US teens say they have new proof for Pythagorean theorem(theguardian.com) |
US teens say they have new proof for Pythagorean theorem(theguardian.com) |
I expect that an "AI" should be able to give a thorough and transparent explanation to an unseen and unsolved mathematical problem with a vigorous proof.
But alas after years of AI hype, nothing of the sort has come out of that (yet). Instead we get hallucinating chatbots fuelling the hype.
What a shame for the AI hype squad.
Seems you will need to wait.
https://meetings.ams.org/math/spring2023se/meetingapp.cgi/Pa...
In the 2000 years since trigonometry was discovered it's always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.” But that isn’t quite true: in our lecture we present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry—the Law of Sines—and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1.