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Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33 (2019)
- airocker 6y ago"""Answer to the Ultimate Question of Life, The Universe, and Everything from the supercomputer Deep Thought, specially built for this purpose. It takes Deep Thought 7 1⁄2 million years to compute and check the answer, which turns out to be 42.""" . Any co-incidence 42 is still unsolved?
- neotriple 6y ago42 has been solved. See the update at the bottom of the page.
- jl2718 6y agoWasn’t the earth the supercomputer that was trying to come up with the question to the answer of 42? If they just found it, does that mean that they’re done with us?
- deleted 6y ago[deleted]
- edoceo 6y agoSo long! And thanks for all the fish.
- deleted 6y ago[deleted]
- em-bee 6y agoyup, that's why earth is now scheduled for destruction to make space for an intergalactic highway.
- pricechild 6y agoIt's been a while... but I'm pretty sure the opening of the book explained that there was a theory that should both the question and the answer exist in the same universe, it would instantly collapse on itself and begin anew. There was also a theory that this had already happened.
- mxcrossb 6y agoMaybe you should add (2019) to the title
- dang 6y agoAdded. Thanks!
- mynegation 6y agoThat looks similar to factoring - in a sense that it is “hard to solve, easy to verify”. Could this be a new basis for asymmetric cryptography?
- metalliqaz 6y agoNot unless there is proof that any number has one and only one set of three cubes. I don't think that is true.
- vbezhenar 6y agoWhy do you need that property?
- exged 6y agoWhat you want for asymmetric cryptography is "always hard to solve, easy to verify". Only a very small number of problems are believed to fall in this category, including factoring and discrete logarithm. It's far more common to have problems that are "sometimes easy to solve, sometimes hard to solve, easy to verify". That describes this problem as well as most NP-hard problems that with good heuristic solutions. The problem is those "sometimes easy to solve" cases break your cryptography!
- xmprt 6y agoHow do elliptical curves fit into this?
- pdpi 6y ago“Discrete logarithm” in this context alludes to the problem of calculating discrete logarithms for elliptic curves over finite fields.
- ColinWright 6y agoNot necessarily, the term "discrete logarithm" also alludes to calculating them in other contexts such as modulo p for p prime. It's not always on elliptic curves, and when I started in this field it was never on ECs. But your comment is largely true, this is a minor point ... I make it only for completeness, and for people who later find this comment.
- saagarjha 6y agoEarlier discussion: https://news.ycombinator.com/item?id=19492091 https://news.ycombinator.com/item?id=19492091 Related: https://news.ycombinator.com/item?id=20895776 https://news.ycombinator.com/item?id=20895776
- bryan0 6y agoThey’ve since solved 42 as well. This problem is detailed in a series of Numberphile videos which popularized the problem.
- jansan 6y agoDo you know which is the lowest currently unsolved number?
- jhncls 6y agoWell, wikipedia writes The only remaining unsolved cases up to 1,000 are 114, 390, 579, 627, 633, 732, 921 and 975. [0] https://en.wikipedia.org/wiki/Sums_of_three_cubes https://en.wikipedia.org/wiki/Sums_of_three_cubes
- TwoBit 6y agoDoes this pursuit amount to anything more than mathematical masturbation?
- TwoBit 6y agoCan PC GPUs solve this kind of problem?
- pdpi 6y agoOne of the terms in the solution is a bit bigger than 2^51 so its square is around 2^102. Assuming the methods used need to actually compute these numbers, you’ll need something bigger than a 64-bit int. Not sure how good GPUs are going to be at bignum-ish stuff, but it’s not the most obvious fit
- meddlepal 6y agoExcuse me for being a bit of a moron here, but why do we spend so much time, energy, and money trying to solve these weird mathematical questions? What's the practical application of any of this that can justify the cost?
- Kranar 6y agoIt's a fair question mostly because of how effective math has been at solving practical problems, but honestly working on problems like these is usually due to a genuine appreciation and enjoyment of mathematics. I'd even say the majority of mathematicians study math strictly out of a sense of wonder and curiosity rather than towards a commercial application and that the vast majority of math research is not at all practical. The cost is justified due to a common shared interest in the subject, many other people are interested in math and pay people to work on it. It's not all that different than paying someone for music, or a painting, or to write a work of fiction. People get a profound sense of enjoyment and happiness from this work and are happy to pay the cost for the continued advancement of this field.
- marcianx 6y agoThe article touches on this with: > k = x³ + y³ + z³ is what number theorists call a Diophantine equation — a kind of algebraic structure whose properties have fascinated mathematicians for millennia. “They’re rich enough to encode [other mathematical] statements that have nothing to do with Diophantine equations,” said Browning. “They’re rich enough to simulate computers.” More specifically, equations of such form come up in a proof of Godel's first incompleteness theorem. That being said, yeah, this effort is mostly a mathematical curiosity, mapping out the domain of knowledge of mathematics increasingly more completely. Sometimes an application comes about where either the solution or novel techniques used to arrive to the solution can become useful, but pure math research isn't typically driven by any existing applications as much as a "because it's there" attitude.
- redis_mlc 6y ago> Excuse me for being a bit of a moron here It's beyond being a moron - you're acting like a caveman. Math is the language of logic and science, and allows the world to express how everything works. Once a problem is solved mathematically, that can be used as a tool forever. You should be asking why HN has a weekly UFO post, or what will be accomplished in killing people by sending them on a one-way trip to Mars. The fact that you don't understand an enormous field like math should make you respect the people who can even more.