[halperter]

The following paragraph: >In a typical American or British arithmetic textbook of the same period — or, frankly, today — the topic “primes” would consist of the definition of a prime, a list of the first few, and perhaps a procedure for testing primality. The infinity of the primes would be asserted, if at all. The proof would not appear, and the argument that no list of primes can be completewould not be made.

I think they meant to imply that "other", maybe western, mathematical education emphasizes learning "facts" over a more demonstrable experience. The author compares how textbooks would frame the multiplication of positives and negatives in the same sense later in the article.

>The point is not that “minus times minus is plus” because some external authority says so. It is that, if we want our rules to give consistent answers when applied to physical quantities that point in two opposite directions, this is what the rules must look like.