Math Terms

The conventions of math exposition can be really off-putting to people who are new to it. My running list of translations of mathspeak to normal human:

• “Consider x,…” –> “We’re about to talk about a thing called x”
• “Let x be…", “suppose that x…” –> “x is a thing that has the following properties…”
• “Recall that…” –> Don’t feel dumb if you don’t “recall that”. This just indicates that the expression isn’t coming out of the blue and was defined earlier or in previous work.
• “simply multiplying by [expression that equals 1] yields…” –> It took some cleverness and false starts to come up with this non-obvious but useful expression of 1.
• “It is trivial to show…” –> “It is possible to show (potentially with non-trivial work) that…”
• “is easily”, “trivially”, “simply”, “obviously”, “straightforward”, “it is clear” –> This is an annoying tick, but it means that the step isn’t anything sneaky or something that a reviewer/expert reader would object to.