How does the Pythagorean theorem work, and why is it true?
a² + b² = c² is one of the most famous results in mathematics. What is the geometric meaning of this statement, and how can it be proved?
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Mathematics
Pure and applied mathematics and statistics
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Why are there different sizes of infinity?
Georg Cantor showed that some infinities are larger than others. How can one infinite set be larger than another, and what does that even mean?
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What is Euler's identity, and why is it considered beautiful?
The equation e^(iπ) + 1 = 0 is often called the most beautiful in mathematics. What does it mean, and why does it connect five fundamental constants?
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Why does 0 factorial equal 1?
The factorial function is defined as the product of all positive integers up to n. So why does 0! = 1? Is it just a convention or is there a deeper reason?
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