The problem was the Brachischrone Curve, which was a curve which if you slide a frictionless object down it it gives the fastest time possible to get from the start to the finish.
From Wikipedia:
Johann Bernoulli posed the problem of the brachistochrone to the readers of Acta Eruditorum in June, 1696.[8][9] He said:
I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise
Bernoulli wrote the problem statement as:
Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time.
Johann and his brother Jakob Bernoulli derived the same solution, but Johann’s derivation was incorrect, and he tried to pass off Jakob’s solution as his own.[10] Johann published the solution in the journal in May of the following year, and noted that the solution is the same curve as Huygens’s tautochrone curve. After deriving the differential equation for the curve by the method given below, he went on to show that it does yield a cycloid.[11][12] However, his proof is marred by his use of a single constant instead of the three constants, vm, 2g and D, below.
Bernoulli allowed six months for the solutions but none were received during this period. At the request of Leibniz, the time was publicly extended for a year and a half.[13] At 4 p.m. on 29 January 1697 when he arrived home from the Royal Mint, Isaac Newton found the challenge in a letter from Johann Bernoulli.[14] Newton stayed up all night to solve it and mailed the solution anonymously by the next post. Upon reading the solution, Bernoulli immediately recognized its author, exclaiming that he “recognizes a lion from his claw mark”. This story gives some idea of Newton’s power, since Johann Bernoulli took two weeks to solve it.[5][15] Newton also wrote, “I do not love to be dunned [pestered] and teased by foreigners about mathematical things…”, and Newton had already solved Newton’s minimal resistance problem, which is considered the first of the kind in calculus of variations.
1 Comment
Context:
The problem was the Brachischrone Curve, which was a curve which if you slide a frictionless object down it it gives the fastest time possible to get from the start to the finish.
From Wikipedia:
Johann Bernoulli posed the problem of the brachistochrone to the readers of Acta Eruditorum in June, 1696.[8][9] He said:
I, Johann Bernoulli, address the most brilliant mathematicians in the world. Nothing is more attractive to intelligent people than an honest, challenging problem, whose possible solution will bestow fame and remain as a lasting monument. Following the example set by Pascal, Fermat, etc., I hope to gain the gratitude of the whole scientific community by placing before the finest mathematicians of our time a problem which will test their methods and the strength of their intellect. If someone communicates to me the solution of the proposed problem, I shall publicly declare him worthy of praise
Bernoulli wrote the problem statement as:
Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time.
Johann and his brother Jakob Bernoulli derived the same solution, but Johann’s derivation was incorrect, and he tried to pass off Jakob’s solution as his own.[10] Johann published the solution in the journal in May of the following year, and noted that the solution is the same curve as Huygens’s tautochrone curve. After deriving the differential equation for the curve by the method given below, he went on to show that it does yield a cycloid.[11][12] However, his proof is marred by his use of a single constant instead of the three constants, vm, 2g and D, below.
Bernoulli allowed six months for the solutions but none were received during this period. At the request of Leibniz, the time was publicly extended for a year and a half.[13] At 4 p.m. on 29 January 1697 when he arrived home from the Royal Mint, Isaac Newton found the challenge in a letter from Johann Bernoulli.[14] Newton stayed up all night to solve it and mailed the solution anonymously by the next post. Upon reading the solution, Bernoulli immediately recognized its author, exclaiming that he “recognizes a lion from his claw mark”. This story gives some idea of Newton’s power, since Johann Bernoulli took two weeks to solve it.[5][15] Newton also wrote, “I do not love to be dunned [pestered] and teased by foreigners about mathematical things…”, and Newton had already solved Newton’s minimal resistance problem, which is considered the first of the kind in calculus of variations.