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DJ KAPUT wrote
If we were to find life on another planet at least advanced as ourselves or more so, do you believe that they will have created a system of mathematics in any way similiar to ours. I tend to think they would and here is my reasoning behind that: It seems the first step in mathematics would be simple addition and subtraction which, at least in our history, has been an important ability even in our most primitive stage. Also considering that animals can, to a degree, also understand simple addition it seems likely that this would be the base for almost any life form capable of understanding it. The next step would likely be multiplication and division which, much like addition and subtraction, are fairly simplistic and helpful. Our entire system of mathematics seems to follow a logical path and so it seems reasonable to assume that if somebody started from the exact same idea of simple mathematics, that their more complex ideas would progress at least similiar to ours. The only problem I can see with my logic is assuming that their brain would function similiar to ours. For example, we use various different methods to find convergence of sumations. If an alien mind were capable of performing thousands of sumations in a very short amount of time I can see how their take on math might be entirely different from ours.
Discuss.
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Many aspects of our mathematics originate with discoveries or invented conventions. Without some bright guy to dream up keeping a tangible tally of goats and rice and such, mathematics might all be strictly mental and perceived as a kind of useful and reliable intuition.
We could still be stuck trying to multiply Roman numerals (what a chore that was) and, because of it, not progressed any farther. Whole branches of mathematics might not have been discovered, like topology, non-Euclidian geometry, calculus.
Your alien might, early-on, have contemplated nature and decided to define a line as a contiguous series of points in 3-space (translated to English from the Asdfjkah dialect). They might have concentrated on curves and how to manipulate them, treating straight lines as very special and not very useful cases.
I am afraid that it is arrogant to think that aliens who know how to form sustained toroidal bubbles of air in their water environment (Porpoises) will recognize the universality of Maxwell's equations. Apologies to Sagan and "Contact".