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Mathematics and Philosophy

 Mathematics and Philosophy

In the contemporary world, it may feel counterintuitive to some people to even consider the relation between mathematics (widely regarded as a quantitative or structural discipline) and philosophy (widely regarded as a theoretical or ethical subject). But it’s a fact that these two disciplines are deeply intertwined even more so than we realize.

Especially considering the history of western civilization, these two disciplines were once considered a single subject matter. Though their applications and study practices may look broadly branched apart in the 21st century, it is intriguing to know about their origins, their marriage as well as the relevancy of their juxtaposition in the present world.

Most of us already have a decent level of knowledge about the origins of mathematics. They have been around for more than 5000 years since ancient civilizations like Egyptian, Babylonian, and Chinese civilizations; some consider mathematics even older than that. However, the substantial advancement and unification of mathematics, particularly in geometry, logic, deductive reasoning, and proofs, occurred in the Greek period along with major contributions in other fields like number theory, combinatorics, mathematical physics, and astronomy.

Pythagoras, arguably the most popular and influential mathematician, founded his philosophy primarily based on mathematics. For him, the mystical truths of nature and the very basis of reality were to be found in mathematics, which was thought to be precise, exact, and practically useful. The logical inferences and established formulas developed in this era still pass the rigors of present-day mathematicians.

Even Plato’s academy demanded the complete knowledge of geometry. He was so fascinated that he made mathematical knowledge the methodology of philosophical knowledge even more so than empirical experience. Archimedes, widely regarded as the father of mathematics, advanced and applied mathematical concepts not only in physics but also in philosophy, particularly in metaphysics.

Logic and reasoning are central to both disciplines. Mathematics is widely used in confronting complex issues in philosophy. Also, the philosophy of mathematics is properly established and followed before working with and tackling mathematical problems. Philosophy guides mathematics towards a particular direction while mathematics acts as a foundation and a tool to philosophy.

Many influential mathematicians in the post-Hellenistic period were also great philosophers. They embodied the language of mathematics and expressed their philosophical arguments in terms of them. Some of the most renowned names are Rene Descartes, Bertrand Russell, Blaise Pascal, Gottfried Leibnitz, and David Hilbert, among others.

Even from a surface analysis, mathematics and philosophy seem to be interwoven in the fabric of reality. When specific concepts are considered, there are countless tools and ideas we may have been using without even consideration of the discipline it is from. Therefore, we can conclude that the nature of these seemingly dichotomous disciplines is essentially interchangeable, if not identical.


-Amrit Shakya


 

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