What I mean by this is primarily the following: Upon the discovery of (usable) electricity, and means to use it correctly, engineering in general has advanced a lot. Warfare has radically changed since ancient times, and people are constantly stringing up new theories in regards to physics, biology, chemistry, etc. that completely change the way we see those fields. In mathematics, however, I have the feeling that it hasn't changed much. We still use the basic principles laid out by Greek and Roman philosophers, and others are merely 'added on' to the existing ones. How true or false is this?
Considering that much of the modeling and design of electrical systems use lumped element model, which itself corresponds to spring and mass rigid body physics elements, both of which are solved using differential equations (either partial or ordinary); I'm not sure how you are exactly defining "change" and "evolution".
Are you saying that the contributions of modern calculus are simply "adding" to basic principles laid out by classical-era philosophers? One can give a large number of examples of significant innovations in mathematics, including graph theory, complex numbers and exponents, logarithms, transforms, modern algebra .... all of which have made significant practical impact.
Due to its abstract nature. Mathematics can exists more on a continuum. Unsolved problems in Mathematics are solved, by reducing them into components that have been solved before, which is what gives the effect that things are being built layer by layer. The first person that solves a problem or proves something is the ones that typically get's their name applied to it. Take for example the Pythagorean Theorem which you probably know as A^2 + B^2 = C^3. Which is also completely different from what the greeks understood. That formula is algebraic in nature, which relies on the number "0" and negative numbers, that we're formalized until the 7th century CE, more than a millennium later. What's happens is the same concept of proof, and been reworked over the centuries using different newer, and more generalized mathematical techniques. All while still being referred to as Pathagoreses Proof
With a very broad brush ancient mathematics was built on the the axioms and proofs of plain geometry. Modern Mathematics is built on the axioms and poofs of set and model theory. Two very different frameworks that can be leverages to solve the same problems.
So back to you question. In Mathematics, when something is proved, either via Euclidean Geometry or Set Theory, it stays proved. Even a completely new discipline of mathematics going to alter the fact that 2+2=4. The new mathematics might let you solve new problems but its not going to change the nature of the currently solved problems, and provide only limited insight. With Mathematics the revelations come from how a problem is solved, and less via the solution to the problem
There are two questions I feel you can ask.
One is how mathematics has changed in the sense of "what is mathematics", "how do we derive truth", "how do we know we're correct", etc, and how those concepts have evolved over time. And they have, by a lot.
The other is: what mathematical progress have we made? What fields, applications, tools, methods, have sprung up in the last X-number of years? Whatever X is, no one post will do it justice, but it can be fun to try.
It's kind of funny that you should compare these two. Advances in engineering would not have been possible without the math that has been invented since 1500.
The Cartesian coordinates are an essential first step. Newton's immediately applied his work on calculus to his work on the laws of motion.
Mechanical Engineering would just be rules-of-thumb and a bit of geometry if it weren't for the work of Fourrier, and later the development of finite element analysis. It would be tough to build a cell phone without complex numbers. The Greeks hadn't even gotten to negative numbers.