Pure mathematics is worthwhile

By definition, things are worthwhile if they should be done. Things can be done for two reasons: for their own sakes or to help reach another goal. It stands to reason that things desired in themselves are greater goods than those that are desired for other ends. What, then, is the greatest good, for this thing will surely be the primary end desired in itself? Since the concept of “good” can only be known to an individual living as such, life qua man must be required for anything else to be valued, and, as such, it must be the ultimate value towards which all things are aimed.If life is the only end-in-itself, and things are judged to be good or bad in relation to this, then that which furthers life is the good and that which destroys it is the bad. As such, for abstract maths to be worthwhile, it must further life. For something to further life, it’s clear that it must have a direct impact on it. In other words, for a thing to be good, it must be directly applicable to life, since all goods are aimed towards life and none are good in themselves outside of their relationship with life. My opponent defines pure maths as something which “does not neccessarily have a direct application outside of itself.” Given the previous line of reasoning, it’s clear that pure maths cannot be valuable, since it does not further life.Responses: 1) It gives people pleasureMy opponent makes the argument that, since people gain pleasure from maths, maths is worthwhile. This only works if it is assumed that things should be done not for any rational reason but solely because of “pleasure” (however that’s defined). This ignores the fact that there are many things that people find pleasurable that I doubt my opponent would advocate – for instance, the habitual use of cocaine or meth. If pleasure isn’t the standard of what is worthwhile or my opponent cannot justify why it should be, then this point fails.He also makes the point that many other things (like art) are unnecessary, but are still commonly accepted as worthwhile. This argument is entirely dependent on consensus being infallible, which is faulty reasoning, considering that 50,000,000 Frenchmen can be just as wrong as one. Without a basis in consensus, my opponent will need to show why art, poetry, sport, etc., should be valued, rather than just saying that they are. He needs to provide a complete moral framework to support his stance.2 + 3) Here my opponent claims that there are “indirect” applications of abstract maths, whether intentional or not. He says that maths that was originally useless could later turn out to be useful and that the process of doing maths is able to help the study of other fields. However, even if these claims are true, they don’t make abstract maths worthwhile if there are much better ways to achieve its effects. For instance, if a new maths theorem is needed for a present problem, it’s much more reasonable to try to find it with the goal in mind and with a focus on direct applicability than to rely on the random tangents abstract mathematicians with nothing better to do go on. In the same way, even if abstract maths will help with logical skills, the direct study of logic with a view towards its application to the situation at hand will, in pretty much every case, produce better results. Given that the alternatives are much better than the study of abstract maths, such maths haven’t been shown to be worth the time and effort. 4) Numbers are a part of our universe, to study maths is to study the worldMy opponent says that the abstract laws of maths are “fundamental” and that knowledge of them is valuable. However, he never justifies why this knowledge is useful. For his argument to work, such knowledge would have to be an end in itself, which, as discussed earlier, is impossible. Applied maths is applicable to life. Pure maths is not. As such, applied maths is infinitely more worthwhile, regardless of its “beauty” – such things are irrelevant. 5) It doesn't really cost anythingEven if it costs almost nothing to do maths, it still costs something, so this argument begs the question – it only works if it is assumed that maths has some redeeming qualities in the first place.____The Romans, under your comparison, were much more respectable. They improved their lives via the work they did – they didn’t just do anything for the sake of it. The Romans had a vast empire that far overshadowed the Greeks precisely because the Romans were earth-oriented, as opposed to mystical and idealistic.