one of the most beautiful identities i've ever figured out on my own.. (φ is the Golden Ratio)pic.twitter.com/nfRGWISqTl
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i figured this out when i was an undergrad and thought i found something new and then when i showed my professor he said "ah, this was one of my favorites as an undergrad as well" the end
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When I was a youth I proved that the chance of two large numbers being relatively prime was 6/pi^2. I was very excited and tried to publish this, but of course it was known: https://en.wikipedia.org/wiki/Coprime_integers#Probability_of_coprimality … You rediscover old stuff, then newer stuff, then finally discover something new.
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In contrast, one of my teachers expressly cautioned me against spending time sleepwalking into others' results. Instead he recommended learning about the state-of-the-art of a subject and the current open problems. Too much is known, and life is too short.
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Kudos for doing it nevertheless. In 10th grade i had an alternative formulation for paulis exclusion to fill up electrons in shells n = 1,2,3 ..turned out it was just a very minor rearrangement that looked different .
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Sounds like me playing with odd square matrices in undergrad and realised there was always a number in the center that formed a series given by f(n) = (1/2)*(n^2-1) where n is 3,5,7,9...
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I was so excited and even gave it a name, only to go to google to find the series existed in number theory, the way I got disappointed. But I found solace in the fact that I discovered it independently.
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