In general, mathematicians speak in non-normal ways which don’t have simple translations when they project into English grammar.
Allow me to break this down for you:
- Pedestrian speak: means usually. In general, I get to work on time, but today I was late.
- Math speak: means always. It’s always true in a larger sense. ie: In general, every element in a field has an inverse, not just 2.
- Pedestrian speak: a property which most things are assumed to posses. ie: It’s normal to hate Mondays.
- Math speak: a nice property most commonly associated with group structures. ie: H is normal in G when gHg^-1 = H.
- Pedestrian speak: a negative property, sometimes suggesting mental disabilities. ie: That man is simple. or That puzzle is too simple for one of my intellect.
- Math speak: a nice property. If a proof is simple, then we like it better than a complex one. Also a group theory property for which a group has no subgroups but 1 and itself.
- Pedestrian speak: the act of interpreting one language into another, requiring alterations in some of the meanings perhaps. ie: I read a translation of The Iliad because I can’t read Greek.
- Math speak: The act of sliding something on a surface without changing it’s shape. ie: translate a line to the right by adding 1 to every point.
- Pedestrian speak: To enlarge an image through the use of shaped glass and a light source. ie: Movie theaters project the movie onto the big screen.
- Math speak: a map which loses some information in order to better understand a multi-dimensional object. ie: the cube projects a shadow onto the floor.
- Pedestrian speak: the language which normal people speak, except the mathematicians for whom standard English is not good enough.
- Math speak: the language we butcher and redesign to fit our needs. Also a form of communication we deign to use when we have to include some explanation, but we would rather just use symbols (σψμβoλσ?).
Many people complain about the use of English in the mathematicians world. But what are they going to say about it? “This is the sort of utter nonsense, up with which I will not put?”