Opinion- The Most Beautiful Equation in Mathematics

The editorial board of Sankhya, department of mathematics of Miranda House, is elated to bring to you an opinion article on 'The most beautiful equation in mathematics' written by Shagun Singhal, a second-year mathematics honors student.

In 1988, Springer’s quarterly journal Mathematical Intelligencer conducted a poll that voted Euler’s identity as the most beautiful equation of all of mathematics.

Leonard Euler, the Shakespeare of modern-day mathematics stated in his identity: e^( ℼ*i)+1=0

The identity synthesizes the 5 most important elements of Mathematics into a single beautiful coalescence.

The identity was obtained after taking in a particular case of Euler’s formula when we put in x to be equal to ℼ

When x is equal to 2π, the formula yields the elegant expression e2*i=1.

Let's get to the formula’s different terms

1. The Exponential Function 'e'- ‘e’ is its derivative. If we see e^x as position, and its derivative as position, this means that the speed is always equal to the position. It is a gift to a big selection of physical phenomena, and a key part of radioactivity, electronics, and the rate of population.

2. Imaginary Number 'i'- At their birth, imaginary numbers were formed as a mathematical tool for having the ability to work with square roots of negative numbers, and therefore the term ‘imaginary’. 'i', the letter denoting imaginary numbers, is equal to the root of -1.

3. Pi-π - Pi(π) is the most prominent pearl in the necklace of mathematical constants. Pi is the 16th letter of Greek. Mathematically it is the ratio of a circle's circumference to its diameter. Archimedes of Syracuse in his treatise “Measurement of a Circle”, approximated this ratio of the circumference and the diameter of a circle to be between 3*1/7 and 3*10/71, this value later materialized as the constant Pi and acquired the irrational value of 22/7.

4. Zero and One(0 &1)- 0 and 1 are the most fundamental numbers of mathematics. They serve as the source of the derivation of all the other numbers. They together with e, Pi, and 'i' gave the equation its multifaceted beauty in the true sense.

Besides the use of the 5 elements, Euler’s Identity also takes into account the operations of addition, multiplication, and exponentiation

Geometric and Mathematical Interpretations of the Euler’s Identity

The intermediate form e^(iπ)= −1 is common in the context of a trigonometric unit circle in the complex plane: it corresponds to the point on the unit circle whose angle with respect to the positive real axis is Pi.

The sine, cosine, and exponential expansion of the Taylor series come together mathematically to form the famous identity.

Way Forward

Euler’s Identity is transcendental for the way through which it amalgamates together all the different elements, operations and for its mathematical and scientific meaning.

The identity is the symbolism of nature’s beauty in its flawless form through mathematics