1. The Pythagoras Theorem: In mathematics, the Pythagoras theorem states the relation between the sides of a right angled triangle. It is the basic theorem of geometry.
2. Calculus: The differential calculus developed by Newton in the 17th century changed the course of history. Without calculus, we cannot study the dynamics of the universe.
3. The Law of Gravity: Newton’s law of gravity tells that the force of gravity between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. The law of gravity ultimately helped in explaining how planets move around the Sun.
4. Square root of -1: The square root of -1 by Euler was the beginning of complex analysis. It paved the way for Fourier transforms that has applications in signal processing.
5. Wave Equation: D’Alembert developed the wave equation. It is a second order partial differential equation that explains the behavior of waves in water or on a vibrating guitar string.
6. Fourier Transforms: Developed by Joseph Fourier, the Fourier transforms are at the heart of signal processing. They are the key to communication.
7. Maxwell’s Equations: The 4 Maxwell’s Equations changed the way we look at the world. James Clerk Maxwell brought these 4 equations together to show that electricity and magnetism are deeply connected. Maxwell’s equations along with Lorentz force law are all you need to study electrodynamics. Maxwell’s equations combine Gauss’ law for electricity and magnetism along with Ampere’s law and Faraday’s law.
8. Second Law of Thermodynamics: This is one of the most fundamental law of nature. It tells an important thing about the nature of time. It says that time flows in the direction of increase in entropy. The entropy or the disorder of the universe stays constant or increases. Entropy never decreases.
9. Mass Energy Equivalence: The flagship equation of physics, Einstein’s E = mc^2 is an integral part of theory of relativity. This equation means that mass and energy are the same thing. This equation is a part of Einstein’s special relativity. Without this, there is no particle physics, no LHC and no Higgs Boson.
10. Schrodinger Wave Equation: The flagship equation of quantum mechanics, the Schrodinger equation means that the total energy of a particle is the sum of its kinetic and potential energy. The Schrodinger wave equation lies at the heart of quantum physics. It was derived the Erwin Schrodinger in the third decade of 20th century.