There is a deep truth behind this conventional wisdom: probability is the mathematical extension of logic, augmenting our reasoning toolkit with the concept of uncertainty. Making better decisions under uncertainty is the ultimate life hack.

I see practitioners rushing to learn the latest LLM framework while treating the underlying mathematics as a "black box" to be dealt with later. But frameworks become obsolete in months. While the calculus of optimization, and the logic of linear transformations are forever.

Mathematics is taught wrong. Its power is buried under convoluted formulas and technical jargon. But also mathematics changed everything for me: how I reason, how I build systems, and how I approach complex problems. I write to give you the same clarity.

Most math education hides the useful parts behind notation and formalism. Over 20 years, math has transformed how I think, solve problems, and see patterns everywhere. My goal is simple: make that transformation accessible to you.

My goal was never to keep up with the AI news. Instead, I'm building a library of evergreen ideas. Writing the posts you’ll still find useful 5 years from now regardless of which LLM is topping the benchmarks. At the end of the day, fundamentals are the only thing that scale.

Mathematics is taught backwards. We learn formulas before understanding why they matter. But math has shaped how I solve problems, think more clearly, and build things that (actually) work. I'm building The Palindrome to show you the same path.

Mathematics is taught wrong. Its usefulness is hidden behind convoluted formulas, technical nuances, and abstract nonsense. Throughout the years, math enhanced my professional and personal life in ways I can’t even begin to describe. My mission is to take you to the same place.

The hype is good and everything but you only need 3 things from this list: 1. Linear Algebra 2. Calculus 3. Probability Theory That's it. If you want a more comprehensive list per topic, here you go:

The hype is good and everything but you only need 3 things from this list: 1. Linear Algebra 2. Calculus 3. Probability Theory That's it. If you want a more comprehensive list per topic, here you go:

Why "adding zero" is the most elegant trick in mathematics: In the "Camel Principle"—an old mathematical fable—a problem that seems impossible is solved by: • Temporarily adding something • Rearranging the system • And then taking it away We do this in ML and math constantly.

"Probability is the logic of science." There is a deep truth behind this conventional wisdom: probability is the mathematical extension of logic, augmenting our reasoning toolkit with the concept of uncertainty.

The most life-altering realization I've ever had is buried under a heap of probability theory. Every mathematician knows the idea but they call it trivial. It's hidden in plain sight, obscured by simplicity. Here it is: If you want to hit your target, take more shots.

There's beauty in seeing how the golden ratio hides in Fibonacci or how gradient descent mimics the physics of a ball rolling. Mathematics isn't just a tool for building models but the language of the world. If we treat it as a chore we miss the best part of being an engineer.

When the Super Bowl ad department actually does their homework:

Why "adding zero" is the most elegant trick in mathematics: In the "Camel Principle"—an old mathematical fable—a problem that seems impossible is solved by: • Temporarily adding something • Rearranging the system • And then taking it away We do this in ML and math constantly.

The most powerful tool in your mathematical toolkit isn't a formula, it's a change in perspective: Take Linear Algebra, for example. We’re taught to see matrices as "grids of numbers." But to a machine learning engineer, a matrix is often secretly a graph.

Mathematics is taught wrong. Its usefulness is hidden behind convoluted formulas, technical nuances, and abstract nonsense. Throughout the years, math enhanced my professional and personal life in ways I can’t even begin to describe. My mission is to take you to the same place.

You don’t need to read every SOTA paper to be a top-tier ML engineer. You need to master the math that hasn’t changed in 50 years.

Most people fail to understand the differences between probabilities, statistics and machine learning. The interactions between these fields are so rich that they are easy to conflate with each other. However, there are vast differences:

Machine learning practitioners don't even need half of this. This is the math you actually need (thread):

The Fibonacci numbers form one of the most famous integer sequences. They relate to the golden ratio, sunflower spirals, mating habits of rabbits, and several other things. Because of its recursive nature, computing the Fibonacci via brute force is computationally expensive.

In 2021, I had failed a startup, burned all my savings and wasted two years of my life. Then everything changed:

I’ve spent 10 years teaching math to machine learning engineers. 80% of university math is irrelevant to your actual job. Here's the 20% you actually need to build models (and how to learn it fast): thepalindrome.org/p/the-roadm...

The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices. Encoding matrices as graphs is a cheat code, making complex behavior simple to study. Let me show you how!

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:

I’ve spent 10 years teaching math to machine learning engineers. 80% of university math is irrelevant to your actual job. Luckily, I've created a FREE roadmap to teach you the 20% you actually need. Like, retweet, and comment "roadmap" and I'll DM you the link.

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!

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!

I’m convinced mathematics is taught wrong. Its beauty is buried under technical jargon and lifeless formulas when it should 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...

If I had to learn the mathematics of machine learning from scratch, I'd follow this roadmap:

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’ve spent 10 years teaching math to machine learning engineers. 80% of university math is irrelevant to your actual job. Here's the 20% you actually need to build models (and how to learn it fast):

Where does our fear of failure come from? For me, it’s probably from my earliest years in elementary school.

The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices. Encoding matrices as graphs is a cheat code, making complex behavior simple to study. Let me show you how!

At some point everyone will tell you that you can do this alone. You got this. You can figure this out. You're smart. It turns out I rather surround myself with people whose skillset is as disjoint from mine as possible. You need to kill your ego if you want to grow.

Visual representation of the behavior of the DFS algorithm. It tries to explore new unvisited vertices until it is stuck. Then, it backtracks to the closest vertex with an adjacent non-visited vertex left and continues exploring.

A stage of the generic algorithm for finding the connected component of S. Red vertices represent the current state of set D. Discontinued lines have one endpoint in the set D and the other outside of it. Nodes S and T belong to different connected components.

If there's something I'm proud of in 2025 is the reception of my book, Mathematics of Machine Learning. With a whooping 5000+ sales across all formats, I'm humbled. Thanks to everyone of you for your interest in the fundamentals of math & machine learning.

If you are indulging yourself this Christmas, I got good news for you! The digital version of my new book, Mathematics of Machine Learning is now $9.99 for a limited time. Get your hands on it if you're upping your machine learning game in 2026: www.packtpub.com/en-us/produ...

The 10 most popular posts of The Palindrome in 2025 (chosen by you): 1. The Roadmap of Mathematics for Machine Learning: thepalindrome.org/p/the-roadm...

I had to come up with a way of visualizing the chain rule because I could never remember the formula. Here I show you all about it: thepalindrome.org/p/visualizi...

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:

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...

The singlemost useful realization to achieve all your goals: If you want to hit your target, take more shots. Here's the science-backed article: thepalindrome.org/p/if-you-wa...

The single most life-altering realization I've ever had is buried under a heap of probability theory. Every mathematician is familiar with the idea. They call it “trivial”, move on to study virtuoso mathematical feats, and spend no time pondering the consequences of such short computation.

The Palindrome now has 100+ deep dives on math & ML. So I organized them into a single “library” page where you can: 1. Pick a learning track 2. Find the right article in seconds 3. Start learning right away Bookmark it. Future-you will thank you: thepalindrome.org/p/the-palin...

If I had to learn Math for Machine Learning from scratch, this is the roadmap I would follow:

The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices. Encoding matrices as graphs is a cheat code, making complex behavior simple to study. Let me show you how!

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:

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!