Every year, members of some of the biggest and most influential mathematics associations get together to dedicate the month of April to math awareness. The initiative was set in motion in 1986 by President Reagan, who said, “To help encourage the study and utilization of mathematics, it is appropriate that all Americans be reminded of the importance of this basic branch of science to our daily lives.”

We couldn’t agree more! This year’s theme, as the title of this blog post suggests, is “Mathematics, Magic, and Mystery.”

Now, of course there’s no “real” magic in math—everything in math must be proven, or else it’s not math yet. But there are certainly a lot of intriguing concepts, mysterious paradoxes, and even totally baffling unsolved problems that make this subject feel somewhat magical at times.

Take, for instance, physically impossible geometric shapes:

Penrose triangle

Freemish crate

impossible torus

Understanding that what you perceive may not always be truth is fundamental in the fields of math and science. Are the two gray areas in the circle below the same? How do you know? Can you tell for sure just by looking at it?

bullseye illusion

And some things don’t make any intuitive sense at all, just by looking at them…

.9999... = 1

In fact, for most people, the notion of infinity doesn’t sit very well. Surely there must be a 0.0000…0001 somewhere to subtract from the 0.9999…9999, so it’s not really equal to 1. Except, for that to be true, you would have to write infinity zeroes before you wrote “one” at the end—but there’s no end to infinity, remember? All you would end up doing is writing “zero” for all eternity. And infinity zeroes most definitely equals zero.

And if that’s not bordering on the magical/supernatural for you, how about these suckers?

vampire numbers

All right, so there’s nothing really mysterious or magical about vampire numbers, but they are still a rather interesting phenomenon. (No? Just me who thinks that? All right, all right, moving on…)

What are the chances of interesting you with this example? In reality, gauging your odds may not always be as simple at it seems:

Monty Hall problem

Named after the famous game show host, the Monty Hall problem illustrates how an informed outside source affects the probability of the desired outcome. In reality, since that outside person is not choosing a door at random, but is always eliminating one wrong choice for you, your chances of winning if you switch your answer always increase.

Writing out the different scenarios is the easiest way to wrap your head around the problem. We have doors 1, 2, and 3, and we pretend there are goats behind doors 1 and 3 and a car behind door 2. So: 1 (goat), 2 (car), 3 (goat).

Trial 1: You pick door 1 (goat). The host opens door 3 (goat). You switch to door 2 (car). You win!

Trial 2: You pick door 2 (car). The host opens door 1 (goat) or 3 (goat). You switch to door 3 (goat) or 1 (goat). You lose.

Trial 3: You pick door 3 (goat). The host opens door 1 (goat). You switch to door 2 (car). You win!

When you choose to switch, you have a 66% (two-thirds) chance of winning and only a 33% (one-third) chance of losing. Yay, math!

And if you’re looking to pull off a real mathematical miracle, then we recommend tackling this 54-year-old unsolved problem—who knows, you may snag the $1,000,000 reward for figuring it out!

Swinnerton?Dyer conjecture

Happy Math Awareness Month!

 

 

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