Leonhard Euler: Mathematical Genius in the Enlightenment, Ronald S. Calinger

I didn’t realize how little I know about Euler until I read this book. I had a hazy awareness of him as one of the great mathematicians (along with Gauss) and knew he had worked on number theory, was related to imaginary numbers, of course, the Konigsberg Bridge problem, Euler’s identity and my favorite number, e. I also knew that he worked at St. Petersberg and was almost blind when he died. 

This exhaustive (exhausting?) biography of Euler opened my eyes to the breadth of topics he worked on – not just mathematics, but also mechanics, optics, music and astronomy. I have a better understanding of how he is placed with respect to other mathematicians and how he contributed to the development of science and pushed the boundaries of what was possible. 

I recently re-read (for the nth time)  The Structure of Scientific Revolutions and the parallels in development as described by Kuhn and what Euler does is amazing. Two striking points are – first, applying Newton’s laws to explain e.g., the motion of the moon was not straightforward and took plenty of debate and trial and error before it was accepted. I did not know this! Second, developing the calculus needed developing fundamental concepts like functions, logarithms of negative numbers  and 

It’s easy to study calculus today but to be in a state where even fundamental concepts of functions or co-ordinate systems do not exist

I’m actively thinking about current paradigm shifts, especially with respect to AI, and  

Newton’s laws were being debated for quite some time! How to derive the lunar orbit (3- body problem, but not like the book!) was a huge problem, and Euler relied on the ether to account for discrepencies

Motivation for deriving new maths (what is the current analogy?) ML is a paradigm shift, but no new maths (not that it is necessary…) well, maybe the attempt to describe how a NN works…

The energy and time spent on the Maupertuis-Koning affair are idiotic — it’s unknown today! (at least to me, till I read this book)

The effort to explain the motion of the moon & planets using Newton’s laws is fascinating. 

Before this, Euler was more than just a name, but mostly associated with e^i pi, series expansions and the bridges of konigsburg. Now he’s more real

would like to understand the proofs from number theory better. Add it to the list!

In those days mathematics and scientists had to contend with religion

So much of stuff we take for granted today had to be developed from scratch. eg differential equations, elliptic integrals, …

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