The most beautiful formula in mathematics

I was always interested in mathematics and always fascinated by this formula:



What is so fascinating about this number? Well, first of all these are the five most important numbers in mathematics, and they all appear exactly once.

1: The number all counting is based on; also the multiplicative identity. without 1 there would be no mathematics at all.

0: The number which allows us to use a place-value system for numbers in mathematics and also the additive identity. 1 and 0 are also actually the only digits needed in mathematics; the other digits we use in the decimal system are a mere luxury.

π: The ratio of a circle's circumference and his diameter. The most important number in geometry; it is ubiquitous there. It is an irrational and transcendental number whose first digits are 3.14159265358979...

e: The base of natural logarithm and the most important number in calculus; it is equally ubiquitous there as π is in geometry. It is also an irrational and transcendental number whose first digits are 2.718281828459045...

i: The square root of -1. The base of the imaginary numbers, which together with the real numbers constitute the complex numbers. Extremely important in algebra; without it many algebraic equations could not be solved. And complex numbers open a whole new branch of mathematics.

But that's not all: The three most important mathematical operations (addition, multiplication and exponentiation; subtraction, division and root extraction are only the inverses) also appear exactly once.

And the most important relational operator, =, also appears exactly once.

But that's still not all. These five numbers also stand for five important concepts.

1 stands for the concept of unity.

0 stands for the concept of nothingness.

π stands for the concept of circularity.

e stands for the concept of growth and decay since growth and decay processes can be described using the exponential function with this number as basis.

i as an imaginary number stands for the concept of imagination.

So this formula actually reads: Take growth to the power of imagination and circularity and add unity to arrive at nothingness, whatever that means (and take this with a grain of salt).

But flip the two terms on each side of the equation sign and write the 1 first in the addition, and it makes a bit more sense: Out of nothingness come unity plus growth through the power of imagination and circularity. Now if you believe in a deity that uses evolution for creation this reads like the formula for world creation (again, take this with a grain of salt and a bit tongue in cheek; I am definitely not serious here).

In 1988 there was a poll of mathematicians around the world for the most beautiful formula in mathematics, and this formula got the most votes. And I think rightly so.


Edited by BaldFriede - February 24 2016 at 07:56

BaldFriede wrote: 1 stands for the concept of unity. 0 stands for the concept of nothingness. π stands for the concept of circularity. e stands for the concept of growth and decay since growth and decay processes can be described using the exponential function with this number as basis. i as an imaginary number stands for the concept of imagination.

Ugh. Please. Don't.

Logan wrote: I would say the Dirac equation.

The Dirac equation is physics, not mathematics.

3,14 or PI

or Maxwell equation http://www.maxwells-equations.com/maxwells-equations.gif

BaldFriede wrote: I was always interested in mathematics and always fascinated by this formula: What is so fascinating about this number? Well, first of all these are the five most important numbers in mathematics, and they all appear exactly once. 1: The number all counting is based on; also the multiplicative identity. without 1 there would be no mathematics at all. 0: The number which allows us to use a place-value system for numbers in mathematics an also the additive identity. 1 and 0 are also actually the only digits needed in mathematics; the other digits we use in the decimal system are a mere luxury. π: The ratio of a circle's circumference and his diameter. The most important number in geometry; it is ubiquitous there. It is an irrational and transcendental number whose first digits are 3.14159265358979... e: The base of natural logarithm and the most important number in calculus; it is equally ubiquitous there as </span><span ="te"="">π is in geometry. It is also an irrational and transcendental number whose first digits are 2.718281828459045... i: The square root of -1. The base of the imaginary numbers, which together with the real numbers constitute the complex numbers. Extremely important in algebra; without it many algebraic equations could not be solved. And complex numbers open a whole new branch of mathematics. But that's not all: The three most important mathematical operations (addition, multiplication and exponentiation; subtraction, division and root extraction are only the inverses) also appear exactly once. And the most important relational operator, =, also appears exactly once. But that's still not all. These five numbers also stand for five important concepts. 1 stands for the concept of unity. 0 stands for the concept of nothingness. </span><span ="te"="">π stands for the concept of circularity. e stands for the concept of growth and decay since growth and decay processes can be described using the exponential function with this number as basis. i as an imaginary number stands for the concept of imagination. So this formula actually reads: Take growth to the power of imagination and circularity and add unity to arrive at nothingness, whatever that means (and take this with a grain of salt). But flip the two terms on each side of the equation sign and write the 1 first in the addition, and it makes a bit more sense: Out of nothingness come unity plus growth through the power of imagination and circularity. Now if you believe in a deity that uses evolution for creation this reads like the formula for world creation (again, take this with a grain of salt and a bit tongue in cheek; I am definitely not serious here). In 1988 there was a poll of mathematicians around the world for the most beautiful formula in mathematics, and this formula got the most votes. And I think rightly so.

That's beautiful actually. I love math and you just made me love you at the same time. Now my mind is going to wrapped around this all day. Of course, I'm looking at the formula and trying to apply a different metaphor to it. If I come up with one, I'll post it.

Edited by Prog Snob - February 24 2016 at 07:06

BaldFriede wrote: "Oh? So waves, which are based on circularity, are a mythical concept? The growth of an organism is? Vacuum, which is based on nothingness, is? Complex systems, which are based on the idea of unity as a complex and systematic whole, are? And, last but certainly not least, human imagination is"? I think I made it clear that my "mystical conclusion" was tongue in cheek. But to deny the fact that these numbers stand for concepts is nonsense, though I admit that i standing for imagination is a bit keen. But it was not I ho named the imaginary numbers.

What the hell are you talking about?

I was just saying your mysticism was extraneous and wrong.

I dont know much about Math but i like to be better at it, and its facinating how much importans Math is to both science and art, how much the beuty of both can be said to be liing in the elegant presission of Math, by that i hail Pythagoras as the one who understood the line between numbers, shapes and beauty.