I see a great deal of beauty in mathematics. There is much beauty in a well-described, step-by-step proof of a theorem.

Lately I have been learning algorithms for parsing and compilers from a pair of marvelous books. [1] I think the author is one of the best technical writers in the world, which makes learning very enjoyable. As I learn the parsing and compiler algorithms described in the books, the same sense of beauty rises up inside me as with a good math theorem proof.

So both Mathematical theorems and Computer Science algorithms have tremendous beauty. Nonetheless, I think that Computer Science algorithms are way better than Mathematical theorems. Here’s why:

In Mathematics there is a tightly constrained framework in which one operates. There is a limited set of building blocks (axioms) and rules that one uses to perform work. Conversely, in Computer Science algorithms there is no such finite, well-defined set of building blocks and rules. Although there are commonly used techniques – recursion, closure, induction, etc. – there are an infinite number of concepts that may be used to create an algorithm. That infinite variety provides enormous power and complexity, and requires great creativity and ingenuity, and is why I think Computer Science algorithms are way better than Mathematical theorems.

[1] “Parsing Techniques” by Dick Grune et al, “Modern Compiler Design” by Dick Grune et al.

### Like this:

Like Loading...

*Related*

Tags: algorithms, axioms, beauty, closure, Compilers, Computer Science, Dick Grune, induction, mathematics, Modern Compiler Design, Parsing, Parsing Techniques, recursion, theorems

This entry was posted on January 24, 2015 at 8:22 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
You can leave a response, or trackback from your own site.

September 1, 2015 at 7:54 am |

Dijkstra on the relevance of the algorithmic approach to mathematics:

“The one reason is that the calculational proofs are almost always more effective than all informal alternatives, the other reason is that the design of calculational proofs seems much more teachable than the elusive art of discovering an informal proof.”

How Computing Science created a new mathematical style, https://www.cs.utexas.edu/users/EWD/transcriptions/EWD10xx/EWD1073.html