio and Fibonacci Numbers
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