Post by rubl on Sept 17, 2019 14:50:49 GMT 7
simple
Spoiler alert! The article contains the solution. If you're still working on your own solution and think you will spend less than the 1,000,000 computing hours these two mathematicians needed, don't read.
"Life, the Universe, and Math: 42 Proven to be the Sum of 3 Cubes
The problem of 42 — at least as it relates to whether the number could be considered the sum of three cubes — has finally been solved. The question of whether every number under 100 could be expressed in this fashion has been a long-standing puzzle in the world of mathematics. Now, two mathematicians, Andrew Sutherland of MIT and Andrew Booker of Bristol, have jointly proven that 42 is indeed the sum of three cubes.
For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1-100. By 2016, researchers had demonstrated that this theory held true in all cases except for two unproven exceptions: 33 and 42. The formal theory, as expressed by Roger Heath-Brown in 1992, is that every k unequal to 4 or 5 modulo 9 has infinitely many representations as the sum of three cubes. By closing this particular gap, we’ve now proven that all numbers below 113 fit this theory.
Earlier this year, Andrew Booker of Bristol was inspired by a Numberphile video to begin working on a solution. We’ve embedded that video below:"
www.extremetech.com/computing/298112-life-the-universe-and-math-42-proven-to-be-the-sum-of-3-cubes
Spoiler alert! The article contains the solution. If you're still working on your own solution and think you will spend less than the 1,000,000 computing hours these two mathematicians needed, don't read.
"Life, the Universe, and Math: 42 Proven to be the Sum of 3 Cubes
The problem of 42 — at least as it relates to whether the number could be considered the sum of three cubes — has finally been solved. The question of whether every number under 100 could be expressed in this fashion has been a long-standing puzzle in the world of mathematics. Now, two mathematicians, Andrew Sutherland of MIT and Andrew Booker of Bristol, have jointly proven that 42 is indeed the sum of three cubes.
For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1-100. By 2016, researchers had demonstrated that this theory held true in all cases except for two unproven exceptions: 33 and 42. The formal theory, as expressed by Roger Heath-Brown in 1992, is that every k unequal to 4 or 5 modulo 9 has infinitely many representations as the sum of three cubes. By closing this particular gap, we’ve now proven that all numbers below 113 fit this theory.
Earlier this year, Andrew Booker of Bristol was inspired by a Numberphile video to begin working on a solution. We’ve embedded that video below:"
www.extremetech.com/computing/298112-life-the-universe-and-math-42-proven-to-be-the-sum-of-3-cubes
