Sunday, October 18, 2015

A Short Journey through Genius Summary

Journey through Genius: The Great Theorems of Mathematics.

 I'll say this book became was an interesting read for a guy that hasn't read a book for pleasure in years. The history, mathematical methods, and sheer intelligence relayed in this book made for a well rounded, exciting read. This book takes us through the start of mathematics, although it jumped quickly through everything up until Hippocrates. It breaks down and illustrates the evolution of what it means to do math, both practically and theoretically. And, gives us insight into the greatest minds of history. From pure will and concentration of Isaac Newton, to natural talent and common sense of Euler. From public debates and "math offs," to winner take all published math problems, this book had it all.

We start off with a history of mathematics. From early number systems and counting techniques, to mentioning some of the great mathematicians before Hippocrates. The first chapter sets the tone for the book and already we can see some of the great strides in mathematics.  Next, Plato creates enthusiasm for mathematics, making it a noble field of study. Exodus who was known for theory of proportion and proof by exhaustion, saw a practical use for mathematics in the branch of astronomy and planetary motion. Then, Euclid, the most notable up to this point, gathered and perfected all know mathematical conjectures with his Book of Elements. In a very precise, non-circular way, he proved 465 theorems, one after the other, most relying on the proof that came before, with just 25 definitions, 5 postulates, and 5 axioms. Arguably the most studied book for centuries to come. All 465 theorems still hold true to this day. Worth noting in this summary is Postulate 5 concerning parallel lines. Now we realize how initiative and clever these guys were. In Chapter 3 we get a inside look at Euclid's book of elements: Euclid set the bar for geometric algebra, plane geometry, and number theory. In book 8 we see a great theorem in the form of number theory concerning prime numbers and their infinitude. In Chapter 4 we meet the great engineer and absent minded Archimedes who studied Euclid. He developed a genius way to prove the area of a circle. He was famous for shrinking the number of cases in a proof and favored the proof by contradiction. He united all circular shapes the constant pi and estimated it to within 2 decimal places and with his method and computers we now know pi to half of a billion decimal places. By chapter 5 we are introduced to Heron and his great formula for calculating triangular area. Here is the point where things started to click for me. I started putting the pieces together from what I had learned early in mathematics to what I know now about what it means to be a mathematician. Then, in chapter 6, we learn how doomed Cardano was from the start, yet gives us the formula for solving cubics. A trend starts to develop in the form of diversity. From many different backgrounds and nationalities, these mathematicians are as diverse as the fields in which they study. From Geometry, to number theory, and from application to theoretical; the branches of mathematics continue to grow and spread out as each mastermind finds his niche. Newton in physics and then the Bernoullli brothers in analysis, The 1500-1700s saw an explosion of great minds. Some great minds studying under the previous, some enemies and some with a competitive spirit. Euler is now my favorite mathematician after reading this book. He overcame some physical set-backs to contribute half of the know theorems in analysis, and up to 1/3 of all published text up to this point all the while remaining a good guy who cared about education and put forth the effort to convey his thoughts and practices in an easily understood manner for any pupil.

Overall, this book has both inspired me and intimidated me. Oh how I wish I could have studied under Euler, heck, I'd even take Newton. I'm a believer in a growth mindset and that with enough time, anyone can learn anything, however the concentration and determination of the mathematicians outlined in this book is not a skill that can be learned, just admired. After reading this book, I have a greater appreciation for old fashioned, pen and paper mathematics. Not only did this book provide us with the history of math and those who practiced it, but told a story of perseverance, and patience. I would recommend this book to anyone who decides to major in mathematics.