[vario]

Wow, thank you for this great answer!

It makes me wonder though why previous published mathematics about computer programming has been allegedly faulty. Since I don't know enough math to objectively see whether Knuth has succeeded in his task or not...

TAOCP could have benefited a lot if someone had written a simpler on-ramping version, with examples in a powerful but newbie-friendly industrial-grade language, such as C#.

[svat]

Knuth wrote that preface in the early 1960s, when it was indeed true that much of what little there was of published mathematical study related to programming was faulty. He succeeded incredibly well: he kickstarted the entire field of "analysis of algorithms", got all the details right and organized them extremely clearly, put it on a sound footing, and now mathematicians take it seriously, and published work in the area is of high quality.

[vario]

Thank you very much, for educating me.