Tuesday, May 6, 2014

Daily 1: What is Math?

Mathematics is the study of quantity, space, change, and other abstract ideas such as sets. The sub-disciplines of math concentrate on these various ideas. For instance, calculus is used to study change, and abstract algebra is used to study sets and the relations that can be defined between these sets.

While one can study math in a pure or theoretical sense, the discipline is applicable to a broad variety of other fields. Indeed, many fields of study would lack substance and rigor if it were not for their use of mathematics. Those studying business or economics can use mathematics to identify market trends, and scientists can apply mathematics to their studies in astronomy, biology, chemistry, ecology, physics, and every other conceivable field.

One of the biggest moments in the history of math was the publication of Euclid’s Elements. This work was one of the first texts in history to begin formalizing math, and was certainly one of the most important. The book contained many axiomatic statements, definitions of mathematical terms, and included proofs of theorems. Another historical moment was the independent discovery of calculus by Newton and Leibniz. Calculus has become indispensable in both the natural and social sciences, helping to explain everything from the effects of a particular phenomenon on an economic system, to the movement of solar bodies. Additionally, the work done by Einstein, including his famous e = mc2, has revolutionized the way we study physics. Further, Alan Turing was extremely influential with his contribution of the Turing machine, which helped to start the field of modern computer science. Turing aided in developing procedures and algorithms to be done by a computer that would have otherwise been difficult to do efficiently by hand.

In addition to the contributions described above, many mathematicians aided in establishing math as a rigorous, proof-based area of study in the twentieth century. As such, math has been universalized into a system that has both convention and method, allowing mathematicians to write and review ideas and theorems with one another. Without such a system, it would be much more difficult to make progress in mathematics, which would in turn delay the progress of the many fields that rely on its use.

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