**By James Dacey**

Earlier this year I wrote about a psychology experiment that revealed that mathematicians appreciate beautiful equations in the same way that people experience great works of art. In the experiment, which conjures up a slightly comical scene, mathematicians were hooked up to a functional magnetic resonance imaging (fMRI) machine and asked to view a series of equations. When the subjects looked at equations they had previously rated as beautiful, it triggered activity in a part of the emotional brain associated with the experience of visual and musical beauty. The formula most commonly rated as beautiful in the study, in both the initial survey and the brain scan, was Euler’s equation, **e ^{iπ}+ 1 = 0**.

Inspired by this study, we have put together this infographic to dissect the Euler identity and try to understand why so many mathematicians are enamoured with this little equation. Let us know what you think of the infographic and what you think are the most beautiful equations. Either post a comment below this article, or let us know on *Twitter* using the hashtag #BeautifulEquations.

The De Broglie equation:

λ = h/p,

h: the Planck constant; p, the momentum of the particle and λ, its associated wavelenght. This equation led to the “particle- wave dualty concept” and exraordinary idea of “wavefunction” and the Schrodinger’s equation.

But this is a definition rather than an equation. De Broglie’s gives sense to a particle’s wavelength, while in Euler’s all terms have been previously defined in other ways. I mean, no one says “-What is 1? +1 is -e^i*π”, what is actually true.

I like the Infographic, but you’ve reversed the captions for the basic operators. FYI.

Trackback: Mathematicians appreciate beauty in equations | art and math

And this whole time I thought I had addition “+” and multiplication “x” backwards!

I prefer to think of it as saying that e^pi is the ith root of -1.

Thank you for pointing out that we had the addition “+” and multiplication “x” symbols in the wrong order. This article now contains an updated version of the infographic.

Although it is a mite complicated, I find the Lorentz Transform equations to be gorgeous considering how much they do with so little.

In fact, they are Pitagoras applied to velocity watched from another point of view.

I like 6^3 – 5^3 – 4^3 – 3^3 = 0 similar to 5^2 – 4^2 – 3^2 = 0, and the cyclic number 0.142857

What a beautiful topic! However, I am missing Einstein’s field equations of gravitational interactions, or have I overlooked it?

Great post, but you missed out the crucial importance of the “=” sign. Until we had that, we had no equations

Ah, my favourite equation. I think an equation is beautiful when it is simple and yet connected to many different ideas.

I like the Euler-Lagrange equation from variational calculus. So simple yet powerful.

Trackback: Physics Viewpoint | What makes an equation beautiful?

Registering with A1 Articles is completely free and we respect your privacy, meaning your email address will not be passed onto a third party.

If you want even better deals than what a 720 score will get you, then your aim should be at

least minimally 760. Neither does telling a collector

you are aware of an old (SOL-expired) debt,

or can’t pay back the debt.

Whether you are downsizing your living quarters,

organizing your household, or just need a place to store your belongings while you

move, mini storage facilities can be extremely helpful.

According to wat they have inn the storage unit

as well as according to tueir personal finances at the time, can dictate whether the auction takes place or not.

So if you know anything about the Midwest, sometimes the wnter weather can bee nasty.