How does the formation of mathematical knowledge differ from that of scientific knowledge and artistic knowledge?

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In this world, the amount of knowledge that exists is limitless. The more we learn, the more we come to the point of realization that there are more things we have yet to know. Quoting the word of Confucius, real knowledge is to know the extent of one’s ignorance. There are several areas of knowledge, including the arts, history, mathematics, languages and scientific knowledge. The question is, how does these different field of knowledge relate to each other or there absolutely no connection between them at all? To what extend does this contribute to the formation of knowledge, in this case the knowledge of mathematics, science and arts.

Mathematics is often seen as the study of pattern, that when placed systematically and used in certain areas of knowledge, can be manipulated to make more sense and order of the world we’re living in. However there have been some arguments between mathematicians regarding whether mathematical knowledge is discovered in the real world or is it invented in our minds? According to ancient Greek, mathematics bring the meaning of subject instruction. Numbers are merely products of human mind but somehow, they seem to fit in and blend in the real world. Scientists then use this numbers and arrange them into formulas. Amazingly, some formulas like Pi and the Fibonacci sequence is found naturally in our world.

On the other hand, the scientific knowledge is a series of scientific discoveries made by scientists, proven by their paperwork. Their discoveries are then presented in a seminar and using compilation of their discoveries, will convince the intellectuals. There will be two possibilities here ; either their discovery widely accepted or rejected due to non-concrete proofs presented. Other intellectuals might conduct the same experiment and find different or even new findings. The former part will be where a specific scientific knowledge is formed and generally perceived by the public until the next discovery challenges...
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