The most important theorem in differential geometry: Gauss-Bonnet theorem
Mathemaniac
The most important theorem in differential geometry: Gauss-Bonnet theorem
22:09
Why is 4-color theorem easier on a torus?
Mathemaniac
Why is 4-color theorem easier on a torus?
17:27
You are probably wrong about Euler's formula (it's an inequality!)
Mathemaniac
You are probably wrong about Euler's formula (it's an inequality!)
14:13
How physics solves a math problem (and a 3D graphics problem)
Mathemaniac
How physics solves a math problem (and a 3D graphics problem)
17:42
The clever way curvature is described in math
Mathemaniac
The clever way curvature is described in math
16:17
Lie algebras visualized: why are they defined like that? Why Jacobi identity?
Mathemaniac
Lie algebras visualized: why are they defined like that? Why Jacobi identity?
44:31
Matrix trace isn't just summing the diagonal | Lie groups, algebras, brackets #5
Mathemaniac
Matrix trace isn't just summing the diagonal | Lie groups, algebras, brackets #5
22:44
Can we exponentiate d/dx? Vector (fields)? What is exp? | Lie groups, algebras, brackets #4
Mathemaniac
Can we exponentiate d/dx? Vector (fields)? What is exp? | Lie groups, algebras, brackets #4
30:09
What is Lie theory? Here is the big picture. | Lie groups, algebras, brackets #3
Mathemaniac
What is Lie theory? Here is the big picture. | Lie groups, algebras, brackets #3
21:57
How to rotate in higher dimensions? Complex dimensions? | Lie groups, algebras, brackets #2
Mathemaniac
How to rotate in higher dimensions? Complex dimensions? | Lie groups, algebras, brackets #2
13:23
Why study Lie theory? | Lie groups, algebras, brackets #1
Mathemaniac
Why study Lie theory? | Lie groups, algebras, brackets #1
4:26
How many terms do we need in the exp series?
Mathemaniac
How many terms do we need in the exp series?
14:02
Queuing theory and Poisson process
Mathemaniac
Queuing theory and Poisson process
25:25
Theorema Egregium: why all maps are wrong
Mathemaniac
Theorema Egregium: why all maps are wrong
40:13
The biggest misconception about spin 1/2
Mathemaniac
The biggest misconception about spin 1/2
34:06
I use PowerPoint to edit all* videos (and hit 100k subs!)
Mathemaniac
I use PowerPoint to edit all* videos (and hit 100k subs!)
20:33
The deeper meaning of matrix transpose
Mathemaniac
The deeper meaning of matrix transpose
25:41
How hard was my Cambridge interview? (ft. @TomRocksMaths)
Mathemaniac
How hard was my Cambridge interview? (ft. @TomRocksMaths)
54:32
Random walks in 2D and 3D are fundamentally different (Markov chains approach)
Mathemaniac
Random walks in 2D and 3D are fundamentally different (Markov chains approach)
18:22
The weirdest paradox in statistics (and machine learning)
Mathemaniac
The weirdest paradox in statistics (and machine learning)
21:44
Why you can't solve quintic equations (Galois theory approach) #SoME2
Mathemaniac
Why you can't solve quintic equations (Galois theory approach) #SoME2
45:24
The simplest reason why π/4 = 1 - 1/3 + 1/5 -...
Mathemaniac
The simplest reason why π/4 = 1 - 1/3 + 1/5 -...
19:13
The geometric interpretation of sin x = x - x³/3! + x⁵/5! -...
Mathemaniac
The geometric interpretation of sin x = x - x³/3! + x⁵/5! -...
22:02
Complex integration, Cauchy and residue theorems | Essence of Complex Analysis #6
Mathemaniac
Complex integration, Cauchy and residue theorems | Essence of Complex Analysis #6
40:45
What if we define 1/0 = ∞? | Möbius transformations visualized
Mathemaniac
What if we define 1/0 = ∞? | Möbius transformations visualized
25:27
What do complex functions look like? | Essence of complex analysis #4
Mathemaniac
What do complex functions look like? | Essence of complex analysis #4
28:33
The 5 ways to visualize complex functions | Essence of complex analysis #3
Mathemaniac
The 5 ways to visualize complex functions | Essence of complex analysis #3
14:32
What are complex numbers? | Essence of complex analysis #2
Mathemaniac
What are complex numbers? | Essence of complex analysis #2
32:11
Why care about complex analysis? | Essence of complex analysis #1
Mathemaniac
Why care about complex analysis? | Essence of complex analysis #1
3:55
Green's functions: the genius way to solve DEs
Mathemaniac
Green's functions: the genius way to solve DEs
22:52
From miller to entering Cambridge at age 40 - George Green
Mathemaniac
From miller to entering Cambridge at age 40 - George Green
12:58
Solved simply: the impossible integral
Mathemaniac
Solved simply: the impossible integral
15:13
What is Jacobian? | The right way of thinking derivatives and integrals
Mathemaniac
What is Jacobian? | The right way of thinking derivatives and integrals
27:14
The numerical simulation is NOT as easy as you think! - Average distance #2
Mathemaniac
The numerical simulation is NOT as easy as you think! - Average distance #2
11:05
Dream cheating scandal - explaining ALL the math simply
Mathemaniac
Dream cheating scandal - explaining ALL the math simply
26:05
What is the average distance of two points in a disc? (PART 1)
Mathemaniac
What is the average distance of two points in a disc? (PART 1)
8:55
Icosahedral symmetry - conjugacy classes and simplicity
Mathemaniac
Icosahedral symmetry - conjugacy classes and simplicity
12:28
Without integration, why is the volume of a paraboloid half of its inscribing cylinder? (DIw/oI #8)
Mathemaniac
Without integration, why is the volume of a paraboloid half of its inscribing cylinder? (DIw/oI #8)
4:39
Problem of Apollonius - what does it teach us about problem solving?
Mathemaniac
Problem of Apollonius - what does it teach us about problem solving?
11:47
Burnside's Lemma (Part 2) - combining math, science and music
Mathemaniac
Burnside's Lemma (Part 2) - combining math, science and music
10:00
Burnside's Lemma (Part 1) - combining group theory and combinatorics
Mathemaniac
Burnside's Lemma (Part 1) - combining group theory and combinatorics
13:45
Limitations of mathematical models; historical context of BGW process [PART III]
Mathemaniac
Limitations of mathematical models; historical context of BGW process [PART III]
9:27
How likely is coronavirus (COVID-19) eradicated? [PART II]
Mathemaniac
How likely is coronavirus (COVID-19) eradicated? [PART II]
10:11
Alternative to SIR: Modelling coronavirus (COVID-19) with stochastic process [PART I]
Mathemaniac
Alternative to SIR: Modelling coronavirus (COVID-19) with stochastic process [PART I]
12:00
Summary: an example covering ALL group theory concepts!! | Essence of Group Theory
Mathemaniac
Summary: an example covering ALL group theory concepts!! | Essence of Group Theory
11:27
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
Mathemaniac
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
10:51
Two opposite games involving golden ratio (ft. Tom Rocks Maths)
Mathemaniac
Two opposite games involving golden ratio (ft. Tom Rocks Maths)
13:41
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
Mathemaniac
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
12:47
Chapter 5: Quotient groups | Essence of Group Theory
Mathemaniac
Chapter 5: Quotient groups | Essence of Group Theory
12:37
How will the COVID-19 (coronavirus) epidemic end?
Mathemaniac
How will the COVID-19 (coronavirus) epidemic end?
9:41
Chapter 4: Conjugation, normal subgroups and simple groups | Essence of Group Theory
Mathemaniac
Chapter 4: Conjugation, normal subgroups and simple groups | Essence of Group Theory
12:03
Chapter 3: Lagrange's theorem, Subgroups and Cosets | Essence of Group Theory
Mathemaniac
Chapter 3: Lagrange's theorem, Subgroups and Cosets | Essence of Group Theory
13:40
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
Mathemaniac
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
12:27
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
Mathemaniac
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
6:07
Power rule of integrals not using integration; definition of e | DIw/oI #7
Mathemaniac
Power rule of integrals not using integration; definition of e | DIw/oI #7
7:25
How do I love math? (Part II - Proof without words)
Mathemaniac
How do I love math? (Part II - Proof without words)
3:40
How is pi calculated to trillions of digits?
Mathemaniac
How is pi calculated to trillions of digits?
6:52
Why does R(4,4)=18?
Mathemaniac
Why does R(4,4)=18?
4:39
Proof of Ramsey's theorem
Mathemaniac
Proof of Ramsey's theorem
5:28
Rhapsody on Ramsey numbers (and aliens?)
Mathemaniac
Rhapsody on Ramsey numbers (and aliens?)
14:02
15-year-old did mathematical research?! What was my thinking process back then?
Mathemaniac
15-year-old did mathematical research?! What was my thinking process back then?
10:02
The art of generalization in Mathematics | DDC #4
Mathemaniac
The art of generalization in Mathematics | DDC #4
6:30
More ways of deriving Catalan numbers | DDC #3
Mathemaniac
More ways of deriving Catalan numbers | DDC #3
10:03
Catalan numbers are not in Catalan | DDC #2
Mathemaniac
Catalan numbers are not in Catalan | DDC #2
11:13
Crash Course in Combinatorics | DDC #1
Mathemaniac
Crash Course in Combinatorics | DDC #1
11:28
Deep Dive into Combinatorics (Introduction)
Mathemaniac
Deep Dive into Combinatorics (Introduction)
4:34
A mistake that is not wrong | Shorts #3
Mathemaniac
A mistake that is not wrong | Shorts #3
4:15
What is mathematical elegance? How do I love math? | Shorts #2
Mathemaniac
What is mathematical elegance? How do I love math? | Shorts #2
3:00
Using physics to compute integrals | DIw/oI #5
Mathemaniac
Using physics to compute integrals | DIw/oI #5
5:23
Indefinite integrals? Cavalieri’s quadrature? Complex analysis? | DIw/oI #6
Mathemaniac
Indefinite integrals? Cavalieri’s quadrature? Complex analysis? | DIw/oI #6
8:09
Ancient Greeks (Archimedes) almost discovered calculus! | DIw/oI #4
Mathemaniac
Ancient Greeks (Archimedes) almost discovered calculus! | DIw/oI #4
10:05
Algebra vs Geometry in Trigonometry | DIw/oI #3
Mathemaniac
Algebra vs Geometry in Trigonometry | DIw/oI #3
7:47
We can compute the integral of sine geometrically? | DIw/oI #2
Mathemaniac
We can compute the integral of sine geometrically? | DIw/oI #2
8:48
Doing integrals without integration (Part I)
Mathemaniac
Doing integrals without integration (Part I)
7:49
What is the next term of a sequence? | Shorts #1
Mathemaniac
What is the next term of a sequence? | Shorts #1
4:28
Everything you need to know about operations in modular arithmetic
Mathemaniac
Everything you need to know about operations in modular arithmetic
16:07
Untold connection: Lagrange and ancient Chinese problem
Mathemaniac
Untold connection: Lagrange and ancient Chinese problem
12:56
Finding Fibonacci general term using LINEAR ALGEBRA
Mathemaniac
Finding Fibonacci general term using LINEAR ALGEBRA
6:03
5 ways to derive the general term of Fibonacci sequence
Mathemaniac
5 ways to derive the general term of Fibonacci sequence
10:18
STAIRS reveal the relationship between Fibonacci and combinatorics
Mathemaniac
STAIRS reveal the relationship between Fibonacci and combinatorics
0:56
What do Fibonacci numbers have to do with combinatorics?
Mathemaniac
What do Fibonacci numbers have to do with combinatorics?
10:02
4 DIFFERENT ways to prove Heron's formula
Mathemaniac
4 DIFFERENT ways to prove Heron's formula
14:47
Cosine law and properties of cyclic quadrilaterals
Mathemaniac
Cosine law and properties of cyclic quadrilaterals
2:44
Generalizing methods to calculate square roots to cube roots
Mathemaniac
Generalizing methods to calculate square roots to cube roots
7:00
EXPLAINED: Calculating square roots easily (BABYLONIAN and more)
Mathemaniac
EXPLAINED: Calculating square roots easily (BABYLONIAN and more)
9:29
Calculating square roots easily IN 3 WAYS (BABYLONIAN and more)
Mathemaniac
Calculating square roots easily IN 3 WAYS (BABYLONIAN and more)
6:53