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## 2007/05/01

### Fundamental Theorem of Software Engineering

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At times when I try to come to grips with this question, I find myself almost convinced that algorithmic thinking is really like mathematical thinking, only it concentrates on more "difficult" things. But at other times I have just the opposite impression, that somehow algorithms hit only the "simpler" kinds of mathematics. Clearly such an approach leads only to confusion and gets me nowhere.

While pondering these things recently, I suddenly remembered the collection of expository works called Mathematics: Its Content, Methods, and Meaning, so I reread what A. D. Aleksandrov had to say in his excellent introductory essay. Interestingly enough, I found that he made prominent mention of al-Khwârizmî. Aleksandrov listed the following characteristic features of mathematics:

• Abstractness, with many levels of abstraction.
• Precision and logical rigor.
• Quantitative relations.