Which areas of math are the most fundamental in your opinion?
64 - 47
Do you usually avoid hard math problems because they’re hard or because of what failing might reveal about yourself?
88 - 28
Mathematics has thousands of theorems and conjectures, but there are just a few that are essential and foundational.
Some of them have been proven, others are still waiting for their solution. The goal here is not to deeply understand all the intricacies of each result, but to acquire a general idea of what mathematicians work on in their daily lives.
This approach will help you to learn what interests you the most and how to start your journey on becoming an expert in it. Let’s see what they are.
Click on the video below!
watch video on watch page
58 - 0
SHARE YOUR OPINION
What is Pure Mathematics? What is its scope?
Up coming video...
54 - 17
Einstein cracked the code of spacetime not with numbers, but with tensors. But the truth is, tensors don’t just describe physics. They are the geometry of the universe we live in.
In this video you will learn what tensors are, and once you understand how they work, you’ll never see space, time, geometry and motion the same way again.
What is a tensor?
Watch this video to find out!
watch video on watch page
55 - 0
SHARE YOUR OPINION
What is the Definition of a Mathematician?
Do you need a diploma to be called a mathematician?
Is doing math everyday enough to be called a mathematician?
Does this person need to make original contributions to pure mathematics?
49 - 22
When looking at the right-hand side of Einstein’s field equations, mathematicians and physicists see different things from each other.
For the mathematician, the constant 8πG/c^4 is just that, a constant. He’s not interested in the fact that it involves two of the most fundamental quantities in nature (i.e. the gravitational constant G and the speed of light c). So the mathematician sees it as nothing but a scaling factor that might as well be called κ = 8πG/c^4 , for example.
This tensor T_µνis described as a rank-2 symmetric object (2 indices). It is defined pointwise. Its components vary smoothly with the coordinates. And it is covariant under coordinate transformation. It does not depend on the local coordinate choice, it is an intrinsic geometric object.
If you want to know more about it... check out the video below!
watch video on watch page
69 - 1
The mathematical description of many physical systems relies on differential equations. These can be ordinary differential equations (ODEs), partial differential equations (PDEs), or even a mix of both.
The main goal in studying these equations is to find their solutions. But in practice, this is often extremely difficult, and sometimes impossible. The truth is, all known methods for solving these equations depend heavily on the specific structure of each individual equation. A technique that works beautifully for one class of equations might be completely useless for another.
It’s fair to say that, if we were able to solve all differential equations in mathematical physics, we would, in principle, be able to predict everything that has ever happened or will ever happen, assuming no undiscovered “exotic” physics lies beyond our current theories (which, to be honest, is totally possible).
If you want to learn more, watch this video! See you there ;)
watch video on watch page
40 - 0
In the beginning of the 20th century, Einstein developed his theory of General Relativity (GR), which described gravity not as a force, but as the curvature of spacetime itself. When he applied his equations to the entire universe, he expected a static cosmos (i.e. no expansions or contractions of spacetime) and added a cosmological constant to prevent it from collapsing or expanding. However, Russian physicist Alexander Friedmann and later Belgian priest-physicist Georges Lemaître independently found that Einstein’s equations naturally predicted a dynamic universe. Though Einstein initially dismissed these solutions, the mathematics was clear: GR allowed (and even required!) cosmic evolution.
One question that keeps coming back to people's minds from time to time is:
If the universe is expanding, what is it expanding into?
Check out the video below to find out!
watch video on watch page
40 - 0
Mathematicians and physicists often look at the same problem in completely different ways.
- A mathematician might look for rigor, structure, and proof.
- A physicist might look for intuition, models, and applications.
We’d like to know:
Do you feel closer to the mindset of a mathematician or a physicist?
And most importantly, why?
Your answers will help us better understand the kinds of perspectives and approaches you favor in math.
168 - 56
We're Luca & Sophia Di Beo.
Luca is an ex-PhD Math student from the University of Udine, Italy, with a degree in Physics at the University of São Paulo (USP), Brazil, and a Master’s degree in Mathematics at the University of Kyiv, Ukraine.
Sophia has an MA in History, from Northumbria University in the UK. She makes all of the animations that you see in our videos.
Our goal is to be the #1 math channel in the world. Please, give us your feedback, and help us achieve this ambitious dream.
Ask for any video or course about any topic related to Mathematics & Mathematical Physics, and we will create a very simple explanation and pack it all in a very visual and easy to digest video.
Please, let us know in the comments what kind of content you want us to post about (related to Math & Mathematical Physics) so that we can help you!
Contact us at:
dibeos.contact@gmail.com
Or visit our website:
dibeos.net