[ExI] Euler day

[Anders Sandberg]

On 2013-04-15 06:59, spike wrote:
> Happy 106th birthday Leonard Euler!

Indeed.


> I try to imagine what emotions must Euler have felt when he discovered that
> e^i*pi = -1.  That must have been such a mind-blowing discovery.  It is
> astonishing enough to learn of it today, but what must it have been like to
> be the first person to discover it?

In "Euler: the Master of Us All" William Dunham writes that he concluded 
his proof of he de Moivre formula with evident satisfaction in his 
Introductio in analysin infinitorum.

However,
http://www.maa.org/editorial/euler/How%20Euler%20Did%20It%2040%20Greatest%20Hits.pdf 
makes a argument that he might have known the formula long before (in 
1729), likely having learned it from Johann Bernouilli. There is more 
sleuthing at
http://www.maa.org/editorial/euler/how%20euler%20did%20it%2046%20e%20pi%20and%20i.pdf

Dunham's book is great fun, because it shows just how wild Euler's 
approach was. This was no holds barred math, long before boring 
epsilon-delta formalists made calculus tame and safe. Infinite degree 
polynomials! Sums of products of sums! Limits nobody would expect to 
converge!


-- 
Anders Sandberg
Future of Humanity Institute
Oxford University