Let’s learn about mathematical mysteries

Mathematicians are still learning new things about the nature of numbers, shapes and more

a jumble of glowing mathematical symbols shimmer against a dark background

Many mysteries about the nature of numbers, shapes and other features of math remain unsolved to this day.


Most of us have only ever worked on math problems that have known solutions. Even if a puzzle stumped us, we could trust that some set of textbook facts or formulas would get us to the right answer. Or that a teacher could demonstrate the solution. But there are plenty of enduring mysteries in math that continue to confound even experts.

For instance, a mathematician recently solved a decades-old mystery about Möbius strips. The question was seemingly simple: How short could these twisty loops be? But the answer had long eluded math-curious minds.

That’s not the only longstanding math mystery to be cracked this year. After half a century of searching, mathematicians finally discovered an “einstein tile.” This weird shape can cover an infinite flat surface but only in a pattern that never repeats.

Math detectives are still seeking solutions for other problems. For example, how big of a couch can be pivoted around a corner? Or how small a blanket can cover a sleeper in any position? Such unsolved puzzles remind us that not even pro mathematicians know everything. And that, in turn, can help us conquer our own math fears.

Want to know more? We’ve got some stories to get you started:

A twisty mystery about Möbius strips has been solved at last Turning to paper and scissors helped one mathematician finally figure out just how short the twisted loops can be. (11/20/2023) Readability: 6.4

An ‘einstein’ shape eluded mathematicians for 50 years. Now they found one The shapes can form an infinite tiled pattern that never repeats. The first is a 13-sided shape nicknamed “the hat.” (6/23/2023) Readability: 6.0

Let’s learn about dealing with math anxiety Writing about math anxiety and maintaining a “growth mindset” can help soothe stress about the subject. (9/6/2023) Readability: 6.0

Here are a few mysteries in math that still need solutions.

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Word find

If you’re looking for fun math puzzles with known solutions, play the brain teaser game “24” online. Each set of four numbers can be combined through addition, subtraction, multiplication or division to reach 24. The real mystery is how. 

Maria Temming is the Assistant Managing Editor at Science News Explores. She has bachelor's degrees in physics and English, and a master's in science writing.

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