I've been studying on my master thesis about "Stochastic Differential Equations". Since I'm new to this topic, I couldn't understand the relation between "white noise" and mathematics. I searched about it. I guess it's actually related to sound or signals. But why are we using "noise" or "white noise" terms in maths if they really are related to sound? What is the point of using a term about sound in maths?
Edit : And why are we using "noise" term to denote random terms? (Like in the introduction part of Stochastic Differential Equations). Can't we just use like "random term" instead of "noise"?
In my understanding the term "noise" does not refer to sound in general. Of course in the specific case of sound it can be, but in my opinion its meaning lies more in a more general notion of an additional observation that makes the information you are really interested in more unclear. Like the static noise from a radio when you try to understand the news. Or in SDE, $dX_t = f(t)dt + dB_t$, where $f$ is the information and Brownian motion is the noise. Mainly, the trajectory of $X_t$ would follow $f(t)$, but there is a random effect that pushes the "observable" information away from the real information by a whirring, or "noise".
To answer to your edit: In fact, the description "random term" is used when you speak about SDEs, due to the fact that the randomness comes only from $B_t$. But since the noise in reality is such pure randomness to our human senses and minds, it is reasonable to introduce it as notion for such random terms. Moreover, it is convenient to have the notion of "noise" attached to this specific topic, such that it exists separated from the in fact really general notion"random term".