Daniel Lemire's blog

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The best software developers are great at Mathematics?

One of the upsides of working for a university are the stimulating academic discussions. Yesterday, a philosopher challenged me a question:

Beyond the fact that software is expressed in Mathematics artefacts (bits, algorithms), are Information Systems fundamentally Mathematical?

For my convenience, I temporarily rephrase the question to something simpler and more concrete:

How are Software Developers limited by their mathematical weaknesses?

I plan several blog posts around this question, but let me start with an example.

A common and powerful language to process XML is XPath. XPath is used within web applications, scripts, databases, and so on. I often ask students the following question about XPath. Are these two expressions equivalent?

$x="some string"


not($x!="some string").

(The symbol “!=” means “different from”.)

Invariably, most students conclude that they are equivalent. Wrong!

Let us examine the semantics.

  • The expression $x="some string" means that at least one element of $x is equal to "some string".
  • The expression $x!="some string" means that some element of $x is different from "some string".
  • The negation of $x!="some string" is that all elements of $x are equal to "some string". (Sorry if it sounds confusing.)

Thus, the expression not($x!="some string") is a more restrictive condition than the expression $x="some string".

Great software developers routinely think through far more complex mathematical problems. Yet, they do not think of them as being Mathematics.