This article is a few days old but I want to make sure I don't miss it, as it makes a point that (to my mind) challenges the idea that there is one set of basic 'foundational' principles in mathematics. Mark Guzdial introduces us to the work of Kenneth E. Iverson on a computing language called J (more here). "The attempt to 'fix' mathematical notation ("suggestions for improvement," to be exact) is bold and interesting," writes Guzdial, as is attempt to prove the utility of the notation by using it to teach mathematics. His introductory textbook introduces counting as succession, talks about inverses and domains, and then into nouns and verbs. His proposal for Mathematical Notation (MN) is an equally non-standard approach to the subject. So when people say that mathematics, as taught, is foundational, you have license to raise an eyebrow and say, "Is it? Really?"
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