Curated watch path · 10 videos
Mathematical Intuition Through Visual Math
See vectors, change, curves, frequency, probability and information before formal notation takes over, with each video preparing an idea used by the next.
Who this is for
Programmers, designers and self-directed learners who want visual mathematical intuition for graphics, signal processing, machine learning or technical problem solving.
Before you start
No proof background is required. Pause to sketch the diagrams and treat linked series entries as starting points rather than complete formal courses.
How this mathematical intuition route was selected
The route establishes vectors and calculus, applies them to complex numbers and smooth curves, follows a three-step Fourier sequence, and closes with probability and information.
The independent site operator reviewed the October 31, 2026 source records for direct topic fit, learning order, evergreen status and positive Hacker News recommendation history. Titles, summaries, levels and labels come from the public dataset and may contain model-generated errors. This is an editorial ordering of source records, not a claim that every video was watched end to end. Read the source methodology and limits, or report a mismatch or broken video.
What the route connects
The sequence is designed to connect vectors, rates of change, frequency, probability and information to pictures and practical problems instead of leaving them as isolated formulas.
How to study it
- Pause during the animations and redraw the objects and directions yourself; continue to the notation only after you can explain what the picture is doing.
- Keep the three Fourier videos in order. Probability and error correction can become a separate study session rather than one long sitting.
A visual mathematical intuition path
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↗course · intro
Vectors | Chapter 1, Essence of linear algebra
Begin with vectors and a geometric language for linear algebra.
17 positive HN recommenders across 18 recommendation months
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↗course · intro
The essence of calculus
See derivatives and integrals as ideas about change and accumulated area before formal technique.
10 positive HN recommenders across 9 recommendation months
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↗course · intro
Imaginary Numbers Are Real [Part 1: Introduction]
Treat imaginary numbers as a natural extension of the number line and prepare for frequency-domain ideas.
7 positive HN recommenders across 7 recommendation months
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↗explainer · intro
The Beauty of Bézier Curves
Apply vectors and interpolation to the curves used in type, animation and graphics.
16 positive HN recommenders across 13 recommendation months
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↗explainer · intermediate
The Continuity of Splines
Continue from Bézier curves into derivatives, continuity and smooth spline design.
10 positive HN recommenders across 11 recommendation months
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↗explainer · intro
But what is a Fourier series? From heat flow to drawing with circles | DE4
Use heat flow and rotating circles to see how functions can be decomposed into waves.
4 positive HN recommenders across 4 recommendation months
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↗explainer · intro
But what is the Fourier Transform? A visual introduction.
Extend Fourier series into a visual model of general signals and frequency components.
16 positive HN recommenders across 15 recommendation months
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↗explainer · intermediate
The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?
Connect Fourier intuition to convolution, polynomial multiplication and a practical fast algorithm.
7 positive HN recommenders across 8 recommendation months
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↗explainer · intro
The medical test paradox, and redesigning Bayes' rule
Build probability intuition through base rates, medical tests and Bayesian updating.
4 positive HN recommenders across 4 recommendation months
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↗explainer · intro
But what are Hamming codes? The origin of error correction
Finish with an intuitive construction of parity, information and error-correcting codes.
4 positive HN recommenders across 4 recommendation months
A checkpoint for your study notes
Try it: sketch a vector transformation
Build on the vectors video with 3Blue1Brown’s linear-transformation lesson. You need addition and scaling of two-dimensional coordinates.
- Let T(x, y) = (x + 2y, y). Draw the images of (1, 0) and (0, 1), then use them to predict the image of (2, −1). Is S(x, y) = (x + 1, y) also linear? Start by checking where it sends the origin.
- Write out your reasoning before opening the answer below.
Show the answer and checks
The basis vectors become (1, 0) and (2, 1), so T(2, −1) = 2(1, 0) − (2, 1) = (0, −1). T preserves addition and scaling. S moves the origin to (1, 0), so it is not linear. Sketch both before moving on to matrix notation.
Open the vectors video · Read 3Blue1Brown’s linear-transformation lesson ↗
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