Response to Euler: The Master of Us All

In a nutshell, the book Euler: The Master of Us All seeks to detail a number of mathematical questions/scenarios left open that Euler either solved or addressed. William Dunham would begin a section explaining the problem and the previous progress made on it, Euler's particular progress detailed in proofs/mathematical work, and then later contributions, as well as open questions left to future researchers.

The book really highlighted the brilliance of Euler, as well as the seeming absurdity that is his style of analysis. On multiple occasions Euler would simply write an object in terms of an infinite series and then take logarithms of each side, and vice versa. Euler techniques were purely for the purpose of analysis, lacking the formalism of proof writing. However, one could argue that this let Euler be more creative as he simply pursued mathematics in terms of reaching results, without regards to crippling  cases and full comprehensiveness. On occasion Euler can be faulted for his lack of rigor, but then again one can hardly imagine the number of successes if he restricted his particular style. As the author stated, "One could reasonably ask whether modern mathematics would even exist without him." Euler also loved to tackle the same problem from multiple directions in order to solidify the strange results he derived to his doubters, as well as test his understanding and prowess.

Another observation I made is the sheer volume, as well as variety, of Euler's contributions. His work ranged from geometry, to number theory, to infinite series, and to complex analysis; this is an incredible body of work for one man. Interestingly enough, every area he brought his unprecedented analytical abilities and insight, even areas such as geometry where proofs were usually performed using clever insights rather than analytical techniques. His willingness to examine old topics in new ways (e.g. the relationship between the centroid, circumcenter, and orthocenter of a triangle) as well as work with new topics that others refused to consider (e.g. complex numbers) is simple incredible.

Although not comprehensive, this work gives the reader enough material to come to an appreciation of Euler and his works. Although Euler may not be the master of us all, he was certainly a master of his craft and was a person is not easily equaled.