10 of the Most Important Equations in History

These 10 equations helped shape our modern world. Without them, things might look very different indeed.
Christopher McFadden

Equations are an essential tool for describing how many things in the natural world function and interact. But some equations have had a more far-reaching influence than others.

Here we present 10 such equations, and also help answer some common questions about equations on the net.


What is the longest equation in the world?

According to Sciencealert, the longest math equation contains around 200 terabytes of text. Called the Boolean Pythagorean Triples problem, it was first proposed by California-based mathematician Ronald Graham, back in the 1980s. 

Why are equations important?

Equations are used every day for many, many, things. They help you search the internet, make your computer function, and keep planes in the air, to name but a few. 

What is the chaos theory equation?

"Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems, there are underlying patterns, constant feedback loops, repetition, self-similarity, fractals, and self-organization." - Wikipedia.

The equation is as follows:-

important equations chaos
Modified from news.bitofnews.com

This theory effectively helps us deal with complex systems whose behavior is highly sensitive to slight changes in conditions so that small alterations can give rise to unintended consequences.

Chaos Theory is the science of surprises, and not always pleasant surprises.

10 equations that changed the world

Here are ten of the most important equations that have changed the world. This list is far from exhaustive and is in no particular order.

1. Pythagorean Theorem

important equations pythagoras
Source: Maxpixel

A staple of school mathematics lessons, this equation is one that actually changed the world. It enabled us to be able to formulate better maps and help find the shortest distance between things; amongst other things.

It is also used heavily in architecture, woodworking, and many other fields. 

2. Calculus

"Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way, that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations." - Wikipedia.

It was developed independently by the great Isaac Newton and Sir Gottfried Leibniz. After its invention, it joined algebra and geometry as one of the pillars of mathematics.

3. Logarithms

Logarithms are another type of equation that changed the world. They helped us make tedious calculations before calculators existed

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A logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Using logarithm tables allowed the elimination of many tedious steps in calculations in fields such as surveying, navigation, and engineering.

4. Relativity

important equations einstein
Source: Peat Bakke/Flickr

Einstein's famous equations on Relativity not only answered many previously unsolved questions, but it also helped change the way we look at time, space, and gravity. 

It is used to assist in explaining everything from black holes to the big bang, to nuclear power, and also GPS on our phones.

5. Normal distribution

We are all familiar with bell curve graphs today. They help to describe the distribution of data in a given set. 

It can be used for anything from IQs within a population to the results of an exam amongst a group of students. Within a normal distribution, most data points will fall somewhere in the middle, with fewer individuals towards each extreme. 

6. Schrodinger’s Equation

important equations schrodinger
Source: YassineMrabet/Wikimedia Commons

Schrodinger’s Equation is essential for modern computer chips and lasers. It also helps keep cats in a form of suspended animation between life and death, apparently. 

But seriously, this equation literally changed the field of quantum physics forever. It is a linear partial differential equation that describes the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. 

7. Newton's Law of Gravity

"Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers." - Wikipedia. 

Newton's Law of Gravity is one of the most fundamental equations in physics. 

8. Wave Equation

"The wave equation describes the behavior of waves — a vibrating guitar string, ripples in a pond after a stone is thrown, or light coming out of an incandescent bulb. The wave equation was an early differential equation, and the techniques developed to solve the equation opened the door to understanding other differential equations as well." - businessinsider.com

It effectively forms an essential component of electromagnetism, optics, fluid dynamics, and heat transfer.

9. Second Law of Thermodynamics

"This states that, in a closed system, entropy (S) is always steady or increasing. Thermodynamic entropy is, roughly speaking, a measure of how disordered a system is. A system that starts out in an ordered, uneven state — say, a hot region next to a cold region — will always tend to even out, with heat flowing from the hot area to the cold area until evenly distributed." - businessinsider.com

It helps us, among other things, to understand the direction of heat transfer. This theory can be expressed in terms of the change in entropy of a system (dS). In this equation, dS is calculated by measuring how much heat has entered a closed system (δQ) divided by the common temperature (T) at the point where the heat transfer took place.

10. Fourier Transform

Thıs equation is basıcally at the heart of modern sıgnal processıng. It is also essential for signal analysis and data compression. 

"The Fourier transform is essential to understanding more complex wave structures, like human speech. Given a complicated, messy wave function like a recording of a person talking, the Fourier transform allows us to break the messy function into a combination of a number of simple waves, greatly simplifying analysis." - businessinsider.com.

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