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The Basel Problem

This is my attempt at explaining how Leonhard Euler solved the Basel problem after 90 years of no success by other great mathematicians.

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Integrate x^-x dx
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Integrate x^-x dx

1995 British Mathematics Olympiad problem
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1995 British Mathematics Olympiad problem

Why is pi here?  And why is it squared?  A geometric answer to the Basel problem
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Why is pi here? And why is it squared? A geometric answer to the Basel problem

Romanian Mathematics Olympiad
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Romanian Mathematics Olympiad

Cauchy's Proof of the Basel Problem | Pi Squared Over Six (3blue1brown SoME1 Entry)
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Cauchy's Proof of the Basel Problem | Pi Squared Over Six (3blue1brown SoME1 Entry)

Euler's Original Proof Of Basel Problem: Σ(1/n²)=π²/6 — BEST Explanation
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Euler's Original Proof Of Basel Problem: Σ(1/n²)=π²/6 — BEST Explanation

Ramanujan's favorite coincidence (it's not a coincidence)
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Ramanujan's favorite coincidence (it's not a coincidence)

The Simple Math Problem Nobody Could Solve
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The Simple Math Problem Nobody Could Solve

Prove that the nested radical is less than 2 for all n
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Prove that the nested radical is less than 2 for all n

Mathe-News 🚨 KI löst das Erdős-Einheitsabstand-Problem!
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Mathe-News 🚨 KI löst das Erdős-Einheitsabstand-Problem!

A System of Prime Equations
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A System of Prime Equations

Find all natural numbers for which n^10 + n^5 +1 is prime
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Find all natural numbers for which n^10 + n^5 +1 is prime

Lucas Sequence
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Lucas Sequence

How Euler and Ramanujan would explain the most viral equation.
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How Euler and Ramanujan would explain the most viral equation.

Prove that n⁷ +7 is never a perfect square.
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Prove that n⁷ +7 is never a perfect square.

An integral with a classic result
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An integral with a classic result

a spectacular solution to 1+1/2^2+1/3^2+... (Basel problem)
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a spectacular solution to 1+1/2^2+1/3^2+... (Basel problem)

Lambert W Function
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Lambert W Function

But HOW did Euler do it?! A BEAUTIFUL Solution to the FAMOUS Basel Problem!
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But HOW did Euler do it?! A BEAUTIFUL Solution to the FAMOUS Basel Problem!

When Math Isn’t Based in Reality
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When Math Isn’t Based in Reality

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