Here's something a Highschool student would ask: If I have something considered a disability in mathematics i.e visual thinking LoL , using a computer to visualize mathematics would be considered a useful tool. Pure mathematics is defined as generalizing abstraction , it is the how's and why's of mathematics. If applied mathematics is supposed to be ugly and dull under a physical truth in a mathematical framework , would using a computer to study as well as create the beautiful and brilliant be considered pure? Computational Mathematics , is often a hybrid of the two , so why is it filed under applied? Is it because of the implementations and designing of algorithms to study mathematics , but I only want to use a computer to visualize things I can't and to represent my output - my creations? I guess I'll need to use them anyways. Can we open our minds here? I just need reinforcement the main answer is blatantly yes. -------------------- This started out because an opinion made by Hardy in a Mathematicians Apology is mostly being misunderstood by me , if physical truth is ugly and dull , why do other's consider it beautiful , he thinks one aspect of reality is more prettier than the other , he's just making biased comparisons. But it still haunts me to this day , is it really ugly and dull just applying? Am I ruminating too much? I am also asking this question because I have a future career in computational geometry and I would want to know if this is considered pure , as the idea of purity being the purist of the water seems to intrigue me , but it's nothing important.