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"Mathematical theorems rely on a logical process and once proven are true until the end of time," says Simon Singh, on page 21 of this impressive exposition of scientific method and the history of mathematics.
The author points out, under the rubric "Absolute Proof," that there is a difference between the "hard science" of mathematics and the guesswork, maybe, and make-believe of the "pseudo-sciences" (sociology, anthropology, linguistics, psychology and others). Singh goes on to say that the proofs acceptable in these pseudo-sciences "rely on observation and perception, both of which are fallible and provide only approximations to the truth."
Simon Singh has a Ph.D. in particle physics from Cambridge University. He worked for the BBC where he co-produced and directed their documentary film Fermat's Last Theorem, which is at the heart of the PBS/BBC/NOVA production The Proof, outlining Princeton professor Andrew Wiles' solution to Fermat's 400 year old problem. (I tried to purchase Fermat's Last Theorem directly from the BBC, when I could not get it from Amazon.com, but BBC prices are too steep for a poor "Yank")
Fermat's Enigma is the story of Frenchman, Pierre de Fermat, who happens to be one of the greatest mathematicians of all time. It is the story of the world's 400-year-long effort to solve a problem he discussed, later to become the "Holy Grail of Mathematics." The dust jacket says it is a "human drama of high dreams, intellectual brilliance, and extraordinary determination, it will bring the history and culture of mathematics into exciting focus for all who read it."
Every innocent school child, with an IQ greater that his shoe-size, is familiar with the Pythagorean theorem, which states that, in a right-triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The mystery of Fermat's last theorem is directly rooted in Pythagoras and ancient Greece.
Here's the problem under consideration by Fermat: x(to the power "n") + y(to the power "n") = z(to the power "n") where "n" is any number greater than 2. Can it be proved?
The equation represents an infinite series of equations each with a different value for "n". An infinite number of equations can never be solved, therefore it has always been impossible to prove that the underlying equation has no solution; i.e. there is no value for "n" which would make the equation balance.
This is exactly what the genius Frenchman, Pierre de Fermat, claimed to have done, almost 400 years ago, when he noted in the margins of Diophantus' Arithmetica: "I have discovered a truly marvelous proof which this margin is too narrow to contain." Thus was created a mystery and a problem not solved until Andrew Wiles came along.
"Wiles proof of the Last Theorem is not the same as Fermat's," Singh says on page 283. Fermat noted in the margin of his Arithmetica that his proof could not fit in the space available. "Wiles 100 pages of dense mathematics certainly fulfills this criteria," Singh continues, "but, surely the Frenchman did not invent modular forms, the Taniyama-Shimura conjecture, Galois groups and the Kolyvagin-Flach method centuries before anyone else.
So, if Fermat did not use Wiles' method and the tools available to Wiles, what did the Frenchman use? What was Fermat's actual proof and how did he arrive at his result? Wiles arrived at his own proof, his own way, and officially, Wiles has solved Fermat's Last Theorem.
While it appears that nobody knows for sure, exactly what Fermat did, or how he did it, I believe that [one person] knows, but remains incommunicado, like Lawrence of Arabia and Gordon of Khartoum. Fermat's mystery will have to wait just a little longer.
I cannot recommend this work too highly. A masterly performance that will reward the reader with at least a small appreciation of the power, the beauty of the human mind.
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I stongly recommend this book.
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The book also goes beyond the scope of grammar sketches. It starts with a history of the Pacific region. It then discusses commonalities of the Pacific languages. Next come chapters dealing specifically with each of the three languages families (above). He then discusses the development and current use of pidgins, including Tok Pisin, Bislama, and Hiri Motu (including where the name "Hiri Motu" comes from). Following this is material on cultural use of language: politeness registers, gender registers, kinship terms, areas of social importance, etc. Lastly, he discusses language shift, death, and revival.
Overall, this is an excellent work for anyone who has any interest in Polynesian languages. As I said, I will probably read it again next year so more information can sink in.
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The book may be a little difficult to get into, but by the time Jesus is lost in the temple, you can't put the book down. Truly a wonderful insight into Mary as she "pondered these things in her heart."
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Fermat was a great mathematician. In one of his notebooks he stated an equation and mentioned that the margin was too short for the proof of the statement. Later mathematicians found it impossible to prove this math statement. So hard was the problem that it became one of the most popular problems in mathematics and remained unsolved for centuries! Recently, a math professor from Princeton proved this theorem after a marathon effort.
The book introduces the reader to a lot of key mathematicians and interesting anecdotes associated with them. The best aspect of the book is that it presents events spanning centuries, in a manner that fits them together as parts of a solution to a single problem. Its not a sequential narration of events, instead its a coherent presentation of what was done over the years and how it contributed to the final assault.
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This book was a very good opportunity to learn some practical skills from an investment professional of Peter Lynch's Calibre.
Filled with examples, experience and non-technical investment strategies, this book should be among your investment references.
Peter's core approach and message: * Anyone (with a bit of sound research) is able to amass money in the stock market (I would advise a course that teaches basic financial management though, if you intend to manage your own investment portfolio). * Avoid the noise and sentiment, stick to the fundamentals. * A well broken down and explained segmentation of shares/companies (Turn arrounds, asset plays, stalwarts, etc)
Who should buy this book: Anyone with a desire to take takle charge of their own financial future.
Who should avoid this book: Investors that want information on technical analysis. Investors that invest with dowsing rods. Day traders and short term investors.
Also note that only shares as an investment vehicle are discussed. Very little information on Puts, warrants, futures, etc.