Math

# Are Math Equations Beautiful? Euler's Identity Makes Mathematicians Swoon

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Relationship goals: Find someone who talks about you the way Richard Feynman talks about Euler's identity. In lectures, he called the equation "our jewel" and "the most remarkable formula in mathematics." The equation has not only been called the most beautiful equation in mathematics, it has even been compared to a Shakespearean sonnet.

Related: There's A Formula That Gives The First 18 Trillion Trillion Digits Of The Constant e

## Shall I Compare e To A Summer's Day?

Drumroll, please. Here is Euler's identity: e + 1 = 0. Did that leave you breathless? Have you been swept off your feet? Are you sobbing tears of joy over its alluringly pure beauty? Okay, this may need an explanation. This equation has been renowned for its beauty for a few reasons. It comprises the five most important mathematical constants: 1 , 0 , pi (the number that defines a circle), e (the base of natural logarithms), and i (the most fundamental imaginary number).

Related: Einstein's Famous Equation Isn't The Full Story

Euler's identity also contains the three basic mathematical operations: addition, multiplication, and exponentiation. "Euler's identity is amazing because it is simple to look at and yet incredibly profound," Professor of Mathematics David Percy of the University of Salford in the UK told the BBC. "What appeals to me is that this equality connects some incredibly complicated and seemingly unrelated concepts in a surprisingly concise form." As for what the equation actually does, it basically describes two equivalent ways to move in a circle.

Related: The Millennium Problems Are Seven Math Problems Worth \$1 Million Each

## Do You Know This Man?

The equation's namesake is 18th-century Swiss mathematician Leonhard Euler. He was one of the most prolific mathematicians of all time, according to the U.S. Naval Academy, with a resume that boasts 886 papers and books published. This guy was responsible for developing many concepts that span various fields of math—geometry, trigonometry, calculus, differential equations, number theory, and notational systems. The principles he came up with laid the foundation for modern mathematics as we know it. No big deal.

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## Watch And Learn: Our Favorite Content About Math Problems

DNews – DNews

### Key Facts In This Video

1. In a study, the more beautiful a math equation was, the more likely it elicited a response in the A1 field of the medial orbitofrontal cortex, which is associated with musical and physical beauty. 00:32

2. Even the brains of people with no understanding of a math equation responded to its beauty. 01:23

3. Euler's Identity is the equation consistently rated as the most beautiful. 01:41

#### E=mc² is Incomplete

##### E=mc² is Incomplete
MinutePhysics – MinutePhysics

### Key Facts In This Video

1. E=mc^2 only describes objects that have mass and that aren't moving. 00:06

2. The equation for the energy of a moving, massless particle (such as a photon) is E=pc. 00:43

3. An object's velocity is equal to the speed of light times the ratio of the object's momentum to energy. 01:08