Actually, what I have read lately is that:
The clocks do not slown down, except due to the increase mass that the clock may gain, but that would be only when an object reaches relativistic (Einstein) speed, and that is only close to the speed of light, which is the fastest speed one can get to, as known. Light (photons) has such a very very small mass (if any at all - it is so small that it can not be measured yet) that it travels the fastest in the Universe.
So, according to the explanation of it, you are the object slowing down, if you could move at such relativistic speeds. And that probably is not possible, unless some sort of field that protects you could be built, and they think that something like a force field will be science fiction for many years, as the scientists think it is just a dream right now!
So, people think of it as the clocks slowing down, but that may only be due to gravity and its affects on the clocks. But you traveling that fast, you would slow down, so heart beat, motions taken, anything, speech even, would all slow down, and become slower, and slower, and slower the faster near relativistic speeds you traveled along.
Actually it may be, that alegbra is the end product of the math, but starting out, may be many calculations of calculus or differential equations (another form of calculus. Once those many limits in math are worked out without running into the stopper which is infinity (you can not use infinity and get the math done), then it may be simplified down to algebra in the end, and a simple equation come out of all of the math that was done!
In math, the purpose of math is to simplify down from more difficult equations that one started out with. And doing that sort of math can take -- years!
Afterall, Albert Einstein took ten years from 1905 when Special Relativity came out, to come up and simplify down to his General Relativity Equation which came out in 1915 --- E=mc^2. (Energy=Mass times the Speed of Light (c) squared.
The Special Relativity Equation was --- E=(pc)^2 + (mc^2)^2 or Energy= (the momentum times the speed of light) squared + (the mass times the speed of light squared) squared!
But now in particle accelerators (smash protons together very fast at relativistic speeds - near the speed of light -- 0.99999999c), there is an additional factor that they consider and that is the number of electronVolts that it gains also -- or the gamma factor.