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November 20, 2025 10:39 pm (EST)
A Superficial Proof of Fermat’s Last Theorem
I mentioned my interest in learning about Fermat’s Last Theorem in an earlier post. As I wrote in that post, the theorem is surprisingly simple to state but the proof required very sophisticated mathematics. Let us recall the theorem here: Fermat’s Last Theorem: For any integer , the equation does not have non-zero integer solutions in…
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November 20, 2025 10:39 pm (EST)
Marriage Lemma
The Marriage Lemma is a neat result that has the following interesting formulation: Consider a group of men and women in a party. Suppose in any group of n men, there are a minimum of n women liked by at least one of the men in the group. Then it is possible to match up each…
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November 20, 2025 10:39 pm (EST)
Mathematical Induction
The Principle of Mathematical Induction is arguably one of the most powerful techniques in mathematics. Formally, the principle asserts the following: Principle of Mathematical Induction: Consider a set of statements where . Suppose: Then is true for all . To appreciate the principle, let us imagine the following scenario. Consider a monkey resting on…