Most of what you think you know about it in relation to Newton is bunk.Newton wasn't the first one to solve it.Newton did not submit a marvellous proof of it.Newton did not submit a proof of it at all.All he submitted was an answer "a cycloid".The cycloid was already a well known curve at the time, due to being proven by Hooke to by a solution to the very similar tautochrone problem.Newton's solution was basically just circling the most likely answer to a multiple choice question.Meanwhile other mathematicians like the Bernoullis actually submitted very good and insightful proofs of the theorem.The story of him solving it in an afternoon is most likely fake and propagated by his socialite niece Catherine Conduitt who had a reputation of telling tall unlikely stories about Newton, such as the story of an apple falling on his head leading to him discovering gravity (an obviously ridiculous story).Catherine Conduitt was a wife of John Conduitt, his first biographer and also his successor as the master of the royal mint.
The famous "I recognize the lion by his claw" quote is popularly taken to imply that the Bernoulli was impressed by the solution, recognizing the mathematical power of it. Meanwhile in reality there was nothing to be impressed by. It was a nonsolution, simply a statement that the correct answer is the cycloid. There was no mathematical prowess demonstrated in it at all, a child could have submitted it. It contained no proof, no argument, nothing but the simple answer.
>>16874225Correction: the tautochrone curve was solved by Huygens, not Hooke. Everything else remains the same.
