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A Mathematician’s Apology

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I recently heard an anecdote about a math teacher who was teaching a group of students about sequences and series. He showed them that a particular sequence of numbers adds up to a certain amount. When he was done, a student asked him, “What’s the point of that?” Now that seriously bothers me because that sequence certainly has a practical application, but you are making a mistake if you believe mathematics is only for practical purposes. Mathematics is the intersection of many subjects like art, music, and science. The practical uses of math might be physics, mechanics, and architecture, but if you only study it for that reason you might miss out on great discoveries that would have an application after the fact. I even hesitate to use that arguments because then I am fighting on their terms that mathematics must have real world applications.

Studying mathematics for its own sake is equally as valid and worthwhile in my opinion. Mathematics is a very creative subject that requires imagination, dedication, guesswork, and passion. When I read about how some great mathematical proofs were found, those mathematicians speak about beauty and elegance. They talk about it like it’s art or music. Speaking of which, what is the practical purpose of music? There isn’t any. We do it because it’s clever and the joy comes from creating something new. But if you approach mathematics like a robot, you most likely won’t go far and make yourself miserable on the way.

Mathematics is the search for truth, which is why some of the greatest mathematicians were also philosophers. But the difference between the two subjects is that mathematicians are searching for mathematical truth that will stay unchanged for thousands of years. But to reduce mathematics to its real world application, you are going to miss out on that truth.

I discussed with Dr. Dorsett why there was so much focus on the application of mathematics today. It seems to have come from the Cold War, which saw a major shift from pure to applied mathematics. Which is understandable because you cannot focus on the latest digits of Pi when you have missiles. But that shift has remained and intensified even after the Cold War.

The reason I believe children might not enjoy mathematics after a certain age, is because we make it seem like only a certain type of person can do math, and that person is usually a boy. We also give them problems about machines crashing into each other sometimes for example, “Two trains are heading towards each other and they are moving at a velocity of 50 mph. They are 4 miles apart, how long until they crash into each other?” Those questions are terrifying to children who are very sensitive to that type of stuff. We also lock them up in dusty and dark rooms and expect them to sit still when the chalk is probably irritating them. If you take all that into consideration it should not be shocking that when they grow up they are conditioned to dislike mathematics.

In the year 1869 Harvard, Yale, and Columbia were in a heated battle to attract students. They were even accepting students as late as September for early October classes. Harvard at the time was advertising how successful students were with the entrance exam, with 185 out of 210 students passing the exam. Keep in mind that these students were 17 years old and lived 145 years ago. I will provide a link to the exam at the end of the article, and I would like you to notice the lack of Biology, Chemistry, and Physics.

I would like to thank Dr. Dorsett for allowing me to speak with him about mathematics, which to me is the only thing that can rival actually doing mathematics. A helpful resource is the University of Cambridge’s Department of Applied Maths and Theoretical Physics video series Quite Easily Done.

Ptolemy Lagides, the ruler of Egypt, asked Euclid if there was a simpler way of learning the Elements. Euclid said, ”There is no royal road to geometry.”

Recommended Readings:

• A Mathematicians Apology by G.H. Hardy

• Apology by Plato

• The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography by Simon Singh

• Enigma: The Battle for the Code by Hugh Sebag-Montefiere

• The Meaning of It All: Thoughts of a Citizen Scientist by Richard Feynman

Harvard Admissions Exam from 1869:

University of Cambridge Quite Easily Done:

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A Mathematician’s Apology