Originally on GitHub Pages, we were using favicon from https://khan.github.io/favicon.ico (), ~which seems to be an old logo of Khan Academy~.
It'd be nice to have a logo of our own, or at least the new Khan Academy logo.
Here's a quick attempt at turning the first two letters of \KaTeX (our current logo) into a square icon:
16x16 favicon:

SVG (doesn't look good in Chrome, but is fine in Illustrator)
High-resolution PNG:

ZIP of generated icons from https://www.favicon-generator.org/ which recommends this code:
<link rel="apple-touch-icon" sizes="57x57" href="/apple-icon-57x57.png">
<link rel="apple-touch-icon" sizes="60x60" href="/apple-icon-60x60.png">
<link rel="apple-touch-icon" sizes="72x72" href="/apple-icon-72x72.png">
<link rel="apple-touch-icon" sizes="76x76" href="/apple-icon-76x76.png">
<link rel="apple-touch-icon" sizes="114x114" href="/apple-icon-114x114.png">
<link rel="apple-touch-icon" sizes="120x120" href="/apple-icon-120x120.png">
<link rel="apple-touch-icon" sizes="144x144" href="/apple-icon-144x144.png">
<link rel="apple-touch-icon" sizes="152x152" href="/apple-icon-152x152.png">
<link rel="apple-touch-icon" sizes="180x180" href="/apple-icon-180x180.png">
<link rel="icon" type="image/png" sizes="192x192" href="/android-icon-192x192.png">
<link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png">
<link rel="icon" type="image/png" sizes="96x96" href="/favicon-96x96.png">
<link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png">
<link rel="manifest" href="/manifest.json">
<meta name="msapplication-TileColor" content="#ffffff">
<meta name="msapplication-TileImage" content="/ms-icon-144x144.png">
<meta name="theme-color" content="#ffffff">
@edemaine it's hard to shrink \KaTeX to fit into a square. Nice work!
Here's another possibility...

Most helpful comment
Here's a quick attempt at turning the first two letters of
\KaTeX(our current logo) into a square icon:16x16 favicon:

SVG (doesn't look good in Chrome, but is fine in Illustrator)
High-resolution PNG:

ZIP of generated icons from https://www.favicon-generator.org/ which recommends this code: