Today we had some discussion about science and proofs in science, to quote my professor:
Do not ever use the word “prove”, except in maths. Only politicians and the lunatic fringe prove things, and nobody believes their “proofs"! Our job is to find the truth, not to “prove” our favourite hypothesis. This is the basis of the scientific method.
It has nothing to do with this post, other than talk and thoughts about math and science and well, beautiful equations. So there it is, a list of five interesting and important, yet BEAUTIFUL equations easy to write/remember but so damn hidden (until discovered).
- Dirac's equation
This equations bridge two most exotic fields yet so different - quantum mechanics, which describes the behavior of tiny-tiny objects, and Einstein's special theory of relativity, which is all about of relativistic objects and space.
And if you are interested to see the derivation of Dirac's equation check out this youtube video.
- Maxwell's Equations of electrodynamics
Maxwell said: "Let there be light!"
Back in 1865 Maxwell demonstrated that electromagnetic field travels through space as waves moving at the speed of light.
- Speaking of light, and waves... The Beautiful 🌊 wave equation.
In this gem, we have all the information we need how the waves propagate, and it applies to all kinds of waves - water ripples, mighty ocean waves, sound, vibrations, light (and once again light = {gamma ray, x-ray, UV, optical(rainbow and all other colors), infrared and radio) waves.
- Next one is Euler-Lagrange equation:
Beautiful and useful in various cases - solutions to this equation are functions for which a given functional is stationary. Allowing us to find local minimum and maximum, and thus finding equilibrium positions, and it is also useful for optimization of problem solving.
A bit tweaked Lagrangian theory is Emmy Noether's theory of symmetry - She is also known as the woman who changed physics.
Informally, the theorem is that if your system has a symmetry, then there is a corresponding conservation law. For example, the idea that the fundamental laws of physics are the same today as tomorrow (time symmetry) implies that energy is conserved. The idea that the laws of physics are the same here as they are in outer space implies that momentum is conserved. Symmetry is perhaps the driving concept in fundamental physics, primarily due to [Noether's] contribution." - Kyle Cranmer
And for the end... two quick ones :)
The basic one - the old one and probably one of the most known theorems.
and a bit complex one - Euler's identity;)
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