Sometimes stuff happens, and so I missed yesterday’s Sciency Words post. Sciency Words is a series here on Planet Pailly where we take a look at some interesting scientific term and try to expand our sciency vocabularies together. I usually post this series on Fridays, but this week I fell behind schedule, so I’m a day off.

So for the first ever Saturday edition of Sciency Words, our word today is:

**MATHEMATICAL THEOREM**

Last week, we talked about the difference between a scientific theory and a scientific law, or rather the lack of any real difference between them. Neither one can ever be taken as 100% certain, but that doesn’t mean that one day a theory (like say evolution) will be discarded completely. New theories seek to refine the old ones, not replace them outright.

Some degree of uncertainty is inherent in science, but that’s not true of mathematics. Two plus two equals four. The sum of the angles of an equilateral triangle equals 180 degrees. Two parallel lines on a flat surface will never intersect. These are incontrovertible facts. Where scientists struggle with their imprecise theories and laws, mathematicians enjoy full confidence in what they call “theorems.”

You’re probably familiar with the Pythagorean Theorem, which states that a^{2} +b^{2} = c^{2} when we’re dealing with the sides of a right triangle. This theorem was first discovered by an ancient Greek philosopher named Pythagoras and has remained unchanged and unchallenged for over 2,500 years. There are literally hundreds of ways to prove the Pythagorean Theorem (click here to see 99 of them), but that’s not really necessary. Where in science we must perform the same experiment hundreds or even thousands of times and still have doubts, mathematics only requires us to prove something once.

So mathematical theorems are 100% certain in a way no scientific theory or law can ever be; however, we must keep in mind that these theorems apply only to our abstract concept of geometry and numbers. Here in the real world, there are no perfect circles, no angles that are exactly 90 degrees, and no two lines that are perfectly parallel. The real world is messy and imprecise, and so science remains our best tool for the study of the universe we actually live in.

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