As a math person, I’ve never heard “gamma” to mean the derivative of a change (a delta). For example, I was always taught that speed is v=delta-x/delta-t (distance over time). I’ve never heard gamma to mean that.
Speaking as a math major, gamma means, like, a million different things. It’s just a letter. There are only 26 latin letters, 24 greek letters, the capitals, and then a few oddities like blackboard bold, fraktur, cursive, etc. You run out pretty quickly and end up reusing letters.
Just like pi means different things in different contexts. It might be a permutation, projection, a function which counts prime numbers, or it might be half the period of sin. I might write π(10) = 4, or π ≈ 3.14…, or for π in P, etc. I might say that π is the right inverse of ι, in other words π∘ι = id, and point to some digram with a bunch of arrows.
Delta is not just “a change” in this context. It is specifically the rate of change of an option’s value with respect to the value of the underlying security. Just like pi, delta and gamma mean different things in different contexts.
