The infamous 'golden ratio' calculation, for example, can be found in nature. This calculation also illustrates how facial symmetry and harmony in things like architecture are linked to the concept of beauty. Links between mathematics and other areas of knowledge such as the arts (where beauty and aesthetics play a role) can lead to interesting knowledge questions.

 

Sometimes, we use mathematics to offer "proof" and produce knowledge in other areas of knowledge. The applications of mathematical knowledge are not confined to its own discipline. In fact, we like to use mathematics to add value to knowledge in other areas of knowledge such as the natural sciences. We also like to use mathematical calculations or mathematical language to explain behaviour in the human sciences.

 

 

 

 

 

 

 

 

 

 

 

 

This utility of mathematics seemingly enhances the credibility of the knowledge it produces. However, we could wonder how useful it actually is to explain, let's say, human behaviour in mathematical terms. Are there circumstances in which applying mathematical knowledge to other areas of knowledge is not useful? The notion of the applicability of mathematics in the world around us leads to one of the most fundamental philosophical questions about the nature of mathematics.

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Philosophers have debated for centuries whether mathematics is discovered or invented. Formalists believe that mathematics has more similarities with a kind of game, which does not need to be reflected by the outer world. Platonists, however, believe that mathematical concepts exist independent of human understanding. The relationship between maths and the world around us is an important one.

 

Other areas of knowledge, such as the natural sciences, are very much dependent on what they observe in the natural world. When we study mathematics, it is as if we enter into its own world, which is removed from what we can or should observe. Although the initial principles of mathematics may be based on what is present around us, we build much mathematical knowledge by following mathematical rules that are independent of the natural world. It is true that most mathematical knowledge will find real-life applications eventually.

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Yet, mathematics has its own methodology, which is very different from, let's say, the scientific method. Mathematics is often very abstract and far removed from every day life. In this sense, it is perhaps no surprise that many ancient mathematicians were also philosophers. these philosophers were very much concerned with the complex relationship between what we can(not) observe around us and what actually is "out there". 

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