I worked at Wolfram about twenty years ago, where I met a guy named Dan who was (at the time) quietly hacking on a side project to put Mathematica on the web. Eventually this project became "The Integrator" (and surprisingly, seems to live on as integrals.com).
At first, The Integrator only returned results in mma syntax. If you entered the expression `Cos[x]`, it would return - literally - `Sin[x]`. This was neat and all, but once you had a result with exponentiation or division or what not, you'd want a prettier result. For example, if you asked for the integral of `Sin[x^2]`, it would spit out `Sqrt[Pi/2]FresnelS[Sqrt[2/Pi]x]`, which, you know, ew.
Twenty years ago, of course, there was no MathML - there wasn't even a working group. So in order to provide a prettier result, he returned a GIF with the Math-rendered output. Because this was back when we were still using client-side imagemaps and some browsers still didn't support inline jpegs. So this quick hack was totally reasonable.
Since The Integrator's compute backend was actually on his desk, he put a caching layer in front of the Mathematica instance. It was a trivial one, so if you asked for the integral of Sin[x], it would just look for Sin[x].gif in the cache directory and if that existed, it wouldn't send the query of to the Mathematica backend.
Unsurprisingly, this led to us kids just stuffing a bunch of crazy GIFs into the cache directory. Dan started it - if you tried to integrate his initials, it would return a picture of him. After that, though, we piled on and eventually you could integrate all our names, as well as a bunch of internal jokes.
I worked on The Integrator after Dan left, and of course I kept the easter eggs, but at some point it was handed off to another team who tried to create some more general web front-end to Mathematica. This team sadly lacked both Dan's cleverness and his sense of humor, so not only was the software slow and clunky, but it also lacked the easter eggs.
I'm always surprised that Wolfram Alpha - twenty years later - still renders its results and returns a GIF. You'd think that we could do a little bit better by now. I just hope that somewhere, one of the people working way too many hours to keep that site online has slid some easter eggs in.
