A maths proof that is only true in Japan • Hacker News Board

Re: A maths proof that is only true in Japan

#71

Post by bubblyworld » Fri, Jun 06, 2025, 4:48 PM UTC

kamaal wrote: post #69

netsharc wrote: post #54

Earlier quoted context omitted.

It's interesting how the debate is transferable to other topics. In theory maths should be able to be broken down to its basic components and be proven to be all true, or if something is false, then the whole thing collapses. But in practice things like this become so complex that it becomes a matter of conviction, influenced by things like ego. Now imagine taking something like biology and vaccines. What happens if…

>>In theory maths should be able to be broken down to its basic components and be proven to be all true, or if something is false, then the whole thing collapses. >>But in practice things like this become so complex that it becomes a matter of conviction, influenced by things like ego. Isn't this like doing a bunch of AND , OR operations? How does ego become a factor here? Either an expression evaluates to true or fa…

That's true, but in practice mathematicians rarely check a proof to that level of detail. In fact, they rarely write a proof at that level of detail. There just isn't enough time to do that for every result/review, so people take shortcuts. Most of the time it's fine because trained mathematicians take good shortcuts, but sometimes things slip through.

Re: A maths proof that is only true in Japan

#72

Post by scentoni » Fri, Jun 06, 2025, 4:56 PM UTC

simiones wrote: post #43

zkmon wrote: post #8

What can be proven depends on what is allowed be a part of mathematics and logic. Zero, negative numbers, imaginary numbers and a lot other stuff had go through the acceptance first before they can be used in proofs. A lot of foundational concepts in logic, reality, causality, boolean exclusivity, spatial locality - had to be rewritten due to advances in quantum physics etc.

While there used to be resistance to coming up with new formal systems that played with loosening certain restrictions in long-used systems, I think this has not been true for a long time. If you want to come up with a new set of axioms of arithmetic today in which pi = 3, and you can actually come up with a set of meaningful axioms and prove some interesting property of this formal system, I don't think it would be…

In taxicab geometry, π=4 https://en.wikipedia.org/wiki/Taxicab_geometry

Re: A maths proof that is only true in Japan

#73

Post by BobaFloutist » Fri, Jun 06, 2025, 5:31 PM UTC

Barrin92 wrote: post #39

Qision wrote: post #32

What is so special about IUT? They say the theory is "out of this world" but in what sense exactly? Did Mochizuki found a new interesting way to look at some ideas?

It's extremely complicated. The original document he wrote up was 500 pages of maths introducing effectively an entirely new theory. I studied number theory in uni, tried to read it, and understood barely anything of it. Which obviously leads to the epistemological problem that the article points out. You had extremely good mathematicians like Scholze look at it and thought he found a flaw, then one guy from Arizona…

It kind of introduces a fun thought experiment, of a super high-level, complex equivalent of the Monty Hall Problem (which is so counterintuitive that even very intelligent and mathematically literate people will outright refuse to accept the established truth). How would we ever establish truth on something so monstrously complicated that only ~10-100 people in the world could possibly understand and at the same time so divisive that there cannot be a strong consensus?

Re: A maths proof that is only true in Japan

#74

Post by cubefox » Fri, Jun 06, 2025, 5:55 PM UTC

thaumasiotes wrote: post #22

KK7NIL wrote: post #18

Earlier quoted context omitted.

We went through this over a 100 years ago, math now sits on very solid axioms (look up ZFC), they're not questioning that.

> math now sits on very solid axioms (look up ZFC), they're not questioning that. People question C all the time. That might be the most prominent ideological difference in mathematical philosophy. Does it matter? Of course not, but people question it anyway.

Logicians and philosophers of mathematics have also questioned ZF set theory and "set theory" more generally.

For example the axiom of infinity (by finitists), the power set axiom and first-order theories in general (the downward Löwenheim-Skolem theorem implies that the infinity and power set axioms can't guarantee the existence on an uncountable power set), the fact that ZF doesn't allow a set of everything, and in particular no proper set complements, the fact that the axiom of regularity seems to be useless, etc.

Of course most ordinary mathematicians don't care about all that, because they don't care about ZF(C) or set theory or the foundation of mathematics in general. They rather care about problems in their specific field, like algebraic topology or whatnot.

Re: A maths proof that is only true in Japan

#75

Post by zkmon » Fri, Jun 06, 2025, 7:12 PM UTC

KK7NIL wrote: post #70

zkmon wrote: post #38

Earlier quoted context omitted.

200 years passed by between Newton and Einstein. 100 years is tiny in the evolution of thought and is no basis for shutting the questions down.

I wasn't trying to make an appeal to authority due 100 years having passed, that was tangential to my point that almost all modern math now sits on formalized axioms, which it did not do before the foundational crisis in math was resolved (about 100 years ago). Comparing the axioms of math to relativity in physics is just nonsensical. Math is independent of observation, if a proof is formally correct now, it will alw…

Math is not independent of observation. Math sits on logic which itself sprouts from human experience with the world around them. Math and logic are not alien pure forms isolated from this world. There is not even single concept of logic that is not fully tied to the human experience and perception (of the world).

The concepts such as true, false, equal, greater than - all refer to human experience with counting things or perception of existence etc.

Re: A maths proof that is only true in Japan

#76

Post by thaumasiotes » Fri, Jun 06, 2025, 7:35 PM UTC

anthk wrote: post #68

david-gpu wrote: post #60

Earlier quoted context omitted.

Spaniard here as well. What we call "ataque de nervios" (a nervous breakdown) in Spain may not match the usage of that term in Puerto Rico, as it is discussed in the Wikipedia article. Just because Puerto Ricans and Spaniards speak dialects of the same language doesn't make our culture all that similar, as you surely know. I would even say there is little in common culturally.

Ah, TIL. Maybe centuries ago all of the breakdowns/dissociations were under the same mental basket...

We have the expression "attack of nerves" in English too, but I wouldn't expect it to represent anything like a nervous breakdown. It's not a strong term. Generally it would be provided as e.g. the reason you changed your mind about something.

Re: A maths proof that is only true in Japan

#77

Post by BrandoElFollito » Fri, Jun 06, 2025, 8:50 PM UTC

bubblyworld wrote: post #27

When the likes of Peter Scholze (fields medal!) and other very high profile mathematicians find (serious) flaws in every posted manuscript about this... I mean, it's pretty clear to me what's going on. The proof just doesn't go through. I think the intrigue is mainly that it's at such a high level that lay mathematicians (like me) have no hope of understanding the debate. It's a situation that lends itself to crazy s…

At some point you need to trust the scientific consensus, you can only go so far in checking the data (or math).

I have a basic understanding of physics, despite having a PhD. I am not saying this to fake modesty - this is a fact. Most of what is happening in physics is beyond me, not to mention maths (which I had at an advanced level).

Physics taught me to have a bullshit detector when I read articles about "soft" science (and let's admit that this is not a very difficult task), but anything that requires deep, hard knowledge I must just trust.

Re: A maths proof that is only true in Japan

#78

Post by Ferret7446 » Sat, Jun 07, 2025, 12:12 AM UTC

BrandoElFollito wrote: post #77

bubblyworld wrote: post #27

When the likes of Peter Scholze (fields medal!) and other very high profile mathematicians find (serious) flaws in every posted manuscript about this... I mean, it's pretty clear to me what's going on. The proof just doesn't go through. I think the intrigue is mainly that it's at such a high level that lay mathematicians (like me) have no hope of understanding the debate. It's a situation that lends itself to crazy s…

At some point you need to trust the scientific consensus, you can only go so far in checking the data (or math). I have a basic understanding of physics, despite having a PhD. I am not saying this to fake modesty - this is a fact. Most of what is happening in physics is beyond me, not to mention maths (which I had at an advanced level). Physics taught me to have a bullshit detector when I read articles about "soft" s…

Science is very different from math. In math you can formally prove hypotheses. In science you cannot formally prove hypotheses, you can only reject hypotheses.

Re: A maths proof that is only true in Japan

#79

Post by [deleted] » Sat, Jun 07, 2025, 12:23 AM UTC

Ferret7446 wrote: post #78

BrandoElFollito wrote: post #77

Earlier quoted context omitted.

At some point you need to trust the scientific consensus, you can only go so far in checking the data (or math). I have a basic understanding of physics, despite having a PhD. I am not saying this to fake modesty - this is a fact. Most of what is happening in physics is beyond me, not to mention maths (which I had at an advanced level). Physics taught me to have a bullshit detector when I read articles about "soft" s…

Science is very different from math. In math you can formally prove hypotheses. In science you cannot formally prove hypotheses, you can only reject hypotheses.

[deleted]

Re: A maths proof that is only true in Japan

#80

Post by lucyjojo » Sat, Jun 07, 2025, 1:15 AM UTC

fallingknife wrote: post #53

bubblyworld wrote: post #27

When the likes of Peter Scholze (fields medal!) and other very high profile mathematicians find (serious) flaws in every posted manuscript about this... I mean, it's pretty clear to me what's going on. The proof just doesn't go through. I think the intrigue is mainly that it's at such a high level that lay mathematicians (like me) have no hope of understanding the debate. It's a situation that lends itself to crazy s…

The most damning part to me is that Mochizuki dismissed Joshi's work and insulted it. That's a crazy response to someone trying to improve on his theory, and shows more of a religious belief that a mathematical conclusion.

there are so many cases of genius weirdos that it seems unfair to judge them using a commoner social framework.

moreover we only have very partial information about the whole thing.

we simply have no idea and can't honestly deduce nothing of value. this was a funny read but i'll forget it in maybe 10 minutes.