How to Free Your Inner Mathematician by Susan D'Agostino

Author:Susan D'Agostino [D'Agostino, Susan]
Language: eng
Format: epub
Publisher: OUP Oxford
Published: 2020-03-26T00:00:00+00:00

Oh, now I see that the collection of prime numbers must be infinite.

My journey may have meandered, but I found my own way to the truth.

Now I really believe that the collection of prime numbers is infinite.

The collection of prime numbers is infinite.

This was a satisfying intellectual journey.

Of course, mathematicians do not write their proofs using words and phrases like “oh no!” “whoops!” and “I don’t want to look like a fool!” Also, they edit out chattiness and, in a nod to all mathematicians who came before them, employ the first-person plural rather than the first-person singular. Still, my not-cleaned-up proof reveals the feistiness that drives a good proof by contradiction. See where crazy assumptions take you. Argue with passion. If you take a wrong turn, simply back up to the last good spot in your argument, make a correction, and then plow forward again. A mathematician at work at a desk is as messy as a painter at work in a studio. Composure in the early stages is overrated. Be contradictory in your mathematical and life pursuits, for you may make progress as a result of your passion.

Problem 28. Are there infinitely many non-prime numbers? Justify your answer.

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