Yes, just as Peng-Fun mentioned, you would probably be referring to “physicists”, not “physicians”. It really gets my goat when people think I’m a “physician”.

That aside, you should probably grab some popcorn, because it’s story time!

Before that, here’s the main point. These equations arise because nature has patterns which scientists find and interpret.

We start our narrative with the Greeks (although they weren’t the first to question), and in particular two very stern blokes: Aristotle and Pythagoras. Aristotle was what we would now call a cosmologist, he was fascinated by how the universe worked and what everything was made up of. By observing the stars and moon and planets, he came up with the conclusion that everything in the universe moved by some perfect laws, that all the planets revolved in circles, because the circle was the perfect shape. But how did he know that the circle was the perfect shape? This was due to the mystical teachings of Pythagoras, who worshipped shapes and mathematics. He believed that everything beautiful could be put into mathematical equations, from art to music to all creation. Therefore, he believed that everything was linked through mathematics, and sought to link everything together through mathematics. This would be a trend in Western science that still continues till today.

Fast forward about 1800 years. We reach this other chap called Johannes Kepler. He had read Aristotle, and he liked the fact that the universe was governed by mathematical laws. He sought to find that out. One day, he had an insight that the universe was governed by polygons and mathematical shapes. He took Tycho Brache’s charts of the precise measurements of the planetary bodies, which he spent an enormous number of years plotting, and he applied his mathematical skills to make sense of it, and to find a low that could make predictions. It wasn’t an immediate bestseller, but it laid the foundation for a mathematical treatment of astronomy.

Finally, we reach Sir Isaac Newton, who had an insight that every particle in the universe is attracted to all other particles of the universe (he didn’t understand atoms as we do now, but apparently he was right!). He went around telling others about it, but no one believed him, so he locked himself in his apartment for years, just to derive a mathematical formulation to prove himself right.

**Kepler and Newton show two ways of applying mathematics to physical laws: Kepler by using mathematics to make sense of the data we get from around us, and Newton by creating a law and using the data to show that his law holds (note: you can’t actually prove a mathematical law “correct”).**

This is an explanation of how mathematical theories arise, which I think is a more interesting question than how constants are derived. Yashraj Singh has already properly dealt with that.

Of course, 800 years before the Greeks, the Chinese were already using mathematics to calculate the time and the ballistics of catapults. The Indians were using Pythagorean numbers 600 years before Pythagoras himself to calculate the timing of festivals. And even waaaay before those 2, the Babylonians were using angles to calculate the time of the day. But going into these would be going way out of my depth.

Things to google if you wanna know more:

Musica universalis - what we now know as “the music of the spheres”

On The Heavens - Aristotle’s treatise where he says the motion of the universe is governed by laws

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