The Language of Mathematics: Making the Invisible Visible by Keith Devlin

By Keith Devlin

"The nice ebook of nature," acknowledged Galileo, "can be learn basically by way of those that be aware of the language within which it used to be written. And this language is mathematics."
In The Language of Mathematics, award-winning writer Keith Devlin finds the very important function arithmetic performs in our everlasting quest to appreciate who we're and the realm we are living in. greater than simply the examine of numbers, arithmetic offers us with the eyes to acknowledge and describe the hidden styles of life--patterns that exist within the actual, organic, and social worlds with no, and the area of rules and strategies inside of.
Taking the reader on a wondrous trip during the invisible universe that surrounds us--a universe made obvious via mathematics--Devlin exhibits us what retains a jumbo jet within the air, explains how we will be able to see and listen to a soccer video game on television, permits us to foretell the elements, the habit of the inventory marketplace, and the end result of elections. Microwave ovens, cellphone cables, children's toys, pacemakers, cars, and computers--all function on mathematical rules. faraway from a dry and esoteric topic, arithmetic is a wealthy and dwelling a part of our tradition.
A very good exploration of a frequently woefully misunderstood topic The Language of Mathematics celebrates the simplicity, the precision, the purity, and the beauty of arithmetic.

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M. Adleman, R. S. Rumely, H. Cohen, H. W. Lenstra, and C. Pomerance found a way to eliminate this uncertainty. Starting with Fermat's little theorem, they developed what has turned out to be one of the best general-purpose methods available today for testing whether a number is prime. If you run this test, known as the ARCLP test, on a fast supercomputer, it will take less than 10 seconds for a 20-digit number and less than 15 seconds for a 50-digit number. The ARCLP test is completely reliable.

While working in Alexandria at the great Library, the forerunner of today's universities, Euclid produced his mammoth, thirteen-volume work Elements. It was a compendium of practically all of Greek mathematics up to the time, containing some 465 propositions from plane and solid geometry and from number theory. Though some of the results were Euclid's own, for the most part his great contribution was the systematic manner in which the mathematics was presented. Over the centuries since it was written, more than two thousand editions of Elements have been published, and though it contains a number of logical flaws, it remains an excellent example of what we call the mathematical method, in which we commence with a precise statement of the basic assumptions and thereafter accept as facts only those results proved from those assumptions.

Message encryption corresponds (very roughly) to multiplication of the two 75-digit primes; decryption corresponds (equally roughly) to factoring the 150-digit product, a task that is quite unfeasible given present-day knowledge and technology. ) Easy to Guess, Hard to Prove Because we are all so familiar with the positive whole numbers—the natural numbers—and because they are so simple, it is easy to find patterns in them. Very often, however, it turns out to be extremely difficult to prove that those patterns are true for all natural numbers.

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