Lack of brackets in spoken language

There are problems similar to those related to order of operations misunderstandings causes by the lack of brackets in language.

For example, if trying to describe \(3^{2x}\), you might say "three to the power of two times x". This could, however, also be interpreted as \(3^{2}x\). One common way to reduce the ambiguity is to pause and speed up, ie say "three to the power of [pause] two-times-x".

Another example are sentences "17 is a factor of 6 more than 15" and "7 is a factor of 6 more than 15". Both can be interpreted as correct under different readings: 17 is (a factor of 6) more than 15, 7 is a factor of (6 more than 15). The first of these could be disambiguated by saying "17 is 15 plus a factor of 6", but there is no obvious unambiguous candidate for the second.

Matthew Scroggs finds this a particular challenge when writing clues for the Chalkdust crossnumber.

The first episode of the All Squared podcast is about spoken mathematics.