Learning math? Think like a cartoonist
&gt; We agree that multiplication makes things bigger, right?<p>Huh!? I have luckily never heard anyone try to explain multiplication that way before. It&#x27;s a <i>horrible</i> mental model for multiplication!<p>&gt; Imaginary numbers let us rotate numbers.<p><i>Kind of</i> ... it&#x27;s useful to visualize <i>multiplication</i> by imaginary numbers as analogous to rotation, but this makes it sound like imaginary numbers are useful <i>because</i> they let us &quot;rotate numbers&quot;, like that&#x27;s something we always wanted to do. This is neither the essence of nor the impetus behind imaginary numbers.<p>&gt; The number e is a little machine that grows as fast as it can<p>No no no! We happen to use <i>e</i> as an exponential base a lot because it&#x27;s convenient, but it&#x27;s exponentiation, not <i>e</i>, that grows quickly! f(x) = 4^x grows faster than e^x does; e^-x shrinks; e^0 stays where it is ... this is a <i>horrible</i> intuition to have!<p>&gt; The Pythagorean Theorem explains how all shapes behave (not just triangles)<p>It works on other shapes <i>because you draw triangles in those shapes</i> ...<p>These are awful, <i>awful</i> intuitions about math. We should not take advice about how to learn math from someone who so deeply struggles with basic concepts about it!<p>Edit: this article is so bad that I just have to add another example:<p>&gt; Euler’s Formula makes a circular path.<p>But you <i>just said</i> that <i>e</i> is a little machine that grows as fast as it can! How can it just spin in a circle!? His own intuitions are completely inconsistent! Besides, Euler&#x27;s Formula has no free variables ...