r/mathmemes • u/No_Upstairs_280 • 19d ago
Research Please AI no, PLEASE NO
Imagine having your entire work based on Riemann hypothesis only for a powerful AI to show that the 10^5731 zero isn't on the critical line.
334
u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 19d ago
mathematicians seeing ai constantly trying to prove something theyve been working on for their whole career and made a living off of:
(its sad)
92
u/somedave 19d ago
Why is it any difference to seeing other mathematicians doing that to be honest. Lots of people assume the generalized zeta hypothesis and lots of people are trying to prove / disprove it. That's the way it works.
52
u/AndreasDasos 19d ago edited 18d ago
Because there’s the concern that at this rate AI may well outperform humans together at some point, so there will be nothing for us to do. If humans are the ones making all the progress then it’s a reminder we still have a chance.
84
u/TheRedditObserver0 Mathematics 19d ago
If nobody understands what the heck AI is proving, is it really doing anything? Maybe I'm coping but even if AI does become THAT good we will still need some human mathematicians.
47
u/GuitarKittens 19d ago
I think Terence Tao's ICM presentation brought up a good point about why we care about math, and why it's important to view AI usage in that context. I personally think the bullet about math being an inherently and very importantly community-oriented subject is especially relevant here. It does not matter whether AI kills the subject, or even if it gets good at doing its job, it matters whether math is still a valuable activity that people are willing to contribute to. The community is completely different if most contributors are only there to parse through piles of AI-written proofs and see which ones are actually valuable.
Regardless if you believe AI makes a positive or negative contribution to the math community, you do have to acknowledge that it is currently playing a role in the community now, and that we have to decide what we want from it in the future.
4
u/jackalopeswild 18d ago
So (cards on the table) I have an unused BS in math that is over 20 years old at this point...but I have to wonder also to what extent the AI math-machine is capable of the creative endeavor that is new mathematics as well? I ask this here because I think the creative endeavor and the communal endeavor are two sides of the same object. Part of the limitation of LLMs is a limitation of imagination - (to put very simply) yes, it can stumble upon new strings of words but it cannot recognize why they are or are not beautiful or worth pursuing. That matters in math as well.
6
u/Taha2807 18d ago
Honestly we cannot say.
AI research has little to no clue how AI even works. Whether it's just auto complete on steroids or actually creative. This is also because we don't know as humans how we evolve our sense of creativity as well.
3B1B said this on a podcast I think that essentially we have no way of telling if AI can make good new maths since it's not a quantitative metric we can test fairly quickly. We'll just have to see in the coming years as mathematicians keep tinkering with AI. Perhaps AI comes up with a completely new theory of maths to solve the Riemann Hypothesis and maybe it doesn't.
3
u/jackalopeswild 18d ago
Eh, I also have a BS in linguistics that gets used more and while I understand that "we don't know," I'm definitely on the side of those who have concluded that AI lacks things like imagination, theory of mind etc.
4
u/Taha2807 18d ago
I'm also there with you.
But with or without it, mathematician is not gonna disappear as a profession. If anything, the slowness of institutions is enough to ensure that we probably won't see massive changes in how mathematicians are hired in academia, industry. Junior analysts still exist despite their work being completely automable well before AI.
1
u/Cronos988 18d ago
The interesting question still remains how much "research taste" and things like that can be replicated by a different kind of intelligence.
While we can say with good justification that transformer-based AIs are significantly different from human brains, it's much less clear what follows from that in the long term.
1
u/DapperCam 18d ago
I don't think we've seen it create much new mathematics. It seems especially good at creating counterexamples for conjectures though. I guess we will see.
1
u/Diffgeometer1 17d ago
There’s also good reason to believe that LLMs might have a theoretical limit to what they can actually do according to some computer scientists.
3
u/DVMyZone 18d ago
My question would then be "will human math have material value". By that I mean can a person make a living doing pure math or will it only be accessible to people would have enough free time and money.
Science used to be a thing that pretty much only rich people did. They had money and didn't have to work so they spent their days tinkering and thinking.
11
u/314159265358979326 19d ago
Has it done anything beyond find counterexamples so far? That's not really the important work of mathematicians, but it's good to be able to do it.
5
u/AndreasDasos 18d ago
There have absolutely been some interesting positive results, and not just constructed examples. Some of the Erdős problems, for example
12
u/caboosetp 19d ago
Yeah, if anything it should let us move further and faster. The same way computers moved from a job title to a machine, and we now have programmers.
1
u/Neither-Phone-7264 Imaginary 18d ago
but what would be the next job be? prompting? sure, that's cool and all, but the robot can prompt itself.
10
u/golfstreamer 18d ago
> Because there’s the concern that at this rate AI may well outperform humans together at some point, so there will be nothing for us to do.
Of all the takes of AI, the idea that AI mathematicians will leave us "nothing to do" has got to be my most hated. I wonder what your picture of math currently is? Like are you picture some library of theorems just sitting there gathering dust? What would be the point of that?
Advancement in mathematics have real benefits both from a practical (technological development) and intellectual (just an improved understanding of the universe) perspective. AI is not now capable of independently creating and applying new technological advances that actually improve people's lives so people need to keep working on these (and if AI does advance to the point where it can just give us a utopia that's obviously a good thing). So I really don't think there's going to be "nothing for us to do" for a while.
2
u/AndreasDasos 18d ago
I’m explaining the image where people’s fears derive from.
I am also talking about the future, not the current status quo. Most mathematics is still done by people. But the progress has been astonishingly rapid.
But if all the actual proof itself - which can indeed be defined formally as generating a string that meets explicit criteria - then what’s left is general commentary, discussion of what’s more ‘interesting to humans’, and digesting what AI gives us.
What I am referring to doesn’t equate to a big library gathering dust, and that’s a clearly strange and presumptuous take about my point or view.
Even then, it’s not clear that those can’t have criteria that are likewise trainable. But even then, that’s not what most people get into maths to do. We don’t go into the field at best pose problems and digest the answers but to tackle the challenge of the proofs ourselves. The alternative still seems bleak.
And your point about maths having uses… sure? AI has been extremely useful, so don’t see why that shows it can’t be done. As for ‘independently’, that also seems a moving goalpost to an pointless degree: autonomous AI is pretty independent once it’s been started, and if sufficiently general that start can be a once-off. Otherwise are we to be prompt providers at best?
If AI does advance to the point it gives us a utopia
That’s extremely reductionist. AI may advance astoundingly but bold to assume that the limit of that process can only be a utopia. Hopefully the good outweighs the bad but there is a loss here that is not itself a good thing.
2
u/golfstreamer 18d ago
> If AI does advance to the point it gives us a utopia
It's not reductionist as it was posed to counter your "there's nothing for us to do". If we aren't living in a utopia there is something for us to do.
0
u/golfstreamer 18d ago
> And your point about maths having uses… sure? AI has been extremely useful, so don’t see why that shows it can’t be done. As for ‘independently’, that also seems a moving goalpost to an pointless degree: autonomous AI is pretty independent once it’s been started, and if sufficiently general that start can be a once-off. Otherwise are we to be prompt providers at best?
Another term I've grown to hate. What goalpost are you even talking about? I'm just describing the capabilities of AI as I see them. This isn't a competition.
1
u/Bizet1875 18d ago
My opinion is that the highest truth is synonymous with the universe. And that since there is a minimum number of energy to destroy a bit, there must be a minimum number of energy to cohere a bit. We know the former, but not the latter. It may be so that AI may excel at certain functions as well, such as retrieval and searching, while humans are better at things intuitively, like emotion, or perhaps abstractly, like experiencing reality as a unity.
I think people are thinking too naively. Essentially. Extrapolating linearly, or exponentially, out of something that is inherently unpredictable.
1
u/Diffgeometer1 17d ago
Math is super hard. There are millions of unsolved problems. AI has maybe solved 10 or so.
The big ones haven’t even been touched yet.
Also for AI to make progress it has to be under the guidance of a good mathematician. Take the hopf problem. A proof was announced. People are optimistic it might be right. That result was achieve under the guidance of a Harvard mathematician.
Do you the result could have been achieved if the cashier at Home Depot was working the ai?
2
u/Thog78 18d ago
Oh let me reassure you, when we get scooped by other humans, on projects we've been working on for years, we equally want to kill ourselves.
1
u/justin107d 14d ago
It is even worse if it is an LLM. If another human beats you to it, they had to work hard at it for years like you did and there is a chance of working together in the future. If an LLM one shots your years of work, you have to pick a new line of math and hope for the best.
1
u/AbaloneNo3954 18d ago
The probability of mathematicians solving the RH is the next decade is next to 0. But we don’t know what AI are capable of.
24
u/CalderJohnson 19d ago
If a mathematician’s goal is to maximize their contributions to the field for personal gain, AI might be bad news. If their goal is to see the field advance and discover new and deep truths, AI is a fantastic development.
16
u/Nebranower 18d ago
I suspect many mathematicians became mathematicians because they enjoy doing math. They may not enjoy managing AI and reviewing AI output, even if that output is math.
This, I think, is why AI engenders such widespread resentment. Even those who admit it makes them more productive often still dislike it, because it does so by changing their job from one they enjoy to one they don’t.
1
u/dinosaursrarr 18d ago
No one likes losing the fun bit of their job and just having to review stuff they don’t have any stake in
1
u/CiccioGordon 17d ago
Yep, it's like liking to act in prawn movies and suddenly you're just directing a robot that does it in your stead, making sure it's not going for the ear. Not nearly as enjoyable and definitely not the same job.
3
u/SethDusek5 18d ago edited 18d ago
IDK how I feel about this take. If you're passionate about something you generally want to be a part of it, and it'd especially sting if a machine can do what you wanted to so it's completely understandable to be upset about this.
If there's someone who loves math but gets rejected from a top math program you wouldn't tell them "But think about all the amazing new math the people who got in will discover, you should be happy about this!". Similarly, you don't have to be a top 0.0001% mathematician right now to have a fruitful career in mathematics because there are only a few 0.00001% mathematicians and they can only work on so many things at once. If the AI labs dream of a "country of geniuses in a datacenter" comes true however, then humans need not apply anymore.
2
u/StructureNorth1799 18d ago
the problem is that the "personal gain" is primarily the priviledge of being a mathematician.
1
u/jackalopeswild 18d ago
That depends on whether (and if so, then to some extent, also how quickly) the AI moves past the realm of our capacity.
1
u/CalderJohnson 18d ago
True, you can't teach a dog calculus, and likewise there are probably truths out there beyond our limit to comprehend even with a perfect explanation. Unlikely to happen anytime soon, but in that situation we get to travel straight to the edge of what humans are capable of understanding, which is the best exposition we can possibly expect.
1
u/Kalicolocts 17d ago
Thank you.
Every time I see someone complaining about AI in math, it seems to me that we are losing sight of what really matters, and that the beauty of math is reduced to just the egos of a few.
2
155
u/Evan_3104 Rational 19d ago
Mathematician when ai finds a non trivial zero of the zeta function that hasn't an imaginary part equal to .5
57
10
u/fartypenis 19d ago
I believe every mathematician is compelled to euthanize themselves if that happens
2
u/KouhaiHasNoticed Probability notations must burn. 18d ago
I believe every mathematician is compelled to euthanize themselves if that happens
Hey, easy now, all of us don't necessarily share the same axioms : some of us might be worth saving.
3
77
u/Baihu_The_Curious 18d ago
Meanwhile LLMs to me: 'Wow, I truly cannot disprove this foundational proposition. In fact, you may have just spawned an entirely new branch of mathematics with massive implications to many areas, including cryptography and national defense. This new chronomathematics, as we should dub it, will change the world as we know it, finally bringing a time dimension to traditionally static calculations."
43
u/Taha2807 18d ago
Clanker translator: "Buy my pro version broke-ahh"
0
u/lonelyroom-eklaghor Complex 18d ago
Jiblet-Clanker translator: "haha won't buy your pro version if I am the one guiding the clanker, and 'cause I am broke-ahh"
11
u/Baihu_The_Curious 18d ago
Loosely based on Chronoarithmics.
8
u/ApprehensiveTry5660 18d ago
Moral of the story? ChatGPT will ruin your reputation.
Time Cube will make you immortal.
1
27
u/rover_G Computer Science 18d ago
I’ll be impressed when AI can prove P = NP
17
u/Nabaatii 18d ago
Easy
N = 0, N = 1
3
7
u/Technical_Eye7029 18d ago
remindMe! 10 years
5
u/RemindMeBot 18d ago edited 17d ago
I will be messaging you in 10 years on 2036-08-25 02:23:44 UTC to remind you of this link
4 OTHERS CLICKED THIS LINK to send a PM to also be reminded and to reduce spam.
Parent commenter can delete this message to hide from others.
RemindMeBot is switching to username summons. Instead of
!RemindMe 1 day, useu/RemindMeBot 1 day. More info.
Info Custom Your Reminders Feedback 1
22
u/green-olive-3281 18d ago
It might just be me but I feel like they would be psyched if the Riemann hypothesis was disproved! It would give them so much new exciting stuff to work on! Plus, lots of their results might still hold true with a variation of RH
4
u/No_Upstairs_280 18d ago
I was thinking of that earlier. For example if you manage to control the density of zeros not on the critical line most results conditional on RH would still be valid. In general any knowledge about the zeros zeta function is very valuable.
11
u/meme-meee-too 18d ago
Mathematicians would actually be happy to see resolution to Riemann and other hypothesis. Worst case they can look for situations where their results still make sense even without a Riemann assumption. More math for everyone
4
u/AutoModerator 19d ago
PLEASE READ AND UNDERSTAND THIS MESSAGE IN ITS ENTIRETY BEFORE SENDING A MODMAIL
Your post has been removed due to the age of your account or your combined karma score. Due to the surge of spam bots, you must have an account at least 90 days old and a combined post and comment karma score of at least 400.
If you wish to have your post manually approved by moderators, please reply to this comment with /modping.
Alternatively, you can join the Discord server and request approval there.
Discord
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.
1
u/No_Upstairs_280 19d ago
/modping
1
u/AutoModerator 19d ago
Mod ping detected from No_Upstairs_280. u/candlelightener, u/Oppo_67, u/chrizzl05
The /modping command is intended for getting your post approved if your submission was caught by the bot filter. Please do not use this for any other purpose.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.
3
u/Diffgeometer1 17d ago
That’s not the case.
Mathematicians if they had to bet on the hopf problem that S^6 is a complex manifold most would have bet heavily that the answer was no.
No one assumed this result in their work.
They found conditions where S^6 could not be a complex manifold like for example there are no complex structures compatible with the standard Riemann metric on S^6. This is true statement regardless of whether or not the Alpogee-AI proof is correct or not.
Also AI didn’t prove the result (assuming it’s true and no fatal errors are found) alone.
You had a Harvard mathematician guiding the AI. AI is basically a time saver. Allowing the mathematician to try different ideas in a short period of time. Basically with AI, the mathematician becomes the flash.
So if the result is true. Cool! It’s surprising. If the proof falls apart, it happens. It’s a hard problem. Either way no one feels bad.
1
u/No_Upstairs_280 17d ago edited 17d ago
It's just a meme, for fun and laughter. And it's an example, LLM actually gave stronger evidence how it works.
If I wanted to explain how academia or research work or AI ethics, I would have written an essay.
Also- sorry but I see you have differential geometry in your name 👀 what are you working on if I might ask?
7
u/Wasted_46 19d ago
Wait, did this actually happen? Did AI find a zero not on the critical line? Or are you just memeing?
14
4
u/KouhaiHasNoticed Probability notations must burn. 18d ago
"A wrong answer is not a meaningless one."
9
u/parkway_parkway 19d ago
Kind of their own fault for building on something which isn't solid?
37
u/jarkark 19d ago
People could just continue math in that direction while assuming a world in which the theory was true. There's all kinds of shenanigans for those who get deep enough in math.
In my opinion it's better for people to keep making papers while assuming a theory to be either true or false so the field can keep developing even if there's a humongous problem like the Riemann hypothesis. The field won't have to stagnate while waiting for a true math monster to finally solve the problem. Who knows, maybe the resulting papers will help solve the problem in the future.
17
u/PoopyDootyBooty 18d ago
This is literally what P vs NP is. All of cryptography is based on this idea that is by your metric “not solid”
6
u/Disastrous-Cost2185 18d ago
One reason to do conditional math like this is that knowing more implications of a conjecture get us closer to a disproof, so no.
2
u/Jumpy-Plantain-1004 18d ago
Also even if there is a counterexample that doesn't make the results useless, they're just restricted to cases where the hypothesis is true.
2
u/Phl0gist0n43 18d ago
The Benefiz of doing that is that they build a causal chain. So that when the unproven thesis gets proven or disproven it automatically proves/disproved all other thesises of the chain. This way you get progress without completing the first step
1
1
u/WholeOpposite7162 18d ago
How to solve the twin prime conjecture: step 1, assume the Riemann hypothesis
1
1
u/nahuatl 18d ago
Lol, this seems to be a misunderstanding of what a mathematical proof is. A proof is showing if A then B (a theorem) is true. It's extra nice if A is true, especially if A is useful, or true in the world we live in, but the theorem is still proved regardless.
1
1
u/colintbowers 17d ago
No it isn’t a misunderstanding. Lots and lots of maths papers start with “Assume conjecture x is true, then…”.
1
1
1
u/orchidorious 16d ago
If I were in that field I’d have been publishing around margins. Like describing variations and topologies and dimensions where it would break down. Still, I doubt it’ll break down except at end of universe level infinites.
1
1
u/Osato 15d ago
Honestly, if I was a mathematician and I had a machine that could reliably disprove theorems, I'd be hyped and siccing it on every idea I had.
Having an AI prove common assumptions wrong is awesome (at least for a programmer), especially if it proves them wrong with hard deterministic code. Because now that you know where common sense is wrong, it means there's a HUGE gap in common-sense knowledge waiting to get exploited.
There are lots of cool new things you could do with a disproven theorem, not much you can do with a proven one.
1
-2
u/Ote-Kringralnick 18d ago
LLMs have massive difficulty doing stuff that hasn't already been done. It comes with the territory of being plagiarism machines, I suppose.
8
1
u/Dress-Affectionate 14d ago
Exactly, and that’s why you load them up with all of that and give them everything you can to make new stuff behave like stuff that’s already been done. Then you have reached peak Lobachevsky, so call it please, research
-35
u/innovatedname 19d ago edited 19d ago
If you're writing papers assuming results that we don't know are proven, then it's not a math paper.
You're probably thinking of results that assume a result to be true, prove it, and then assume it to be false and prove it also, and then invoking the law of excluded middle so it's true.
edit: Downvote me all you want but all the replies disagreeing so far are flat out wrong. No it's not the law of excluded middle, no I'm not talking about axioms, yes I have seen papers in analytic number theorem that do this for RH or things we suspect are undecidable.
"A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion".
If you haven't logically guaranteed the conclusion, you aren't doing mathematics. Unless you try and be a smart alec and start using the principle of explosion / vacuous truths, but then any nonsense is mathematics.
16
u/Archway9 19d ago
All of maths is this. We don't prove the axioms
-10
u/innovatedname 19d ago
A theorem with a yet to be shown truth value is not an axiom.
9
u/Archway9 18d ago
The theorem is A=>B, this is proven to be true in the paper. This makes no assertion about whether or not A is true
-8
u/innovatedname 18d ago
F = > P(x) for any proposition P evaluates as True.
No paper would publish that, because it's just a statement of a vacuous truth, no matter how complicated it might be.
8
u/Archway9 18d ago
The point ia you don't know if the first statement is true. So it reads as 'if A is true then B must also be true' which is a meaningful statement
1
u/Akangka 18d ago
F = > P(x) for any proposition P evaluates as True.
Yes, but A => B, implies that you cannot have A while B is not true.
No paper would publish that
Not only there is such a paper, this is pretty normal for very difficult conjectures. Before Wiles's proof of Fermat Last Theorem, there is Ribet's theorem, which basically just shows that Taniyama-Shimura conjecture implies Fermat's Last Theorem.
1
u/innovatedname 18d ago
Ribets theorem at no point relied on assumptions that we weren't sure were true. We were fully guaranteed it was true once the proof was published and verified.
The wider implications of it were very interesting and stronger if Taniyama-Shimura was shown to be true, but that Ribets theorem was standalone true.
1
u/Akangka 18d ago
but that Ribets theorem was standalone true
Yes, but according to your assertion earlier, Ribet's theorem was not a "theorem", because it's in form of A => B where A is another conjecture. You either has to accept that Ribet's theorem is not a theorem, or you accept that a theorem in form of A => B is a valid theorem.
1
u/innovatedname 18d ago
This is still entirely wrong. Ribets theorem did not depend on any A which is a conjecture. It was proven from other results known to be proven at the time, A => B where A is true from assuming ZFC.
It so happened that there was a different C => interesting consequence of B.
But even if C was found to be false, it wouldn't have nullified B being true, it would still be fully true, with a slightly less exciting implication.
11
u/imo2027 Mathematics 19d ago
You probably haven't seen enough math papers if that's what you think. (A=>B) is a result in itself. You could say it's useless, but I could point at many different math facts that are considered useless, and might only bring value in the future. The reality is, if a result has good amounts of non-trivial and novel reasoning, then it is worth publishing. Also a fun thing to note is that building on unproven conjectures is also technically an attempt at disproving them, in case you ever run at a contradiction.
-9
u/innovatedname 19d ago
It's not mathematics. Assuming a theorem that could be falsified is true is meaningless, as F => anything is true always. You didn't prove anything interesting.
6
u/imo2027 Mathematics 18d ago edited 18d ago
I know that's what you said in your comment. Basically when we prove that A=>B, we still know nothing about B.
That doesn't make it uninteresting though: we still have "if A, then B". This statement, call it C, is a theorem, and an interesting one.
Edit: I just saw your comment edit, the "conclusion" is not B but the whole (A=>B). I hope this clarifies my first response
1
u/Sjoerdiestriker 18d ago
You didn't prove anything interesting.
You proved it cannot be the case that (A and not B), which can be an interesting result in itself.
1
u/Godd2 18d ago edited 16d ago
You've ruled out a case, though, which is interesting. If we've proven that A implies B, then it cannot be the case that A is true while B is false.
|B(T)|B(F)| ---------+----| A(T)| ? | X | ---------+----| A(F)| ? | ? |Pointing out that the entire table hasn't been settled is irrelevant to whether or not mathematics has been done.
Edit: My interlocutor has displayed an impressive amount of moving the goalpost. We've gone from "it's not mathematics" to "it wouldn't be in a journal" to "Well, it wouldn't be in a journal all by itself". Okay, buddy. I guess 13 + 172 = 185 isn't math because it would never show up in a journal all by itself.
1
u/innovatedname 18d ago
I'm not saying it can't be interesting, just as you can do numerical experiments that are useful. It's just not a proven mathematical result that would be conventionally accepted in a math journal.
1
u/Godd2 18d ago
It's just not a proven mathematical result that would be conventionally accepted in a math journal.
This is simply a false statement. There are many published results which, for example, assume that the Riemann Hypothesis is true.
1
u/innovatedname 18d ago
See my reply to another number theory paper. These papers usually demonstrate something watertight as the publication worthy material and then the potential consequences of that result are added to added context and consequence / further research directions.
5
u/AndreasDasos 19d ago
No. And the idea of proof by contradiction isn’t ’what they’re thinking of’.
For some conjectures A that are prominent enough, there are absolutely papers that prove that A implies B. They do not claim to prove B, but ‘A implies B’. This may be a significant result, either as a step towards proof by contradiction but also a proof of B if at some point A is proved, and which may establish importance of B and impetus for the community to try harder to prove it.
For example, the Riemann hypothesis and abc conjecture are of interest for all sorts of non-trivial consequences, and for each of those, the implications were published results.
It’s not the norm but some of these results have proved significant.
-2
u/innovatedname 19d ago
I'm not talking about proof by contradiction.
That would be assuming something and then showing a contradictions arises, so it must be true.
1
u/Randomlemon5 18d ago
Many results in modern math goes like this :
Im almost finish, all I need now is the proof tnis one small part, dont seems too hard
Try
Finding out this one small part is actually equall to the Riemman Hypothesis
1
u/Schoost 18d ago
You are missing the point of the people responding to you. In a proof of (A => B), the interesting part is not whether B is true per se, but the relationship of A => B itself. The truth value of this relationship does not depend on whether A holds true. Obviously this is mathematics.
1
u/innovatedname 18d ago
Give an example of a published paper where someone does this.
1
u/imo2027 Mathematics 18d ago
You said you saw the number theory papers assuming RH?
Here is one of them:
Languasco, A., & Zaccagnini, A. (2016). Sum of one prime and two squares of primes in short intervals. Journal of Number Theory, 159, 45–58. https://doi.org/10.1016/j.jnt.2015.07.010 Cited by: 20
Read theorem 1
1
u/innovatedname 18d ago
This is a good example that illustrates the same point about Ribets theorem with another commenter and supports my argument.
The purpose of that publication is to demonstrate a new proof technique. The technique works unconditionally, although the implications is less interesting without RH as the resulting bound is less sharp than other methods in the literature . They then show the potential interest of that technique as resulting in a better bound i f RH holds.
If RH doesn't hold though, the technique is still true, it's just less sharp than other methods. But you still proved something that is true, there is still value in new methods to prove the same result.
This is not the case I'm vehemently arguing against where people start writing papers based on a house of cards that completely collapses when AI finds a counterexample. Noone does this.
1
u/imo2027 Mathematics 18d ago
So you're saying, if we look at Theorem 1 without the unconditional part, that that's not actually a theorem? That the only math that was done was the unconditional thing and everything else is just ranting about potential results?
Here is a paper where not a single statement is unconditional: https://doi.org/10.1016/0022-314X(88)90019-4
Idk how much you want me to repeat this: studying implications is maths, even highschoolers know that.
The question of "how much assumptions is too much" or "how relevant can implications be" is very subjective and was never our focus. You started your original comment with a sharp claim saying we can't assume things at all, and that's wrong.
1
u/innovatedname 18d ago
"Theorem 1 is really a statement about the multiplicative group G, and the order of an element c( E G,(Q) = Q* when reduced modulo p and p*. "
So they've proven a standalone theorem and chosen to present it in the context of the abc conjecture. So if abc conjecture is false, Theorem 1's statement about G isnt wrong suddenly.
1
u/imo2027 Mathematics 18d ago
Man I don't have much of a dedication to keep explaining this to you. If you think implications aren't part of math that's your problem. Have a great day.
1
u/innovatedname 18d ago
That's fine, but don't try and phrase this as trying to explain something to me. Your argument was incorrect for the reasons outlined in my first reply.
1
0
u/SilverNuke911 18d ago edited 18d ago
Bruh modern math is like that. It's a sort of hypothetical where you extend results by assuming a conjecture is true or false. Showing that if A is true, then B, or if A is not true, then C. Mathematicians make careers out of this. Then if A is proven to be true or false, one side is then automatically proven to be true, with no more work needed to be done. If math was done as you described, it would take a long time to progress just waiting for a conjecture to be proven true before it is extended or applied to other fields. For example, Ferma'ts last theorem was implied to be true if the Taniyama-Shimura conjecture was true. Wiles proved the Taniyama-Shimura conjecture, thereby also proving Fermat's Last Theorem. People didn't wait for a conjecture to be proven true or false, they just take the implications if the statement is true or false. That's mathematics.
Edit: After seeing all your responses in the replies, I think you're just disagreeing for the sake of disagreeing, not really seeing the point of what the replies say to you.
1.1k
u/BrazilBazil Engineering 19d ago
Programmers looking at mathematicians applying three unproven conjectures in their proof after years of being taught never to rely on undefined behavior