This is a larger cultural problem on this site that I bump into so often.

Delusional to think this is a "site problem" rather than a "human nature problem" that this site merely makes manifest

This is a larger cultural problem on this site that I bump into so often.

Delusional to think this is a "site problem" rather than a "human nature problem" that this site merely makes manifest

Resistance to "why is this interesting" is a larger cultural problem, and it is often a sign of rot within a subject. I'd prefer that mathematics give honest answers than go the way of humanities, social science, politics and other areas where bullshit rules.

Really, no. Improving 4 to 3.9999 via an ad hoc argument when the experts think the answer is $\sqrt{2}$, vs showing existence of designs for all parameters where previously none had been known to exist even computationally for small parameters with an interesting and conceptual method.

Have you read the paper in the detail? How do you know if it's ad hoc if the proof is a novel argument? No one knows if in the next few months it would lead to something else.

Also, BTW, though Gowers is harping on about how this is the biggest breakthrough of the last half century etc, he himself has done much more important things, for instance both his work on Szemeredi (which is more important than the Ramsey thing by so much, he might have simply forgotten about it) also his hypergraph regularity work.

Because he had spent many months of his life feeling useless when trying to solve it (as he said)?

This is a larger cultural problem on this site that I bump into so often.

Delusional to think this is a "site problem" rather than a "human nature problem" that this site merely makes manifest

Mostly agree. But I’m not sure if people fume to the same degree over the details of whether this or that is a real success if they don’t have an outlet for their thoughts. Maybe.

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Resistance to "why is this interesting" is a larger cultural problem, and it is often a sign of rot within a subject. I'd prefer that mathematics give honest answers than go the way of humanities, social science, politics and other areas where bullshit rules.

Things become more interesting when you spend time thinking about them. Trying to avoid that level of engagement while expecting someone else to give you a tidy story the way they did in your undergrad classes is sometimes your problem, and certainly that expectation promotes bullshit in the math culture. There is no substitute for thinking yourself about a problem.

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Resistance to "why is this interesting" is a larger cultural problem, and it is often a sign of rot within a subject. I'd prefer that mathematics give honest answers than go the way of humanities, social science, politics and other areas where bullshit rules.

Things become more interesting when you spend time thinking about them. Trying to avoid that level of engagement while expecting someone else to give you a tidy story

People have shown sufficient understanding of what is technically at stake here, without getting any substantive engagement. There was never any request for a "tidy story". Indeed the problem is that we are all too familiar with the tidy stories about this problem, which is what led to curiousity about the actual value and interest of the subject beyond platitudes (which are all you offer in the last few posts).

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Things become more interesting when you spend time thinking about them. Trying to avoid that level of engagement while expecting someone else to give you a tidy story

People have shown sufficient understanding of what is technically at stake here, without getting any substantive engagement. There was never any request for a "tidy story". Indeed the problem is that we are all too familiar with the tidy stories about this problem, which is what led to curiousity about the actual value and interest of the subject beyond platitudes (which are all you offer in the last few posts).

As I said, I’m not an insider here, so definitely can’t say anything of real mathematical content. But I can tell that this is a first breakthrough on a bottleneck problem that has been around for a while. I recognize such situations from my own area, and I know it is not always easy to communicate to outsiders why a breakthrough is a breakthrough. In those situations, it’s because I thought about the problem and developed an appreciation for my total lack of ideas on how to proceed or skirt around the issue.

So I believe people here when they say it is a breakthrough and I am happy for the folks in the area that they have fresh ideas to ponder.

I’m happy to have substantive discussion of the problem. But the negativity! Ugh! Why approach an attempt to learn something in that way?

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People have shown sufficient understanding of what is technically at stake here, without getting any substantive engagement. There was never any request for a "tidy story". Indeed the problem is that we are all too familiar with the tidy stories about this problem, which is what led to curiousity about the actual value and interest of the subject beyond platitudes (which are all you offer in the last few posts).

As I said, I’m not an insider here, so definitely can’t say anything of real mathematical content. But I can tell that this is a first breakthrough on a bottleneck problem that has been around for a while. I recognize such situations from my own area, and I know it is not always easy to communicate to outsiders why a breakthrough is a breakthrough. In those situations, it’s because I thought about the problem and developed an appreciation for my total lack of ideas on how to proceed or skirt around the issue.

So I believe people here when they say it is a breakthrough and I am happy for the folks in the area that they have fresh ideas to ponder.

I’m happy to have substantive discussion of the problem. But the negativity! Ugh! Why approach an attempt to learn something in that way?

Nobody serious is negative about the result. It's the hype machine that pisses them off. Also, there is an element of dick-waving about the whole thing, like, loads of bigshots couldn't do this so it must be important.

As I said, I’m not an insider here, so definitely can’t say anything of real mathematical content. But I can tell that this is a first breakthrough on a bottleneck problem that has been around for a while.

Sure, that is clear from the theorem statement. Sociologically, and presumably technically, it is a big achievement.

The questions about value and interest were about diagonal Ramsey as a stand-in for Ramsey theory in general. Does it have a point as a scientific and intellectual enterprise? Historically the questions were pursued for purely aesthetic reasons, more recently (as said above many times) as a benchmark for the strength of methods, and as an Everest to climb. As far as I can tell, though, this methodological and mountaineering interest is totally decoupled from any intrinsic scientific interest in the exact values of Ramsey numbers, or even the exponent of the growth rate, or even some robust approximation of the Ramsey problem that could conceivably bring it closer to questions where the precise answer becomes important. Are Ramsey type questions just a dead-end variant of the more productive, interrelated and easily stated density questions?

This is a larger cultural problem on this site that I bump into so often.

MJR does more than "make manifest". Like other social media, it amplifies the wannabe edgelords.

As I said, I’m not an insider here, so definitely can’t say anything of real mathematical content. But I can tell that this is a first breakthrough on a bottleneck problem that has been around for a while.

Sure, that is clear from the theorem statement. Sociologically, and presumably technically, it is a big achievement.

The questions about value and interest were about diagonal Ramsey as a stand-in for Ramsey theory in general. Does it have a point as a scientific and intellectual enterprise? Historically the questions were pursued for purely aesthetic reasons, more recently (as said above many times) as a benchmark for the strength of methods, and as an Everest to climb. As far as I can tell, though, this methodological and mountaineering interest is totally decoupled from any intrinsic scientific interest in the exact values of Ramsey numbers, or even the exponent of the growth rate, or even some robust approximation of the Ramsey problem that could conceivably bring it closer to questions where the precise answer becomes important. Are Ramsey type questions just a dead-end variant of the more productive, interrelated and easily stated density questions?

Could we say the same thing about FLT as well? "The methodological and mountaineering interest is totally decoupled from any intrinsic scientific interest in the fact that the equation ${x}^{n}+{y}^{n}={z}^{n}$ has no non-trivial solutions $x,y,z\in \mathbb{Z}$ for any $n>2$"? At the end of the day who cares about whether that equation has non-trivial solutions or not? The main interest was something else, wasn't it?

Could we say the same thing about FLT as well? "The methodological and mountaineering interest is totally decoupled from any intrinsic scientific interest in the fact that the equation ${x}^{n}+{y}^{n}={z}^{n}$ has no non-trivial solutions $x,y,z\in \mathbb{Z}$ for any $n>2$"? At the end of the day who cares about whether that equation has non-trivial solutions or not? The main interest was something else, wasn't it?

Well yes. That's why nobody serious in the 20th century, including Wiles, cared much about Fermat until it was related to objects of core interest: elliptic curves

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Sure, that is clear from the theorem statement. Sociologically, and presumably technically, it is a big achievement.

The questions about value and interest were about diagonal Ramsey as a stand-in for Ramsey theory in general. Does it have a point as a scientific and intellectual enterprise? Historically the questions were pursued for purely aesthetic reasons, more recently (as said above many times) as a benchmark for the strength of methods, and as an Everest to climb. As far as I can tell, though, this methodological and mountaineering interest is totally decoupled from any intrinsic scientific interest in the exact values of Ramsey numbers, or even the exponent of the growth rate, or even some robust approximation of the Ramsey problem that could conceivably bring it closer to questions where the precise answer becomes important. Are Ramsey type questions just a dead-end variant of the more productive, interrelated and easily stated density questions?

Could we say the same thing about FLT as well? "The methodological and mountaineering interest is totally decoupled from any intrinsic scientific interest in the fact that the equation ${x}^{n}+{y}^{n}={z}^{n}$ has no non-trivial solutions $x,y,z\in \mathbb{Z}$ for any $n>2$"? At the end of the day who cares about whether that equation has non-trivial solutions or not? The main interest was something else, wasn't it?

FLT and interest in it basically spawned a large amount of algebraic NT. Wiles solution being a particular example of that. The Ramsey problem has also spawned a large amount of work, but it's the

*lower*bound $R\left(k\right)>{2}^{k/2}$ of Erdos which has been influential.Time will tell whether this new work opens up new vistas or whether it turns out to be an

*ad hoc*curiousity. On a first look at the paper it looks like the latter, but only time will tell.If someone proved a lower bound of ${1.41422}^{k}$ then IMO this would be a massive deal. That would say that random graphs are not the best Ramsey graphs.

It would be hugely impressive, but why would it be surprising? There are lots of graph problems where the extremal and random cases have totally different asymptotics.

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FLT and interest in it basically spawned a large amount of algebraic NT. Wiles solution being a particular example of that. The Ramsey problem has also spawned a large amount of work, but it's the

*lower*bound $R\left(k\right)>{2}^{k/2}$ of Erdos which has been influential.Time will tell whether this new work opens up new vistas or whether it turns out to be an

*ad hoc*curiousity. On a first look at the paper it looks like the latter, but only time will tell.Agree with your sentiment. My prediction is that after the JS et al. paper there will be many boring follow-ups that incrementally move the exponent an iota from 3.9995 to 3.9994, etc. And every time this happens it will be morning sensation on Kalai's blog. Oh a new record has been set!

The situation will be reminiscent of the progress on computational efficiency for matrix multiplication (which has real practical implications). The conjectured exponent is 2. The last time the record was lowered from 2.3728639 to 2.3728596 it triggered a Quanta article!

quantamagazine . org / mathematicians-inch-closer-to-matrix-multiplication-goal-20210323/

[...]

FLT and interest in it basically spawned a large amount of algebraic NT. Wiles solution being a particular example of that. The Ramsey problem has also spawned a large amount of work, but it's the

*lower*bound $R\left(k\right)>{2}^{k/2}$ of Erdos which has been influential.Time will tell whether this new work opens up new vistas or whether it turns out to be an

*ad hoc*curiousity. On a first look at the paper it looks like the latter, but only time will tell.Agree with your sentiment. My prediction is that after the JS et al. paper there will be many boring follow-ups that incrementally move the exponent an iota from 3.9995 to 3.9994, etc. And every time this happens it will be morning sensation on Kalai's blog. Oh a new record has been set!

The situation will be reminiscent of the progress on computational efficiency for matrix multiplication (which has real practical implications). The conjectured exponent is 2. The last time the record was lowered from 2.3728639 to 2.3728596 it triggered a Quanta article!

quantamagazine . org / mathematicians-inch-closer-to-matrix-multiplication-goal-20210323/

Good analogy. I guess showing it is less than 3 was the breakthrough corresponding to $R\left(k\right)<{4}^{k}$, albeit easier mathematically. Has any improvement since actually been interesting?

Combinatorics people have the history of overhyping a nothing burger. Oh Erdős conjectured it 50 years ago and no one was able to solve it!

Let me give you an example. Remember that proof of Sensitivity conjecture by Hao Huang? They said it's a big deal, a tough problem that remained stubbornly unsolved for X years. Well, the proof was only 4 pages of elementary algebra, which was later condensed into 1 page by Don Knuth. They even hyped it so the paper got published in Annals. Logic says it's not a tough problem at all but either (1) Not many people cared about it, or (2) People who tried to solve it before were not very bright. I checked prior works on Sensitivity conjecture and indeed the literature was very thin. It was never a big deal to begin with.

That's why I take Gil Kalai's morning sensation with a grain of salt.

Same thing could be said about Kahn-Kalai as well.

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