Every Crucial Equation in Math and Physics

Some of the Equations the made the modern world.
Timestamps
0:00 The Pythagorean Theorem
0:41 Logarithms
01:39 Calculus
2:37 Law of Gravity
3:33 Square root of -1
4:31 Euler’s Polyhedra Formula
5:39 Fourier Transform
6:22 Wave Equation
7:12 Maxwell’s Equations
8:07 Second Law of Thermodynamics
8:41 Normal Distribution
9:18 Relativity
10:04 Schrödinger’s Equation
10:36 Heisenberg’s Uncertainty Principle
11:08 Navier-Stokes Equations
11:32 Information Theory
12:01 Black-Scholes Equation
12:33 Chaos Theory
- Sources -
In Pursuit of the Unknown by Ian Stewart
- DISCLAIMER -
This video is intended for entertainment and educational purposes only. It should not be your sole source of information. Some details may be oversimplified or inaccurate. My goal is to spark your curiosity and encourage you to conduct your own research on these topics.

[@Xellorated]

The Einstein Field equations should really be shown for relativity instead of E = mc^2. The simplified reduction to rest mass energy is much less important than the other aspects of relativity.

[@ReapersRed]

Definitely not. Special relativity pops out of Maxwells equations, but e = mc^2 is truly something revolutionary. It fundamentally changed our understanding of how every conservation equation works at its core. We learned all chemical and nuclear reactions are fundamentally changing from energy to mass or Vice versa. All continuity equations are just energy balance at the end of the day. The only people that care about space-time curvature from general relativity are astrophysicists, but so many fields care about mass energy equivalence.

[@jespersahnerpedersen]

Bell's Inequality, Euler's Identity

[@LordMarcus]

Woke mathematical justice warriors, whinging about equality and identity maths.😆

[@LordMarcus]

1:19 What, no love for the natural log, base _e??_

[@highviewbarbell]

i was gonna say it had to be higher than base 2 even

[@TheLethalDomain]

The description of the Maxwell's equations apply for a vacuum. Charge and current densities are missing here, and thus do not correlate with what you tried to explain afterwards.

[@levelup2014]

Then why don’t you make a video instead of complain g in the comments?

[@Matt-qm1th]

@@levelup2014he pointed out a flaw in the video so that we can all be better informed, this is not a negative thing

[@lilypad429]

​@@levelup2014hey, if i want to criticise a president, does that mean i have to be a president first to be able to?

[@GarrixianXD]

1:18 “The most common bases are 10 and 2” Natural log/log base e: am I a joke to you?

[@IsaacNewton1687]

Important fact, special relativity doesn't say that the laws of physics are the same for everyone, just for inertial observers. GR says that the laws of physics are the same for everyone. Also E=mc² by far isn't the key equation in relativity. I'd write down the Einstein field equations G=8πT, or the metric dS² (as a function of x,y,z,ct) or both. From these you would be able to deduce everything whike E=mc² isn't even coordinate independent

[@ReapersRed]

I disagree, the field equations have much less of a profound impact on most applications than mass energy equivalence. E=mc² changed our understanding of all chemical and nuclear reactions. It also made every continuity equation an energy balance. I may be biased tho bc I’m a nuclear engineer

[@groinBlaster31]

Love your channel!!!!!

[@kruksog]

When first exposed to logarithms people often get hung up on which base is being used (and it is important in some situations - the natural log in calculus for example), but the properties of logarithms used to simplify arithmetic work in every base. That is what makes them so fundamentally useful.

[@naturallyinterested7569]

Funnily enough the Maxwell Eq's as shown describe none of the effects advertised, bc you only showed the source-free version that can only describe light in an empty space.

[@SobTim-eu3xu]

Great video!)

[@douglasstrother6584]

Decibels are the logs I roll!

[@GamingDudeSUS]

slight mistake, eulers polyhedra formula only states true if the body has no holes aka isnt a torus in topology

[@Morgyborgyblob]

Yes, I've read "17 equations that changed the world" too.

[@shoobaadooboo6453]

7:16 slight mistake, the divergence of the E-field is not 0. Other than that amazing video 😁

[@ptdongiovanni]

Those were Maxwell's equations for vacuum. No charge, no divergence. Same for curl of H: the j current is missing if you want to consider the general case, not only vacuum.

[@enpeacemusic192]

Uhm, the standard model laplacian?

[@brandonpart2ihateap680]

laplacian?

[@aryawijayaa95]

New subscriber

[@cameronspalding9792]

@ 0:39 The analogues of the trigonometric rules in non Euclidean geometry are approximately the same as the ones in Euclidean geometry if the sides are very small

[@Underscores-t4k]

Bro you just explain the book of the king Ian stewart but it s cool

[@h2_]

Isn't black-scholes just navier stokes partial solution recontextualized? Why is navier stokes on there twice?

[@Polynomial186]

Cool

[@honza_88]

3:50 Isn't 0 an Integer, not a Natural number?

[@trananhkiet167]

Nah most of is ODE , when working in classical mechanism, i found that. I cant solve Lagrange equation without know how to solve ODE , so i found the paper in library for a month ,then collect pieces of information in many major from economy, fluid mechanic , social science , chemistry, electrical engineer, industry design, architecture , computer science . i found that all that product/model that the majors are currently using is ODE form or a expression of eignvalue of ODE .😅 i take a advantage that school only teach how to calculate, so if i know ODE form i can solve all topic of relevant major, and it true . in accounting and law they mostly using algebra and tree thoery, mixed human factor . then i reveal the world " godfather" according relevant topic both legal and illegal, then it lead me to a rich rss as know as social science. right now. I m development tool to efficiency the knowledge flow , it will be released in further. Moreover , the value which is the partial value of ODE sometime called as "MARCO" , fine, complex, formula ... It have many form, and suffix "ian" ,which mean perform smt ,make the world " mathematician " really have own. meaning. Thanks to visit my TED talk

[@qracy-kun5288]

From the beginning of video to schrodinger i was like oh i know that but after schrodinger it was like oh its whole new level shit i dont even know about one thing in that equations even though video gives me the information about the terms.Still far away from understanding universe.

[@manhwainfinite]

🤣 same

[@EmosGambler]

What is V + F - E = 2 useful for?

[@eks_0]

Important in material science

[@Yaramy]

Important for graph theory

[@dawoodfarooqi1883]

Topology

[@filipeoliveira7001]

It was literally explained in the video that it was crucial for topology and physics

[@devooko]

for finding the penile length, here V = 2 (2 balls), F = 4 (Number of sperm ducts + fallopian tubes) and E = 2 (Mental agility)

[@Arvl.]

Kewl

[@uwuowo7775]

BREATHE

[@HejHejda-hh3wl]

E = 89875517873681764m