Complete Works of Leonhard Euler Available Online

[Macrobius]

http://www.math.dartmouth.edu/~euler/

Maybe later... the news appears to have hit HNN:

http://news.ycombinator.com/item?id=2346427

and the site is temporarily down.

For now, use Arxiv.org:

http://arxiv.org/find/math/1/au:+Euler_L/0/1/0/all/0/1

Paper Titles, courtesy of the White Race:

'Various observations on angles proceeding in geometric progression '

'On the infinity of infinities of orders of the infinitely large and infinitely small'

'Finding the sum of any series from a given general term '

'A conjecture on the forms of the roots of equations '

'New demonstrations about the resolution of numbers into squares '

'Various considerations on hypergeometric series '

'A more accurate treatment of the problem of drawing the shortest line on a surface'

...

I'm perfectly happy to hear what Blacks have to say about such things.... Still waiting....

[Ixtab]

What was Euler's algebraic proof of the existence of God?

(By the way, did you ever notice how Euler looks a lot like Alexander Pope?)

http://famouspoetsandpoems.com/pictures/alexander_pope.jpg
http://upload.wikimedia.org/wikipedia/commons/d/d7/Leonhard_Euler.jpg

[Monty]

What was Euler's algebraic proof of the existence of God?

How does algebra prove things that aren't numbers?

[Ixtab]

How does algebra prove things that aren't numbers?Some have suggested that the compact formula ei*pi + 1 = 0 is surely proof of a God and have called this formula "God’s formula." Edward Kasner and James Newman in Mathematics and the Imagination note,

"We can only reproduce the equation and not stop to inquire into its implications. It appeals equally to the mystic, the scientists, the mathematician.

"This formula of Leonhard Euler (1707-1783) unites the five most important symbols of mathematics: 1, 0, pi, e and i (the square root of minus one). This union was regarded as mystic union containing representatives from each branch of the mathematical tree: arithmetic is represented by 0 and 1, algebra by the symbol i, geometry by pi, and analysis by the transcendental e.

"Harvard mathematician Benjamin Pierce said about the formula, 'That is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth.'"

[Gedanken]

Cartier's article on Euler's mathemagics (especially 4.5 "Did Euler really fool himself?"):

http://emis.impa.br/EMIS/journals/SLC/wpapers/s44cartier1.pdf

[Impérialiste]

Some have suggested that the compact formula ei*pi + 1 = 0 is surely proof of a God and have called this formula "God’s formula." Edward Kasner and James Newman in Mathematics and the Imagination note,

"We can only reproduce the equation and not stop to inquire into its implications. It appeals equally to the mystic, the scientists, the mathematician.

"This formula of Leonhard Euler (1707-1783) unites the five most important symbols of mathematics: 1, 0, pi, e and i (the square root of minus one). This union was regarded as mystic union containing representatives from each branch of the mathematical tree: arithmetic is represented by 0 and 1, algebra by the symbol i, geometry by pi, and analysis by the transcendental e.

"Harvard mathematician Benjamin Pierce said about the formula, 'That is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth.'"

This is all nonsense. I know exactly what it means and don't understand why prominent mathematicians - assuming honesty - would assume this is a mystical formula. I will explain when time permits.

[Macrobius]

How does algebra prove things that aren't numbers?

Before we talk about God, I want to here Monty explain how Algebra proves things that *are* numbers. I can prove lots of things, but none of them are numbers that I've ever noticed. Let's start with the easier problem first.

[SlagMaster]

Originally Posted by Monty: How does algebra prove things that aren't numbers? Isn't this why algebraic concepts support i numbers? Hahah
A definitive answer if you please, Monty.

[harjit]

My university math is completely out the window, but to Monty's credit I don't think I recall too many problems dealing with sets or spaces that didn't belong to the set of Real numbers.

But, again, that period of my life is very much a blank now. I almost wonder if something truly horrible transpired, in those days, that I'm shutting out.