The Importance Of Intuitionical Mathematics

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“I think we have a stray dog,” I explain while he refills the dog’s bowls. “Can you check under the deck?” “How would an entire dog get underneath our deck?” he asked condescendingly. “I’m not sure! Just believe me, something is under there,” I exclaim pointing at the deck. Despite investigating for a solid thirty minutes, my father returns with no news of seeing a stray dog. While the howling is too loud for me, he sleeps through the night without hearing anything. However, because neither of us has seen the dog, there is no conclusive evidence of any dog, besides our own, being beneath our deck. Therefore, is saying that “I know there is a stray dog” accurate, or is this just a strong belief? While searching for certainty in situations …show more content…
Within this area of knowledge, several of the ways of knowing are employed such as: reason, intuition, and imagination. Because a majority of mathematics occurs within the mind, imagination and intuition are important components in creating logical theorems. It is because of imagination and intuition that theoretical mathematicians can believe in the certainty of their theorems without necessarily having proof, while reason is an important component in the study of practical math in insuring that most everything makes logical sense. In this area, it is important to have evidence or a rigorous proof of knowledge when mathematicians try to transfer their theorems from personal knowledge to shared knowledge. While personal knowledge is mainly based on belief, in order for shared knowledge to become well-known, proof is often considered necessary as a way of proving the logical sense and the conjecture’s infallibility in multiple scenarios. However, a potential problem within my argument is in situations which use intuition, the person is sure of their conjecture, yet there is no known way of possibly providing proof. An example of this in mathematics is Fermat’s Last Theorem. While Fermat claimed he had proof to his conjecture, it was just too large to fit in the book’s margins; the mathematician used his intuition and was certain that it made logical sense. However, because of his lack of conclusive evidence, his theorem was not accepted as shared knowledge until hundreds of years later when other mathematicians were finally able to crack the conundrum. In response to this problem, I believe that in certain situations of Mathematics proof is possible, but not needed for personal knowledge and belief, and a necessity in order to

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