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42 is found to be the sum of three cubes

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Re: 42 is found to be the sum of three cubes

#91

Post by snazz »

jacquesm wrote: post #80
yodon wrote: post #75

Earlier quoted context omitted.

Please don't use code formatting for quotes. It makes the text unreadable on mobile.

Please don't criticize others for using features of the website you are visiting. If you bring a keyhole to view a landscape you won't get the full experience either. Rendering pages is a matter that should be solved by the client.

It seems to be readable on iOS Safari. Scrolling sideways works fine. Worse than a regular quote, but not actually that bad. It is a client issue if it’s more broken than that.

Re: 42 is found to be the sum of three cubes

#92

Post by mombul »

jerf wrote: post #40
mombul wrote: post #22

Earlier quoted context omitted.

Same question. People seem to be researching that kind of stuff (numbers that are sums of 3 cubes). Why?

I only recently heard what I think is a pretty solid answer to this question [1] that put it this way: We've pretty much got addition nailed down. We're pretty solid on multiplication. However, we are surprisingly weak mathematically when we try to put the two together; you can write down some extremely small math statements that baffled mathematicians for centuries, and for such statements that we have solutions for…

I see! I'm math-dumb and always struggle with that sort of research. I need to see practical applications for what seems TO ME like ridiculous questions (I'm not implying they are, I have a feeling PhD+ level people don't usually waste time on pointless stuff). Thanks for the elaborate answer!

Re: 42 is found to be the sum of three cubes

#93

Post by timerol »

whitehouse3 wrote: post #39

Why doesn't this evaluate in Excel? =(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 Returns 1.09785E+36

Excel is probably coercing them to floating point, instead of using infinite-precision integers. Wolfram-Alpha gets it right: https://www.wolframalpha.com/input/?i=%28-80538738812075974%...

Re: 42 is found to be the sum of three cubes

#94

Post by tonmoy »

jacquesm wrote: post #80
yodon wrote: post #75

Earlier quoted context omitted.

Please don't use code formatting for quotes. It makes the text unreadable on mobile.

Please don't criticize others for using features of the website you are visiting. If you bring a keyhole to view a landscape you won't get the full experience either. Rendering pages is a matter that should be solved by the client.

Text after a blank line that is indented by two or more spaces is reproduced verbatim. (This is intended for code.)

Re: 42 is found to be the sum of three cubes

#96

Post by [deleted] »

jacquesm wrote: post #80
yodon wrote: post #75

Earlier quoted context omitted.

Please don't use code formatting for quotes. It makes the text unreadable on mobile.

Please don't criticize others for using features of the website you are visiting. If you bring a keyhole to view a landscape you won't get the full experience either. Rendering pages is a matter that should be solved by the client.

[deleted]

Re: 42 is found to be the sum of three cubes

#98

Post by mombul »

normalhuman wrote: post #74
mombul wrote: post #27

Yeah but now, what? What was learned from this? Why did we look for a solution in the first place? How is it important that a number can be a sum of three cubes?

> Yeah but now, what? "now, what?", what? > What was learned from this? That 42 is the sum of three cubes. > Why did we look for a solution in the first place? They did. I do not believe that you were involved. > How is it important that a number can be a sum of three cubes? People like things for their own sake. How is it important to have sex or drink a beer? Same thing. Also math has this uncanny tendency to turn…

Why are you so bitter? I asked this genuinely. I doubt PhD+ people do that type of research "just for fun", or do that like someone like me drinks a beer. Someone answered elaborately, and I'm glad they did. Thanks anyway.

Re: 42 is found to be the sum of three cubes

#99

Post by alanbernstein »

mzs wrote: post #83
intuitionist wrote: post #73

This is a great announcement; it reminds me of the legendary story of Frank Nelson Cole wordlessly announcing his factorization of 2^67 - 1: https://en.m.wikipedia.org/wiki/Frank_Nelson_Cole

view the source, wasn't really wordless

Is that an HTML joke?

The source says "At a mathematical meeting in New York in 1903, F. N. Cole walked on to the platform and, without saying a single word, wrote two large numbers on the blackboard. He multiplied them out in longhand, and equated the result to 2^67-1."

Re: 42 is found to be the sum of three cubes

#100

Post by intuitionist »

ocfnash wrote: post #61
rank0 wrote: post #6

I must be missing something. Why is this significant?

Mathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Prior to this year, it had been established that this is possible for all k 33, 42, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921, 975. Earlier this year a solution for k=33 was found [1], so 42 was the next unknown value. [1] Brooker, A., "CRACKING THE PROBLEM WITH 33", https://people.maths.bris.ac.uk/~maarb/papers/…

This isn’t quite right, it’s easy to show that if n is 4 or 5 (mod 9), then there are no integer solutions to a^3 + b^3 + c^3 = n. The conjecture is that the mod 9 obstruction is the only one and all other integers can be represented as the sum of 3 cubes.
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