To do this, you only need 2 numbers: the nth digit of pi and the number of digits. Simply convert your message into a single extremely long integer. Somewhere, in the digits of pi, you will find a matching series of digits the same as your integer! Decompressing the number is relatively easy after some sort-of recent advances in our understanding of pi. Finding out what those 2 numbers are--- well, we still have a ways to go on that. Despite the ridiculousness of this example, it does illustrate to the author that there are extremes of compression. The "single mathematical formula" compression method is possible, even trivial. However, the computation time for compression may be unreasonably large. Here is another ridiculous way to compress data: Convert your data into a series of coordinates to a mandelbrot fractal set. The final picture is a fixed size, regardless of the size of your starting data set. From that final picture, you should be able to retrieve your original starting data set. Good luck!