[bubblyworld]

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 speculation, because nothing you say about it can easily be challenged.

[aleph_minus_one]

> 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.

On the other hand, Ivan Fesenko (also a heavyweight; he is for example the PhD advisor of the Fields medalist Caucher Birkar) insists that Mochizuki's proof is correct.

* Here is a popular scientific article from 2016 where Ivan Fesenko presents his perspective on this topic: https://inference-review.com/article/fukugen

* A popular scientific article by David Michael Roberts (also a renowned mathematician) from 2019 about where he believes an important contentious point in the different viewpoints of Scholze/Stix vs Mochizuki lies: https://inference-review.com/article/a-crisis-of-identificat...

[bubblyworld]

Fantastic links, thank you. When I say Scholze and friends disagree I mean they seem to have specific mathematical criticisms with mochizuki's school that have not been addressed publically, not just "structural opinions" (for lack of a better word). For instance, see Sawin's answer here: https://mathoverflow.net/questions/467696/global-character-o...

But that's fair, it's not exactly one-sided, but to my (completely inexpert) judgement the matter seems heavily weighted against mochizuki?

[fallingknife]

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.

[lucyjojo]

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.

[BrandoElFollito]

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.

[Ferret7446]

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.

[BrandoElFollito]

Yes, you are of course right.

My point is that even with a formal advanced education on an area (say -- physics), you are bound to weight the "consensual appraisal" of the authors of a claim to make up your mind.

With my PhD (and having left academia after it), I can easily determine that homeopathy is physical bullshit. It may very well work for different reasons (placebo effect), but when I read about people who try to explain that cosmic rays this or quantum energy that -- I know they are idiots.

And then came Jacques Benveniste who was published in Nature with his "water memory" hypothesis. Holy shit - physics has just changed! Why? Because it was in Nature.

Nature then realized this is a scam, retracted the paper, and physics is back on its (unfortunately) boring track (there is nothing that physicists hope more than a radical revolution in physics)

So we need to trust people who have the right titles, university affiliation, track record on TV and whatnot. In biology, despite having worked in some areas there, I have even less trust in myself.

Then comes the "-logy" soft science where it is not difficult to check that what they say makes sense or not just by looking at the math (which is simple, but can be very deceiving)

And then comes math itself. There can be a definitive answer, as you say, but the proof is completely beyond mere mortals. If you look at the Fermat's conjecture proof (a very simple conjecture, which also makes its beauty), it is completely unreadable for someone who is not in the subject. I did a lot of math and past the 10th line I am done.

[netsharc]

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 you rely on your experts and other rely on theirs, and they disagree?

[kamaal]

>>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 false. There are only two outcomes, why is there a confusion here.

[bubblyworld]

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.

[bubblyworld]

Yeah, it's true, there is politics in mathematical truth, for better or worse. That is slowly changing with the adoption of proof assistants, I think. A lot of well-known names (like Tao and Conrad for instance) are starting to formalise large swathes of modern maths in Lean, for instance. Perhaps it will never get to a point where it is so easy that formal proof is required to publish a result, but who knows? It seems like a start.