Actually, his idea isn't very novel. There's been quite a bit of research done into turning images into mathematical formulas and it actually works, but a hell of a lot of quality is lost in the examples I have seen, so it's not ideal.
Anyway, yeah, this guy's a loon.
That's the difference between lossy and lossless compression.
JPG and MPEG-2/3/4 are all lossy compression schemes. They are all some form of mathematical formula really.
JPEG 2000 uses a type of wavelet compression that transforms the image into coefficients (basically what the loon is talking about), and then compresses that using 'normal' compression algorithms to compress the transformed data.
PNG also has a wavelet transform, but I'm not sure if it is used with all it's options.
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"Replacing 3.14150265 with pi5"
That is the basis of many compression schemes, though the 'dictionary' is usually built from the data itself. It looks for common 'words' in the noise, and compresses based on that. Many compression algorithms use specific modes for certain file types to tweak its effectiveness for those types of files. If the user opts for speed over absolute size for instance, the program might decide not to compress things like mp3, avi or jpg, as the chances of gaining anything from compression is minimal.
Things like text would compress extremely well however, as you would be mainly using alphabet characters, primarily lower case and have lots of spaces and vowels thrown in. Even common words like 'the' 'is' and 'and' would help compression.
The limit or 'entropy' point would be where the dictionary, and the references to the dictionary become larger than the data itself would have been.
--- a basic compression method for images was Run Length Encoding (RLE). It worked quite well for images where lots of solid colours were used. It basically works by saying "Colour X 50 pixels" "Colour Y, 10 pixels". The web page you are looking at would be a prime candidate for this, as it contains a LOT of background colour.
Anyhow... I'm rambling on again...