"Helping humanity" is notoriously hard to measure, not least because people who are going to live in the 25th century are also part of "humanity" and yet we do not know how their world is going to look like.
Mathematics in general is a bunch of stuff that often looks useless to laypeople or even professionals and may look so for 200 years until it very suddenly becomes relevant and crucial.
The computer that you used to post your comment uses a lot of mathematical stuff developed in previous centuries. It is unlikely that Gauss or Euler could have predicted that their work (ink on paper) will one day be used to facilitate completely different modes of communication.
And it is well possible that some priest criticized them for wasting their talents on abstract things that don't help humanity as of 1800.
Apples and oranges. Naming more mersenne primes does not constitute discovering new mathematics. It's really very hard to argue that this is a good use of computing power.
Sure, pure mathematical theory has a tendency to become useful later, but finding specific Mersenne primes is not pure math.
It’s not known if there is an infinite number of Mersenne primes (though it is strongly suspected) - so an interesting mathematical object to discover would be ‘the largest Mersenne prime’ - but this process isn’t going to find that (it might find a candidate but it won’t find a proof). If there are indeed infinite Mersennes then this search is just guaranteed to keep finding more forever.
It’s like looking for green pebbles on a beach. It’s nice when you find one to add to your collection, but it’s not that surprising, and if you keep looking you’ll probably find more. You’re not advancing geological knowledge if you keep looking and finding more.
Yes but if you want to say if there are an infinite number of green pebbles on an infinitely large beach then the problem you need to solve is finding the distribution of the green pebbles on the beach. It's only possible to do that once you've found a few green pebbles and gets much easier if you've found many.
We don't know whether the search for further Mersenne primes eventually gives birth to a new algorithm which will enable further advances in other fields.
Cranking on the current best known algorithm for testing for Mersenne primes does nothing to advance the state of the art for other algorithms, though.
It’s like saying, we have a project that keeps sorting larger and larger sets using quicksort because we believe it will help advance the state of sorting algorithms. ‘We just sorted the largest ever set!’
I'm all for putting work to find things out and I agree with you, but for the sake of argument:
Say these are really relevant 200 years down the line, maybe even 100 or 50, does it really make sense to calculate them now, given that computers 50, 100 and 200 years from now will outperform ours by orders of magnitude?
Say you grab a CPU from the end of the 70s and get it working until now, that'd be about 13*10e15 operations, or about a month of processing in a modern 5GHz CPU. That's 40 years to a month.
Mathematics tends to be upstream of technology. I would expect that improvements in mathematical knowledge in general will help us construct even better computers in the future. We are slowly approaching some physical limits, but algorithmic improvements may get us further speed improvements.
IDK about this particular scientific team, but if you have to run a long-running task, you will be a lot more careful about complexity and speed of your data and algorithms instead of relying on brute force. Maybe you will actually discover some real improvements of existing knowledge.
I can even see the effect throughout my IT life outside science. People who cut their teeth on processors with limited power and not enough RAM tend to produce much more efficient solutions even when programming modern computers. They just don't take the gigabytes and gigahertz for granted.
Agreed with all of this, well put. I’d like to add though that we don’t do math just because we anticipate there will be some practical utility in a different field down the line. Mathematics isn’t merely a prerequisite for engineering. Does it not suffice that we study math for the sake of it?
The Mersenne primes for example are a delightful little mathematical object. IMO they are immediately curious and interesting. I am very grateful that we continue to make progress in understanding them.
I once had a math PhD friend tell me that if they ever became aware of any practical applications to their research, it would probably lose all interest to them. I’ve always found that to be curious and a good reminder that others can have radically different beliefs to my own in unexpected ways.
The best example I can think of is GH Hardy's work on number theory. He was a pacifist and so specifically wanted to work on something that would not help the war effort. Fast forward 100 years and number theory now forms the basis of modern cryptography - securing everything from your banking details to military communications.
We often don't know what the applications are at the time, but that pure mathematics work very often forms the foundation of something important later on.
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Could someone tell me as a layperson, how finding these numbers is helping humanity?
When people give such an argument, they usually mean "I am not interested in this topic" and use "why is this helping humanity" as an excuse for their ignorance.
I’d say it’s worse, they’re usually trying to imply that the people engaged in the activity aren’t sufficiently allied with their pet political or moral causes. If you engage with their tweet-sized sniping the conversation inevitably leads to “why aren’t they spending their time and resources addressing climate change/wealth inequality/poverty/etc.”
Such arrogance. It's funny that you mention climate change because this project is a non-negligible use of energy that is indefensible even in the context of advancing "pure mathematics." It's literally computation for the sake of computing more things that haven't been computed before. The only end result is that we can say we computed more things.
Thanks for the jab but you are wrong, this is not how I meant my question. I am genuinely curious, as someone who has benchmarked their computer with prime95 and is not particularly mathematically inclined.
"When people say that other people usually mean X when they ask something, they are just ascribing that motive to another person, even if it is not what the asker has meant."
On a different eon that might be true but nowadays compute power - electricity - global warming. Given that, “frivolous” work that just burns energy could be potentially postponed until we go fully renewable in our energy stack.
There seem to be many frivolous uses of power to complain about when you get to this level of power use.
GIMPS' ~1PetaFLOPS[1] uses no more than a megawatt [2].
That's about 10 Gigawatt-hours (GWh) over a year [3].
The average US house uses about 10 MWh in a year [4] so GIMPS = the electrical power use of ~1,000 households. Portland reduced their power consumption by 20 GWh by switching their street lights to LEDs[5].
The electrical consumption for Superbowl parties is an estimated 75 GWh [6]. (I think Superbowl parties are far more frivolous.)
I see this question getting downvoted, and some of the responses are strangely hostile strawman attacks based on what those posters are guessing this person "really" means. I think this is a perfectly reasonable question.
A few years ago, I got a PhD in pure mathematics (low dimensional geometry and topology). As someone who loves pure math and spent many years devoted to it, I've had many conversations with mathematicians about whether we should be concerned with practical applications. One common argument, which several people have made here, is that there's been a lot of math that found practical application long after it was done. That really only applies to a very small proportion of math. The vast majority of math done has still never found application. So arguing that we should do that math because it may have applications later is kind of like arguing you should play the lottery since there's a greater than 0 chance that you'll win. Also, from the (admittedly biased) group of mathematicians I've spoken to about this, very few seemed to actually do math in the hope that it would be useful later.
Instead, people do math because it's interesting, beautiful, and challenging. I would argue this Mersenne Prime search is almost more like recreation. I could be wrong, since I never did much number theory, but I don't think this is advancing any research. It's just a fun hobby for people who enjoy math. I think doing math for the sake of its beauty is generally fine. I do have concerns about the climate aspect of this particular project though. This is a lot of power being consumed just for recreation. This project may not be big enough to have much of an environmental impact, but in general, I think we should be more mindful of not wasting large amounts of computing power just for fun.
I don't care about upvotes/downvotes but it was interesting that I got upvoted at the beginning and got a few useful responses, and then at some point a user above made an ad hominem attack and then the mood changed after my motivations were called into question. Suffice it to say, my question came from a place of curiosity not judgment.
RSA cryptography is is based on the assumption that factoring numbers is a hard problem. Isn’t kind of nice to know that there curious people trying their best to see how fast you can actually get?
Primality tests for Mersenne numbers are highly specialized. It's possible that they could advance factorization of general numbers, but extremely unlikely.
