Tivadar Danka
@tivadardanka.bsky.social
I make math accessible for everyone. Mathematician with an INTJ personality. Chaotic good. Writing https://thepalindrome.org
I’m convinced mathematics is taught wrong.
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
Your Machine Learning Library
Your starting point for all your machine learning needs
thepalindrome.org
November 11, 2025 at 7:00 PM
I’m convinced mathematics is taught wrong.
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
Matrix multiplication is not easy to understand.
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
November 11, 2025 at 1:00 PM
Matrix multiplication is not easy to understand.
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
I wrote a 4000-words long article about all the math you need to know for machine learning.
Trust me, you want to bookmark this:
thepalindrome.org/p/the-roadm...
Trust me, you want to bookmark this:
thepalindrome.org/p/the-roadm...
The Roadmap of Mathematics for Machine Learning
A complete guide to linear algebra, calculus, and probability theory
thepalindrome.org
November 10, 2025 at 7:00 PM
I wrote a 4000-words long article about all the math you need to know for machine learning.
Trust me, you want to bookmark this:
thepalindrome.org/p/the-roadm...
Trust me, you want to bookmark this:
thepalindrome.org/p/the-roadm...
One of the coolest ideas in mathematics is the estimation of a shape's area by throwing random points at it.
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
November 10, 2025 at 1:00 PM
One of the coolest ideas in mathematics is the estimation of a shape's area by throwing random points at it.
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
They said “fundamentals don’t grow newsletters.”
We doubled down anyway:
• 35,000+ readers
• 541 premium members
• $44,606 Annual Recurring Revenue
Sometimes the unsexy path is the one with the strongest compounding.
We doubled down anyway:
• 35,000+ readers
• 541 premium members
• $44,606 Annual Recurring Revenue
Sometimes the unsexy path is the one with the strongest compounding.
November 7, 2025 at 1:26 PM
They said “fundamentals don’t grow newsletters.”
We doubled down anyway:
• 35,000+ readers
• 541 premium members
• $44,606 Annual Recurring Revenue
Sometimes the unsexy path is the one with the strongest compounding.
We doubled down anyway:
• 35,000+ readers
• 541 premium members
• $44,606 Annual Recurring Revenue
Sometimes the unsexy path is the one with the strongest compounding.
I used to hate coding on paper as a student.
It’s linear, uninteractive, and tedious. Coding on paper felt like a punishment.
Was there a point?
I used to believe there wasn’t; now I know there is:
thepalindrome.org/p/coding-on...
It’s linear, uninteractive, and tedious. Coding on paper felt like a punishment.
Was there a point?
I used to believe there wasn’t; now I know there is:
thepalindrome.org/p/coding-on...
Coding on Paper
Coding as a process, not a product
thepalindrome.org
November 5, 2025 at 1:56 PM
I used to hate coding on paper as a student.
It’s linear, uninteractive, and tedious. Coding on paper felt like a punishment.
Was there a point?
I used to believe there wasn’t; now I know there is:
thepalindrome.org/p/coding-on...
It’s linear, uninteractive, and tedious. Coding on paper felt like a punishment.
Was there a point?
I used to believe there wasn’t; now I know there is:
thepalindrome.org/p/coding-on...
If you want to become unstoppable in machine learning, master this minimal set of math first:
Linear Algebra → vectors, matrices, and their operations
Calculus → limits, differentiation, integration
Probability → uncertainty, Bayes, distributions
Optimization → gradient descent and friends
Linear Algebra → vectors, matrices, and their operations
Calculus → limits, differentiation, integration
Probability → uncertainty, Bayes, distributions
Optimization → gradient descent and friends
November 4, 2025 at 1:33 PM
If you want to become unstoppable in machine learning, master this minimal set of math first:
Linear Algebra → vectors, matrices, and their operations
Calculus → limits, differentiation, integration
Probability → uncertainty, Bayes, distributions
Optimization → gradient descent and friends
Linear Algebra → vectors, matrices, and their operations
Calculus → limits, differentiation, integration
Probability → uncertainty, Bayes, distributions
Optimization → gradient descent and friends
Everyone is chasing AI headlines.
I’m teaching the fundamentals that make those headlines possible.
I wrote a full explainer on the math that’s beneath all of ML.
Trust me, you’ll want to bookmark this:
thepalindrome.org/p/the-roadm...
I’m teaching the fundamentals that make those headlines possible.
I wrote a full explainer on the math that’s beneath all of ML.
Trust me, you’ll want to bookmark this:
thepalindrome.org/p/the-roadm...
The Roadmap of Mathematics for Machine Learning
A complete guide to linear algebra, calculus, and probability theory
thepalindrome.org
November 3, 2025 at 1:32 PM
Everyone is chasing AI headlines.
I’m teaching the fundamentals that make those headlines possible.
I wrote a full explainer on the math that’s beneath all of ML.
Trust me, you’ll want to bookmark this:
thepalindrome.org/p/the-roadm...
I’m teaching the fundamentals that make those headlines possible.
I wrote a full explainer on the math that’s beneath all of ML.
Trust me, you’ll want to bookmark this:
thepalindrome.org/p/the-roadm...
I’m convinced mathematics is taught wrong.
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
Your Machine Learning Library
Your starting point for all your machine learning needs
thepalindrome.org
November 2, 2025 at 1:32 PM
I’m convinced mathematics is taught wrong.
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
Its beauty is buried under technical jargon and lifeless formulas. It should be be: clear, visual, practical.
My mission is to get you fluent in the math that will still be useful in 50 years.
thepalindrome.org/p/the-palin...
I wrote a 1500-word article to teach you the anatomy of the Least Squares method.
Trust me, you want to bookmark this:
thepalindrome.org/p/the-anato...
Trust me, you want to bookmark this:
thepalindrome.org/p/the-anato...
The Anatomy of the Least Squares Method
Part One: Theory and Math
thepalindrome.org
November 1, 2025 at 1:26 PM
I wrote a 1500-word article to teach you the anatomy of the Least Squares method.
Trust me, you want to bookmark this:
thepalindrome.org/p/the-anato...
Trust me, you want to bookmark this:
thepalindrome.org/p/the-anato...
You kept asking for it so I finally put all my articles in a single place.
Here's your machine learning library.
Trust me, you want to bookmark this.
It's only going to grow from here on: thepalindrome.org/p/the-palin...
Here's your machine learning library.
Trust me, you want to bookmark this.
It's only going to grow from here on: thepalindrome.org/p/the-palin...
Your Machine Learning Library
Your starting point for all your machine learning needs
thepalindrome.org
October 31, 2025 at 1:31 PM
You kept asking for it so I finally put all my articles in a single place.
Here's your machine learning library.
Trust me, you want to bookmark this.
It's only going to grow from here on: thepalindrome.org/p/the-palin...
Here's your machine learning library.
Trust me, you want to bookmark this.
It's only going to grow from here on: thepalindrome.org/p/the-palin...
I wrote a 1000-word long article to teach you the difference between probabilities, statistics, and machine learning.
Trust me, you want to bookmark this: thepalindrome.org/p/machine-l...
Trust me, you want to bookmark this: thepalindrome.org/p/machine-l...
Machine Learning Is Not Just Statistics
The differences, the similarities, and the nuances
thepalindrome.org
October 30, 2025 at 1:34 PM
I wrote a 1000-word long article to teach you the difference between probabilities, statistics, and machine learning.
Trust me, you want to bookmark this: thepalindrome.org/p/machine-l...
Trust me, you want to bookmark this: thepalindrome.org/p/machine-l...
In machine learning, we use the dot product every day.
However, its definition is far from revealing. For instance, what does it have to do with similarity?
There is a beautiful geometric explanation behind:
However, its definition is far from revealing. For instance, what does it have to do with similarity?
There is a beautiful geometric explanation behind:
October 28, 2025 at 1:30 PM
In machine learning, we use the dot product every day.
However, its definition is far from revealing. For instance, what does it have to do with similarity?
There is a beautiful geometric explanation behind:
However, its definition is far from revealing. For instance, what does it have to do with similarity?
There is a beautiful geometric explanation behind:
This will surprise you: sine and cosine are orthogonal to each other.
What does orthogonality even mean for functions? In this thread, we'll use the superpower of abstraction to go far beyond our intuition.
We'll also revolutionize science on the way.
What does orthogonality even mean for functions? In this thread, we'll use the superpower of abstraction to go far beyond our intuition.
We'll also revolutionize science on the way.
October 27, 2025 at 1:30 PM
This will surprise you: sine and cosine are orthogonal to each other.
What does orthogonality even mean for functions? In this thread, we'll use the superpower of abstraction to go far beyond our intuition.
We'll also revolutionize science on the way.
What does orthogonality even mean for functions? In this thread, we'll use the superpower of abstraction to go far beyond our intuition.
We'll also revolutionize science on the way.
Behold one of the mightiest tools in mathematics: the camel principle.
I am dead serious. Deep down, this tiny rule is the cog in many methods. Ones that you use every day.
Here is what it is, how it works, and why it is essential:
I am dead serious. Deep down, this tiny rule is the cog in many methods. Ones that you use every day.
Here is what it is, how it works, and why it is essential:
October 26, 2025 at 1:30 PM
Behold one of the mightiest tools in mathematics: the camel principle.
I am dead serious. Deep down, this tiny rule is the cog in many methods. Ones that you use every day.
Here is what it is, how it works, and why it is essential:
I am dead serious. Deep down, this tiny rule is the cog in many methods. Ones that you use every day.
Here is what it is, how it works, and why it is essential:
The following multiplication method makes everybody wish they had been taught math like this in school.
It's not just a cute visual tool: it illuminates how and why long multiplication works.
Here is the full story:
It's not just a cute visual tool: it illuminates how and why long multiplication works.
Here is the full story:
October 25, 2025 at 12:30 PM
The following multiplication method makes everybody wish they had been taught math like this in school.
It's not just a cute visual tool: it illuminates how and why long multiplication works.
Here is the full story:
It's not just a cute visual tool: it illuminates how and why long multiplication works.
Here is the full story:
Matrix multiplication is not easy to understand.
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
October 24, 2025 at 12:30 PM
Matrix multiplication is not easy to understand.
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
Even looking at the definition used to make me sweat, let alone trying to comprehend the pattern. Yet, there is a stunningly simple explanation behind it.
Let's pull back the curtain!
Graph theory will seriously enhance your engineering skills.
Here's why you must be familiar with graphs:
Here's why you must be familiar with graphs:
October 23, 2025 at 12:30 PM
Graph theory will seriously enhance your engineering skills.
Here's why you must be familiar with graphs:
Here's why you must be familiar with graphs:
One of the coolest ideas in mathematics is the estimation of a shape's area by throwing random points at it.
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
October 22, 2025 at 12:30 PM
One of the coolest ideas in mathematics is the estimation of a shape's area by throwing random points at it.
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
Don't believe this works? Check out the animation below, where I show the method on the unit circle. (Whose area equals to π.)
Here is what's behind the magic:
The way you think about the exponential function is wrong.
Don't think so? I'll convince you. Did you realize that multiplying e by itself π times doesn't make sense?
Here is what's really behind the most important function of all time:
Don't think so? I'll convince you. Did you realize that multiplying e by itself π times doesn't make sense?
Here is what's really behind the most important function of all time:
October 21, 2025 at 12:30 PM
The way you think about the exponential function is wrong.
Don't think so? I'll convince you. Did you realize that multiplying e by itself π times doesn't make sense?
Here is what's really behind the most important function of all time:
Don't think so? I'll convince you. Did you realize that multiplying e by itself π times doesn't make sense?
Here is what's really behind the most important function of all time:
In calculus, going from a single variable to millions of variables is hard.
Understanding the three main types of functions helps make sense of multivariable calculus.
Surprisingly, they share a deep connection. Let's see why:
Understanding the three main types of functions helps make sense of multivariable calculus.
Surprisingly, they share a deep connection. Let's see why:
October 20, 2025 at 12:30 PM
In calculus, going from a single variable to millions of variables is hard.
Understanding the three main types of functions helps make sense of multivariable calculus.
Surprisingly, they share a deep connection. Let's see why:
Understanding the three main types of functions helps make sense of multivariable calculus.
Surprisingly, they share a deep connection. Let's see why:
The Law of Large Numbers is one of the most frequently misunderstood concepts of probability and statistics.
Just because you lost ten blackjack games in a row, it doesn’t mean that you’ll be more likely to be lucky next time.
What is the law of large numbers, then? Read on:
Just because you lost ten blackjack games in a row, it doesn’t mean that you’ll be more likely to be lucky next time.
What is the law of large numbers, then? Read on:
October 19, 2025 at 12:30 PM
The Law of Large Numbers is one of the most frequently misunderstood concepts of probability and statistics.
Just because you lost ten blackjack games in a row, it doesn’t mean that you’ll be more likely to be lucky next time.
What is the law of large numbers, then? Read on:
Just because you lost ten blackjack games in a row, it doesn’t mean that you’ll be more likely to be lucky next time.
What is the law of large numbers, then? Read on:
The single most undervalued fact of mathematics: mathematical expressions are graphs, and graphs are matrices.
Yes, I know. You already heard this from me, but hear me out.
Viewing neural networks as graphs is the idea that led to their success.
Yes, I know. You already heard this from me, but hear me out.
Viewing neural networks as graphs is the idea that led to their success.
October 18, 2025 at 12:30 PM
The single most undervalued fact of mathematics: mathematical expressions are graphs, and graphs are matrices.
Yes, I know. You already heard this from me, but hear me out.
Viewing neural networks as graphs is the idea that led to their success.
Yes, I know. You already heard this from me, but hear me out.
Viewing neural networks as graphs is the idea that led to their success.
What is common between the Fourier series and the Cartesian coordinate system?
More than you think: they are (almost) the same.
I'll explain why:
More than you think: they are (almost) the same.
I'll explain why:
October 17, 2025 at 11:02 AM
What is common between the Fourier series and the Cartesian coordinate system?
More than you think: they are (almost) the same.
I'll explain why:
More than you think: they are (almost) the same.
I'll explain why:
Problem-solving is at least 50% of every job in tech and science.
Mastering problem-solving will make your technical skill level shoot up like a hockey stick. Yet, we are rarely taught how to do so.
Here are my favorite techniques that'll loosen even the most complex knots:
Mastering problem-solving will make your technical skill level shoot up like a hockey stick. Yet, we are rarely taught how to do so.
Here are my favorite techniques that'll loosen even the most complex knots:
October 16, 2025 at 6:00 PM
Problem-solving is at least 50% of every job in tech and science.
Mastering problem-solving will make your technical skill level shoot up like a hockey stick. Yet, we are rarely taught how to do so.
Here are my favorite techniques that'll loosen even the most complex knots:
Mastering problem-solving will make your technical skill level shoot up like a hockey stick. Yet, we are rarely taught how to do so.
Here are my favorite techniques that'll loosen even the most complex knots: