I am attending the Joint Mathematics Meeting as a form of vacation, and will share some observations with the three of you. It is much larger than the IEEE Control and Decision Conference. The crowd is a lot more diverse than the usual bunch of engineers. Mathematics is a much wider subject.
I am mostly attending plenary talks (called invited addresses). The regular sessions are very specialized, not unlike a controls conference, and probably incomprehensible for the uninitiated - a category that for many talks includes pretty much anyone but the coauthors.
Some addresses are very good, and a good fraction are given by women. Conjecture: the 2 facts are related. However they are not heavily attended. Perhaps because the math community is more fragmented, and because there are parallel sessions simultaneous with the plenaries. In general the schedule is a non Cartesian mess. The sessions are not synchronized, and the presentation timing is not uniform. Session hopping would be a challenge. Brings to mind the schedule that an Usp student has to fight against.
The best engineering work holds its intellectual ground compared to the mathematics presentations, but there may be a higher proportion of high level work in mathematics. Control theory in the math community seems to occupy a small corner of math, and cover a small corner of controls. Mathematical control theory at an engineering conference is richer.
The PC is dead. Mostly you see Macs around, many iPads, and a few PC, probably mostly running some sort of Linux. Windows is becoming a niche product for people under the yoke of corrupt and incompetent information technology managers, or left-wingnut government trade protectionists.
The exhibits are incomparably better than at a control conference. More better books by many more publishers, plus puzzles, artwork, t-shirts, and the like. Unfortunately the scarves for sale do not have mathematical motives or patterns - it is cold in Boston.