Friday, December 18, 2015

Journey Through Genius Review

The Journey Through Genius
 by William Dunham is a fantastic overview of critical mathematicians and theorems that created the basis of the mathematics that we have studied since the beginning of our education. William Dunham was originally trained as a topologist but as his mathematical studies progressed, he became more and more interested in the field of mathematical history. He has published several books on this topic and his authority within the field shines through in Genius.

The book is composed of 12 chapters that each focus on a particular time period in mathematics or a specific mathematician's contribution. Mathematicians that are thoroughly covered in this text include Euler, Euclid, Newton, Leibniz, the brothers Bernoulli, and many others. Dunham does an excellent job of giving context to each of the mathematical contributions that he mentions. As a math major, I've often found that the historical context of what I am learning is often not mentioned. Dunham's Genius is an excellent source for filling in this educational gap. 

Although this book was incredibly interesting and eye opening to someone like me who plans to make a career out of mathematics, I do not believe that Dunham directed this novel towards any extensive audience. The historical background is very digestible and anyone with a basic understanding of world history would be able to place each of our mathematical heroes in the proper context.  However, the true appreciation of the geniuses that are covered in Dunham's book lies within their clever proofs which are outlined throughout the chapter. This part of Genius was incredibly interesting to me and the way that Duham outline the groundbreaking proofs was very helpful and insightful. However, this portion of the book would not be approachable for high school students or students very early in their mathematics career as the significance of the proofs may be missed. The book is excellently organized in a chronological fashion that pulls the reader along the history of these mathematical geniuses.

I would highly recommend Genius to anybody who plans to pursue higher mathematics for it provides an excellent narrative of crucial information that is often lost within our course of studies.

Overview of 495

My taking mathematics courses to satisfy my major requirements was incredibly beneficial in thoroughly learning material for each individual topic. Although my education has been excellent, oftentimes the course topics were rather disjoint. If making connections between fields was left up to my own creation, they often were not.

Over my semester in John Golden's Nature of Mathematics course, the connections between mathematical fields were presented directly to me in a very valuable way. Not only how the actual mathematics within the field were connected, but how these fields are connected historically.

Since this course was taught in chronological order, it was very clear to me how mathematical concepts were initiated, developed, and transformed into new ones. This view of the field that I have learned so much about shows mathematics as growing and dynamic. Seeing this development makes math seem much more personal and approachable. Mathematics in a historical context is much more human than the mathematics that is presented in a classroom. Topology wasn't created overnight and Lagrange multipliers weren't developed in a 50 minute block like they are taught.

Another important thing that I've learned during my semester in Golden's class is that mathematics isn't an individual activity. Sure I had done group lab assignments in Calc 3 or met up with my classmates to finish delta-epsilon proofs, but the field in general appeared to be one clever person solving a clever problem in a clever way. 

This course taught me that development in mathematics is the result of multiple sources of man power. For example: Fremat's Last Theorem. The BBC documentary on the solution to Fermat's Last Theorem that I watched as an assignment in Golden's class made me realize how many individuals it takes to make intellectual progress. Although the film focused on Andrew Wiles, the man who finally solved the proof, it also gave an overview of the people and efforts that contributed to the solution. This sort of collaboration wasn't presented in my previous math courses.

Overall, taking John Golden's course has placed mathematics into a context that is more approachable and more enjoyable than before. This class made me excited to continue my mathematics education.