The most beautiful equation ever
Physics Web recently asked its readers to nominate the world's most beautiful equations. The winner? "Euler's identity" equation, depicted above, which respondents variously described as "the most profound mathematical statement ever written", "uncanny and sublime", "filled with cosmic beauty", and "mind-blowing". What's so cool about it? As Physics Web noted:
The equation contains nine basic concepts of mathematics -- once and only once -- in a single expression. These are [in order]: e (the base of natural logarithms); the exponent operation; pi; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero.
As one respondent noted, "What could be more mystical than an imaginary number interacting with real numbers to produce nothing?" Back in the 19th century, the American mathematician Benjamin Peirce gave a lecture proving "Euler's identity", and concluded:
"Gentlemen, 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."
Which is, of course, one of the great charms of hard-core mathematics and physics: If you frontload an equation into your brain that is complex enough, deep enough, and elegant enough, the sensation is pretty much indistinguishable from being baked out of your mind.
(Thanks to Slashdot for this one!)
Posted by Clive Thompson at October 28, 2004 02:44 PM
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Posted by: Joel at October 28, 2004 5:53 PM
Unfortunately, you've misquoted PhysicsWeb's commentary on it -- you left out the pi. Mmmm, pi.
Posted by: Jerry Kindall at October 28, 2004 6:34 PM
What do you get when you cut a pumkin in half?
Posted by: Joel at October 28, 2004 7:40 PM
It's not only beautiful, it's also kind of hot.
Posted by: Emily at October 28, 2004 8:11 PM
Thanks for the correction, Jerry!
Posted by: Clive at October 28, 2004 9:16 PM
although the equation you have used in the illustration appears to be correct, it is not in its most beautiful form, as described in the extract, and at the beginning of the wikipedia article. I still remember reading about it in one of Feynman's bio's and going "wow!"
Posted by: Mark at October 28, 2004 10:03 PM
Just because you've proven something logically, doesn't make it true. Didn't Aristotle "prove" that women have fewer teeth than men because their heads are smaller?
Posted by: Debbie at October 29, 2004 9:20 AM
But... women DO have fewer teeth than men, don't they?
/me goes to Google...
Posted by: Tony at November 1, 2004 10:22 AM
An even more remarkable special case of Euler's formula is i to the i power. That is, the square root of -1 multiplied by itself the square root of -1 times. Solve it for the amazing answer.
Posted by: Bill Levinson at November 5, 2004 6:16 PM
nice blog - love the design
Posted by: cell phone batteries at January 8, 2005 12:08 PM
The equation you quote at the head certainly is A beautiful equation, but it doesn't match your description and has been incorrectly copied from the article! The description is (correctly) describing THE most beautiful equation ever, which is derived from substituting pi into De Moivre's theorem (instead of pi/2 as you have done here).
This gives
e (to the power of) i pi + 1 = 0
This equation uses the two most common transcendental numbers,the zero and unit of all mathematics, the two most basic operations of addition and multiplication (- and * being their inverses) and equality. Sublime in the extreme!
Posted by: Dennis Holman at January 20, 2005 4:36 AM
Post a comment
amen
Posted by: Joel at October 28, 2004 5:53 PM
Unfortunately, you've misquoted PhysicsWeb's commentary on it -- you left out the pi. Mmmm, pi.
Posted by: Jerry Kindall at October 28, 2004 6:34 PM
What do you get when you cut a pumkin in half?
Posted by: Joel at October 28, 2004 7:40 PM
It's not only beautiful, it's also kind of hot.
Posted by: Emily at October 28, 2004 8:11 PM
Thanks for the correction, Jerry!
Posted by: Clive at October 28, 2004 9:16 PM
although the equation you have used in the illustration appears to be correct, it is not in its most beautiful form, as described in the extract, and at the beginning of the wikipedia article. I still remember reading about it in one of Feynman's bio's and going "wow!"
Posted by: Mark at October 28, 2004 10:03 PM
Just because you've proven something logically, doesn't make it true. Didn't Aristotle "prove" that women have fewer teeth than men because their heads are smaller?
Posted by: Debbie at October 29, 2004 9:20 AM
But... women DO have fewer teeth than men, don't they?
/me goes to Google...
Posted by: Tony at November 1, 2004 10:22 AM
An even more remarkable special case of Euler's formula is i to the i power. That is, the square root of -1 multiplied by itself the square root of -1 times. Solve it for the amazing answer.
Posted by: Bill Levinson at November 5, 2004 6:16 PM
nice blog - love the design
Posted by: cell phone batteries at January 8, 2005 12:08 PM
The equation you quote at the head certainly is A beautiful equation, but it doesn't match your description and has been incorrectly copied from the article! The description is (correctly) describing THE most beautiful equation ever, which is derived from substituting pi into De Moivre's theorem (instead of pi/2 as you have done here).
This gives
e (to the power of) i pi + 1 = 0
This equation uses the two most common transcendental numbers,the zero and unit of all mathematics, the two most basic operations of addition and multiplication (- and * being their inverses) and equality. Sublime in the extreme!
Posted by: Dennis Holman at January 20, 2005 4:36 AM