No comments about Apollonius of Perga's Conica: Text, Context, Subtext (Mnemosyne, Bibliotheca Classica Batava Supplementum) (Mnemosyne, Bibliotheca Classica Batava Supplementum).

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1 comments about A Century of Mathematics: Through the Eyes of the Monthly (Spectrum).

1. A common phrase used to describe the experience and qualifications of undergraduates is "mathematical maturity." Well, that phrase can be used to describe the theme of this collection of items from The American Mathematical Monthly. For mathematics has indeed matured in the United States in the last century and this work provides a series of documentary snapshots. A veritable army, this reviewer included, unites in criticizing the current poor state of mathematics education in the United States.
   However, we forget that the United States was a mathematical backwater until large numbers of mathematicians immigrated from Europe in the interwar period. Also, first-year students are now routinely taught material that would have been beyond that of many instructors at the turn of the century. There was a strong movement by colleges to eliminate mathematics requirements in the 1920' s. And the extensive growth in the numbers of mathematics students was largely a direct consequence of World War II.
   The obvious military benefits of technological superiority, largely imported from Europe to win the war, had a mathematical base. Furthermore, the GI Bill of Rights provided the money for thousands to attend college. And the growing conflict with the communist block helped fuel the technological fires, with extensive federal dollars made available for research. In mathematics, this led to a schism into the pure and applied factions that still exists today, although the continuous connections are more apparent than many will admit.
   The editor does a good job in selecting pieces that reflect all of this, providing a good deal of evidence indicating that this is indeed the best of times. Like all other human endeavors, mathematics mimics the society that surrounds it, and many social movements are reflected in the material.
   Like pi and e, some things stay constant. Instructors always question current teaching practices and complain about the poor quality of students. This is not a bad thing, for as long as these complaints are with us, mathematics will continue to thrive and advance.
   If you have any interest in how things have developed over the last one hundred years, pick up this book. Like members of a family, mathematicians have a heritage and roots to their ancestors, and it does us all good to honor them from time to time.

   Published in Journal of Recreational Mathematics, reprinted with permission.

No comments about Breaking 'Fish' Codes at Bletchley Park: General Report on Tunny with Emphasis on Statistical Methods.

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No comments about A treatise on a box of instruments and the sliderule for the use of gaugers, engineers, seamen, and students..

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No comments about Geometrical analysis, or the construction and solution of various geometrical problems from analysis, by geometry, algebra, and the differential calculus; ... and a mode of constructing curves of the.

5 comments about EUCLIDS WINDOW: THE STORY OF GEOMETRY FROM PARALLEL LINES TO HYPERSPACE.

1. This luminous book offers the rare combination of serious scientific contemplation and reader-friendly accessibility.
   
   Starting with the mathematicians and geometers of antiquity, Mlodinow traces the progress of rational thought -- and irrational numbers -- from before Euclid's elucidation of the Elements of geometry to the possibilities which still wait for us to reveal them -- from "A point is that which has no part" straight up to the equally puzzling notion that space and time may only be shadowy hints of some more fully flowering, if abstract, function of mathematics on another plane of reality. Sound like science fiction? Rest assured that Mlodinow has both feet planted square on terra firma. The paradoxes and upsets of his discipline are not lost on the author -- nor, indeed, are the ironies and jokes of history (say what you like about death, but it was the decidedly un-mystical necessity of taxation which launched geometry as a scholarly pursuit in ancient Egypt) -- but the author reminds his reader at various points of the dangers of assuming too readily that any given idea is worthless, too far-out, or obviously and intuitively wrong. Intuition, as it turns out, resists and rebels against much of what has become higher learning in the fields of mathematics and physics.
   
   Mlodinow's dedication to the subject matter at hand matches in beautiful, if heartbreaking, counterpoint to the obscurity in which many of the scholars he discusses labored. Drawing not only on the work of famous theoreticians like Einstein and Hawking, but also on essays and ideas buried in forgotten papers and musty appendices, the author gives full credit wherever it may be due. In the process, whether by design or accident, Mlodinow imparts an even more valuable lesson: the ease with which scientific knowledge can be lost, sometimes for millennia. If Artistotle knew, nearly 2,500 years ago, that the planet must be round, why do we still hear that Columbus' sailors were terrified of sailing off the edge of a flat Earth? (This story in itself is almost certainly apocryphal.) If primitive versions of the Theory of Evolution were kicking around in ancient Greece, how is it we still face voids of serious scientific credibility in modern-day Kansas? Regrettably, superstition, fear, politics, and the manipulation of knowledge -- who gets it and who pays the price for seeking too much of it -- is also part of the history of geometry, as it is part of the history of science in general.
   
   Your reviewer himself studied a fair amount of the history of mathematics and physics in the Western World (starting, in fact, with Euclid, and progressing then through Ptolemy, Apollonius, Descartes, Newton, et al, right up through Einstein and Minkowski) and found certain parts of the curriculum cheerless, if not downright appalling. What a relief and a joy, then, to find Euclid's Window not only concise and readily understandable, but effervescent as well. Author Mlodinow clearly enjoys the subject matter and -- more importantly -- enjoys imparting it to others. As a writer and a teacher, Mlodinow demonstrates that he is gifted and enthusiastic.



2. This book is well-written, easy to follow for the most part. I really enjoyed the history of the math greats and the tidbits surrounding their lives. The Alexandria information was the most interesting to me. Miodinow was aiming for the middle-of-the-road math meddler and hit the target. It inspired me (and challenged me) to search deeper into math literature - and my journey continues...



3. I like math and I am a computer's science teacher in Brazil. But when I read that Dominicans and Franciscans sent teachers to Charlemagne's church schools I became disapointed with this book. The author is very weak in History of the Church. I recomended to him, Kenneth Scott Latourette's book: "History of Christianity".



4. Having a lifelong interest in 2 and 3D "geometry", this walk down memory lane into the future of mathematical theory and application was most informative, enlightening and a learning experience. Being introduced to many personalities old and new such as Edward Witten was a real treat! Mlodinow's approach caused me to think and ponder and his humorous style and personal experiences kept me very interested! I cannot wait to finish "The Drunkard's Walk".



5. "The book of nature is written in mathematics." Galileo
   
   If writing around 1632 Galileo was right that the book of nature is written mathematics then Leonard Mlodinow's book is a kind of Cliff's Notes version.
   
   Mlodinow is a highly experienced writer who collaborated with Oxford's Stephen Hawking when they wrote A Briefer History of Time and his understanding of the material as well as his ability to write accessibly both abound in this work which traces mathematics from the time of Euclid to its present place of prominence on the frontlines of string theory.
   
   Along the way, Mlodinow gives biographies of some of the critical figures like Euclid himself, Descartes, Gauss, Einstein and finally Ed Witten...interestingly enough who works out of the same Institute for Advanced Study that Einstein worked out of in the years prior to his demise.
   
   What makes the study so fascinating is that it tracks a body of study...mathematics...which endeavors to describe reality. In the beginning the story started with Euclid and his fifth postulate...the assertion that parallel lines don't meet.
   
   While it's true that Euclid's postulate produced a self consistent mathematical system, it's also true that eventually (and by eventually I mean like over two thousand years later) it was discovered that you can create yet another self consistent mathematical system which says that parallel lines do meet.
   
   In other words, Euclid created a ruler which is great for measuring flat spaces but later mathematicians in collaborative effort created a special bendable ruler which can measure curved spaces...like a ball.
   
   The significance of this later discovery was made all too obvious when Albert Einstein asserted that gravity bends space...making it more curved and less flat.
   
   So as can be seen the story here is an important one which tells us nothing less than the true emerging story of the universe in which we live and its origins.