What does math look like to mathematicians?

Popular Science | 9/18/2018 | Staff
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To casual fans, π is a mystic rune, a symbol of mathematical sorcery. They ponder its irrationality, memorize thousands of its digits, and commemorate Pi Day on March 14 by combining the most glorious of mankind’s arts (dessert pies) with the least glorious (puns). To the general public, π is an object of obsession, awe, even something approaching worship.

And to mathematicians, it’s roughly 3.

Spool - Places - Laypeople - Mathematicians - Math

That infinite spool of decimal places that so captivates laypeople? Well, mathematicians aren’t that bothered. They know math is about more than precision; it’s about quick estimates and smart approximations. When building intuition, it helps to streamline and simplify. Intelligent imprecision is our next crucial math-reading strategy.

Take the formula A = πr2, which many students have heard so often the mere phrase “area of a circle” triggers them to scream, “Pi r squared!” like sleeper agents programmed by brainwashing. What does it mean? Why is it true?

Mind - Look - Shapes

Well, forget the 3.14159. Let your mind go fuzzy. Just look at the shapes.

r is the radius of our circle. It’s a length.

R2 - Area

r2, then, is the area of...
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