Throughout my reading and exploration of Journey Through Genius by William Dunham I was blown away by the interesting stories behind every mathematicians’ contributions to mathematics. I really enjoyed how he set up each Genius with plenty of background and explanation of where they came from to the point of their written theorem and proof. Dunham fused mathematical explanation with outstanding history to form what may be the most interesting math book I have ever read. Though I am not really one to talk because I have not read a whole lot of mathematics books, I found the book enjoyable, and think it could be enjoyed by high school and even middle school students as well. The theorems are very dense at times, and require much thought to follow, but Dunham makes each and every Genius’s story fascinating through his story telling and brilliant selection of detail. Additionally Dunham did a wonderful job explaining the mathematical problems that have yet to be solved, and sparking the intrigue of the reader by laying them out clearly and showing that some problems carry on for hundreds to thousands of years. These thoughts made me wonder if I could solve one of the great problems of history if I sat in front of it long enough! I could go on and on, but I will highlight a few questions that I wondered about as I was reading, and my favorite math genius’s story and work!
First to the questions,
I wondered what the greatest known prime number currently is? I know that computers now are programmed to find greater prime numbers, but how many digits is the current greatest prime? Over 17 million according to the science daily! Are there infinite primes? Yes Euclid answered that question within the book with his proof of the infinitude of primes.
Will anyone ever write a better or more influential set of math books than Euclid’s Elements? Dunham seems to suggest that will never happen, what do you think?
Is playing with numbers and proofs the same as experimenting? I think that observations clearly occur, but I am not sure I am comfortable calling working with numbers in proofs experimenting. One explanation I favor says that logical deduction is the method mathematicians use to create theorems and prove their results. Recently, some mathematicians have launched simulations which seem to have control and are more experiment like. Does this make math experimentation a reality? I thought experimentation needed control?
I wonder if working mathematics in abstract means will continue to bring us back to concrete real world discoveries?
I really enjoyed learning about Cantor, and found his work to be perhaps the most interesting. Something about infinity just makes me get excited and want to discover more about mathematics! Despite my intrigue in Cantor, I found Isaac Newton to be the Genius I most enjoyed learning about because of his interest in persevering in problem solving. Not only did Newton connect science and mathematics through physics and his work creating and working with calculus, but Newton never backed down from a challenge. He declared that he solved challenging problems by thinking on them continuously. John Maynard Keynes an economist at Cambridge in the twentieth century said, ” I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret.” (Dunham,p.164, 1991) One of my main goals for my students is that they learn how to persevere in problem solving like that. I want them to not give up even when problems are very difficult. Newton exemplified what a great problem solver and hard worker is. He certainly had a growth mindset and was always up for discovering new ideas through his creativity and flexibility in his problem solving approach!
Anyone can learn and benefit a lot from the discoveries and stories outlined in a Journey Through Genius! I really enjoyed this book and found it to have many great insights that scope well beyond mathematics class. Never Give up! Think in different ways! Never be afraid to question the establishment! These practices lead to growth and amazing discoveries like those outlined throughout Dunham’s masterpiece!
Final thought, “Genius is patience.”