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.
Grab the 20-year distillation here: thepalindrome.org/p/the-roadm...
You don't need a PhD. You need these 3 pillars applied correctly.
I’ve condensed two decades of study into a "zero-fluff" roadmap designed specifically for engineers who want to build stuff.
3. Probability Theory:
• Distributions
• Expected values
• Random variables
To know how to model uncertainty, learn from data, and make predictions.
• Multivariable functions
• Derivatives and gradients
• Optimization in multiple variables
To understand the math behind algorithms like gradient descent and get a better feeling of what optimization is.
2. Calculus:
• Series
• Functions
• Sequences
• Integration
• Optimization
• Differentiation
• Limits and continuity
1. Linear Algebra:
• Vectors
• Matrices
• Equations
• Factorizations
• Matrices and graphs
• Linear transformations
• Eigenvalues and eigenvectors
To learn how to represent and transform data.
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:
Grab the 20-year distillation here: thepalindrome.org/p/the-roadm...
You don't need a PhD. You need these 3 pillars applied correctly.
I’ve condensed two decades of study into a "zero-fluff" roadmap designed specifically for engineers who want to build stuff.
3. Probability Theory:
• Distributions
• Expected values
• Random variables
To know how to model uncertainty, learn from data, and make predictions.
• Multivariable functions
• Derivatives and gradients
• Optimization in multiple variables
To understand the math behind algorithms like gradient descent and get a better feeling of what optimization is.
2. Calculus:
• Series
• Functions
• Sequences
• Integration
• Optimization
• Differentiation
• Limits and continuity
1. Linear Algebra:
• Vectors
• Matrices
• Equations
• Factorizations
• Matrices and graphs
• Linear transformations
• Eigenvalues and eigenvectors
To learn how to represent and transform data.
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:
Sometimes, you have to make the problem "more complex" to make the solution obvious.
I love exploring these "hidden patterns" in the foundations of AI.
If you want to dive deep into the craft of math, subscribe to The Palindrome: thepalindrome.org/
We add and subtract the same term to complete a square, or we map data into a higher dimension only to project it back down.
It’s a reminder that the shortest path between two points in logic isn't always a straight line.
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.
Most parodies use gibberish for "genius" scenes.
But the new "Good Will Dunkin’" commercial features the actual non-recursive formula for finding the n-th Fibonacci number.
Here is the beautiful math behind the clip:
youtu.be/UM5EH-ApHY4
When the Super Bowl ad department actually does their homework:
Sometimes, you have to make the problem "more complex" to make the solution obvious.
I love exploring these "hidden patterns" in the foundations of AI.
If you want to dive deep into the craft of math, subscribe to The Palindrome: thepalindrome.org/
