January 27, 2020

Review Magnificent Mistakes in Mathematics by Alfred S. Posamentier & Ingmar Lehmann

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We’ve all be there. Standing at the chalkboard, (remember chalkboards?) we’ve all forgotten to “carry the two,” or made the cardinal sin of mathematics by attempting to divide by zero. Hey, it happens to the best of us sometimes.

So it’s comforting to realize that the rock stars of mathematics are prone to slip up on occasion as well. Only in their case, their mistakes may be so monumental as to approach greatness.  In this week’s review, authors Alfred S. Posamentier and Ingmar Lehmann venture into the exciting realm of mathematical errors with Magnificent Mistakes in Mathematics. Out this month from Prometheus Books, Magnificent Mistakes is a fascinating look at good equations gone bad and some of the brain-bending results.

Fans of this site and Posamentier & Lehmann’s work will also recall our reviews of their fascinating works, The Glorious Golden Ratio & The Secrets of Triangles a while back.

The authors of Magnificent Mistakes have combed history, art, and of course, mathematics to bring you some fabulous blunders. Some are legendary, but a great many of them we’ve never heard off.

Did you know that there is an error in the calculation of Pi inscribed in the Palais de la Decouverte in Paris that you can visit today? Or that a postage stamp honoring physicist Enrico Fermi issued in 2001 actually contains a mathematical error on the chalk board behind him? Or that the Goldbach conjecture, which states that “Every odd number greater than 5 is the sum of three primes” is yet to be solved?

It’s worth keeping a paper and pencil handy reading this book, as you can figure and check many of these errors and assertions yourself.  Aristotle, Galileo, Leibniz and more are just some of the scientific and mathematical luminaries guilty of a mathematical mistake or three from time to time. Many, such as Kepler and Sir Isaac Newton, were lured by the siren song of numerology or chased mathematical rabbits down dead ends. Newton himself became enmeshed in the numerology of the Bible, while Kepler spent much of his life chasing after the perceived link between geometrical perfect solids and the planets.

Other classics, such as Fermat’s Last Theorem, the hunt for prime numbers, and the Fibonacci sequence are presented. It’s fascinating to think that the jury is still out on whether or not prime numbers continue into infinity. The current largest discovered prime number is 257,885,161-1 —that’s a 17,425,170 digit number, just discovered earlier this year on January 25th— and it’s interesting to note that they’re spaced farther apart the larger they get. And speaking of primes, efforts and errors still persist in the realm of Legendre’s Conjecture, which tells us that “for all natural numbers n, between n2 and (N+1)2 there exists at least one prime number.

In the world of the astronomical, Poincare’s conjuncture and attempts to solve the three-body problem (which has applications in the realm of celestial mechanics) is also addressed.

The book is divided up into mistakes in arithmetic, algebra, geometry, statistics and much more. It’s also chalk full of some classics and “should-be classics,” both solved and unsolved, from the Monty Hall dilemma to the Four-Color Map conjecture and many more.

Don’t be scared off by the “mathiness…”  Magnificent Mistakes in Mathematics is an intriguing read. I’ll bet that even old hands at mathematics will find something new here… a great opportunity as the school year begins, giving us a chance once again to “go figure!”


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