The Palindrome

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One of my favorite formulas is the closed-form of the geometric series.I am amazed by its ubiquity: whether we are solving basic problems or pushing the boundaries of science, the geometric series often makes a surprising appearance.Here is how to derive it from first principles.
You are (probably) wrong about randomness. I’ll show it to you. Let’s do an experiment. Pick up a pen, paper, or your favorite text editor, and manually generate a random sequence of ten characters, composed of ones and zeros. My guess is, your answer will be:
The geometric and algebraic interpretation of matrix products
How randomness is averaged out in the long run

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The way you think about the exponential function is (probably) wrong. Don't think so? I'll convince you. Did you realize that multiplying e by itself π…
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(via the magic of power series and generating functions)
The expected value is one of the most important concepts in probability and statistics. For instance, all the popular loss functions in machine…
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Raise your hands if you have seen something like this before.
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices
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Hi there! First of all, thank you for your support! This newsletter has been my main project for the last two months, and I am really glad that I…
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The greatest known computational accuracy in the ancient world
From right triangles to Taylor series
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The Palindrome

Stories about how mathematics impacts science, technology, and society. Told weekly by Tivadar Danka.
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The Palindrome

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