What Are Some Innovative Mathematical Strategies Beyond Traditional Induction?

AI Thread Summary
Cauchy's proof of the AM-GM inequality using forward backward induction highlights an elegant approach not commonly found in traditional discrete mathematics resources. The discussion seeks to uncover other innovative mathematical strategies beyond standard induction methods, inviting contributions on lesser-known techniques. Participants are encouraged to share insights on unconventional induction methods or innovative strategies from various mathematical fields. The thread also references a related discussion on unconventional types of induction for further exploration. Overall, the conversation emphasizes the value of exploring innovative mathematical proofs and strategies.
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I was just recently reading about Cauchy's proof of the AM-GM inequality by forward backward induction and was simply blown away by it's elegance. However, I have never seen forward backward induction in any of my discrete maths books (including the one devoted just to mathematical induction). Even the wikipedia page on mathematical induction has no information about backward forward mathematical induction.

I was just wondering if anyone knows of any other innovative strategies like this that are well known. Altough this question is inteneded to find other obscure methods of induction, innovative strategies from other areas of Maths would be appreciated too.
 
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