Is mathematics invented or discovered? It is this seemingly simple question that I wish to briefly analyze in this essay. Such a question has created an argument among mathematicians for as long as mathematics has existed. Some say that mathematics is completely invented, others claim that it is largely discovered, while a final group says it is a mixture of the two. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get an original essayHere are the three different types of views on this issue. The first two have been associated with schools of thought called formalism and platonism, respectively. The third school brings together the ideas of formalism and platonism, because it mixes them in one way or another. The Platonist side was initiated by Plato and his famous statement that "all mathematical concepts were concrete and as real as the universe itself, whatever our knowledge of them." He believed that we humans had discovered mathematics and he saw it only as a spiritual way to access knowledge that already existed. On the formalism side, Einstein and many other mathematicians like David Hilbert or Georg Cantor thought that mathematics was a set of invented tools. Famous philosophers like Aristotle argued that “mathematics does not exist as an independent entity. Mathematics is simply the result of logical operations based on syllogisms, and research begins with axioms.” Axioms are statements that you assume to be true without having actual proof, for example, if a=b and b=c then a must equal c. This Einstein example is completely made up because there is no real proof: it could not have been discovered. The latter school believes that mathematics is both invented and discovered. A German professor of mathematics declared in the 19th century: "God created the natural numbers, everything else is the work of man." This can be seen for example through integers. Positive integers have always existed, they have meaning in nature. On the other hand, negative integers were just an invention of humans, they have no real purpose in nature. Most mathematicians hold that numbers can exist physically, but mathematical statements cannot. For them, invention and discovery both play a crucial role. Keep in mind: this is just a sample. Get a personalized article from our expert writers now. Get a Custom Essay As the short analysis above shows, some particularly brilliant people have tried to answer the question of whether mathematics was invented or discovered. Since it is very difficult to say with 100% certainty that it is one or the other, it is very likely that this debate will continue. Often in these kinds of situations, the truth lies somewhere in between. Accordingly, I would personally support the third school of thought.