# Cambridge Combinatorics Seminar

1. Top Mathematician
sova

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.

Yeah hyping the sensitivity conjecture like they did was massively stupid.

1 weeksova
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2. Top Mathematician
kegt

It is sad that threads such as this constantly derail into argument about importance of result. The result is clearly interesting and important to some, so in my mind this makes it worthy of discussion and celebration. In truth, it will not be for many years until relative importance of mathematical results is truly understood. But for now we should at least celebrate such progress. As someone previously mentioned in this very thread, progress in mathematics is slow, so why not allow us to cherish this result? Even for outsiders of combinatorics

1 weekkegt
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3. Top Mathematician
kjru

As someone previously mentioned in this very thread, progress in mathematics is slow, so why not allow us to cherish this result?

What's stopping the cherishers from cherishing and celebrating? This is a great occasion to also explain the non-obvious value of the field to people who have the mistaken (or is it?) impression that it's a glass bead game.

1 weekkjru
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4. Top Mathematician
wput

Sensitivity conjecture was a big deal for the field, a lot of people tried for many years and couldn't make progress. Sometimes in math it is way easier to verify a proof works than to find it. It's basically an NP property, easy to verify hard to find. I can understand people outside of CS to not be able to understand this concept and thus naively say "short easy proof means not hard".

1 weekwput
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5. Top Mathematician
othb

Sensitivity conjecture was a big deal for the field, a lot of people tried for many years and couldn't make progress. Sometimes in math it is way easier to verify a proof works than to find it. It's basically an NP property, easy to verify hard to find. I can understand people outside of CS to not be able to understand this concept and thus naively say "short easy proof means not hard".

That conjecture surely triggered a number of sensitive people.

1 weekothb
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6. Top Mathematician
yxtr

Sensitivity conjecture was a big deal for the field, a lot of people tried for many years and couldn't make progress. Sometimes in math it is way easier to verify a proof works than to find it. It's basically an NP property, easy to verify hard to find. I can understand people outside of CS to not be able to understand this concept and thus naively say "short easy proof means not hard".

This is exactly the argument by the charlatans in the tale of the emperor's new cloths. Oh those cloths are made with the most sophisticated material. You cannot see it if you are too dumb!

1 weekyxtr
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7. Top Mathematician
ddby

Sensitivity conjecture was a big deal for the field, a lot of people tried for many years and couldn't make progress. Sometimes in math it is way easier to verify a proof works than to find it. It's basically an NP property, easy to verify hard to find. I can understand people outside of CS to not be able to understand this concept and thus naively say "short easy proof means not hard".

This is exactly the argument by the charlatans in the tale of the emperor's new cloths. Oh those cloths are made with the most sophisticated material. You cannot see it if you are too dumb!

You got it upside down. AG is the most sophisticated material that only indoctrinated charlatans, the mean gossip girls in the realm, revere.

1 weekddby
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8. Top Mathematician
bkiy

All this discussion about the value of the Ramsey numbers is funny.  What is the ultimate value in the study of, e.g., numbers or algebraic varieties that is lacking in the study of elementary discrete structures, like graphs and hypergraphs? Honestly, I do not have a motivated answer to this question, and a priori I cannot say that they do not deserve to be studied. There is actually some additional attraction, as for me, in the simplicity of these abstract objects.  What is their study indeed lacking, is the presence of deep, intricate and complicated structures, like the ones we encounter in the study of numbers, varieties or manifolds. This indeed can be said as making the study of the latter more appealing as the mathematics is exactly the study of hidden structures behind elementary abstract object; and most of the mathematics is naturally happening where there is the abundance of such structures. But I can not really say that such reasoning could be named by the vague term «value». At least, this does not seem motivated for me to be the reason for choosing numbers over graphs as more «valuable» objects of study. (I am not a combinatorist myself, though I have some shallow passion to combinatorics lasting from the olympiad childhood.)

1 weekbkiy
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9. Top Mathematician
yxsj

Why are Ramsey numbers any less intrinsically interesting than elliptic curves?

A hundred problems of independent interest lead you to elliptic curves but nothing other than Ramsey numbers leads you to Ramsey numbers. The lack of interconnection.

“Interconnection” is a bad standard for judging mathematics. Things are beautiful and deep, or they aren’t. There are tons of highly interconnected but boring problems.

1 weekyxsj
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10. Top Mathematician
igej

About the paper itself, it really does look like a complicated ad hoc kind of inductive argument, almost completely elementary. Lots of one-variable inequalities to keep track of parameters. However no use of any tools such as quasirandomness, probabilistic method, entropy.....

1 weekigej
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11. Top Mathematician
djuj

All this discussion about the value of the Ramsey numbers is funny.  What is the ultimate value in the study of, e.g., numbers or algebraic varieties that is lacking in the study of elementary discrete structures, like graphs and hypergraphs? Honestly, I do not have a motivated answer to this question, and a priori I cannot say that they do not deserve to be studied. There is actually some additional attraction, as for me, in the simplicity of these abstract objects.  What is their study indeed lacking, is the presence of deep, intricate and complicated structures, like the ones we encounter in the study of numbers, varieties or manifolds. This indeed can be said as making the study of the latter more appealing as the mathematics is exactly the study of hidden structures behind elementary abstract object; and most of the mathematics is naturally happening where there is the abundance of such structures. But I can not really say that such reasoning could be named by the vague term «value». At least, this does not seem motivated for me to be the reason for choosing numbers over graphs as more «valuable» objects of study. (I am not a combinatorist myself, though I have some shallow passion to combinatorics lasting from the olympiad childhood.)

As many already said in this thread people in Hungarian combinatorics generally care about techniques and methods more than structures. The diagonal Ramsey problem is just one of the oldest and simplest problems that they haven't been able to settle after so many years of intensive effort and whose resolutions are believed to lead to major progress on other problems. Their mindset is different from that of algebraic geometers and number theorists as far as I know.

If you wanna talk about some "deep, intricate, and complicated structures" arising from graphs, then you're welcome to have a look at the so-called Graph Minor Theory of Robertson-Seymour. This is by no means Hungarian combinatorics but is enough to show you the study of graphs is definitely not lacking the presence of "deep, intricate, and complicated structures".

1 weekdjuj
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12. Top Mathematician
djuj

About the paper itself, it really does look like a complicated ad hoc kind of inductive argument, almost completely elementary. Lots of one-variable inequalities to keep track of parameters. However no use of any tools such as quasirandomness, probabilistic method, entropy.....

Well, the Hypergraph Container Method is also based on an "ad hoc" algorithm without any "non-elementary" tools as you said. Yet the method is one of the most powerful in Extremal and Probabilistic Combinatorics that resolves many long-standing open problems...

1 weekdjuj
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13. Top Mathematician
paeg

About the paper itself, it really does look like a complicated ad hoc kind of inductive argument, almost completely elementary. Lots of one-variable inequalities to keep track of parameters. However no use of any tools such as quasirandomness, probabilistic method, entropy.....

Well, the Hypergraph Container Method is also based on an "ad hoc" algorithm without any "non-elementary" tools as you said. Yet the method is one of the most powerful in Extremal and Probabilistic Combinatorics that resolves many long-standing open problems...

Let's see if this paper has the same influence shall we.

1 weekpaeg
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14. Top Mathematician
ectn

All this discussion about the value of the Ramsey numbers is funny.  What is the ultimate value in the study of, e.g., numbers or algebraic varieties that is lacking in the study of elementary discrete structures, like graphs and hypergraphs? Honestly, I do not have a motivated answer to this question, and a priori I cannot say that they do not deserve to be studied. There is actually some additional attraction, as for me, in the simplicity of these abstract objects.  What is their study indeed lacking, is the presence of deep, intricate and complicated structures, like the ones we encounter in the study of numbers, varieties or manifolds. This indeed can be said as making the study of the latter more appealing as the mathematics is exactly the study of hidden structures behind elementary abstract object; and most of the mathematics is naturally happening where there is the abundance of such structures. But I can not really say that such reasoning could be named by the vague term «value». At least, this does not seem motivated for me to be the reason for choosing numbers over graphs as more «valuable» objects of study. (I am not a combinatorist myself, though I have some shallow passion to combinatorics lasting from the olympiad childhood.)

It’s obviously a taste thing. My own taste is toward algebraic number theory and neighboring subjects.

But my answer to the question is historical. I find I’m personally quite attracted to problems considered by the 19th century greats. Of course, my tastes have been influenced by them, and I don’t at limit my interests to things they thought about. But it’s notable that they did not consider this class of problems as far as I know, which were certainly accessible to them.

Happy to hear that I’m wrong about the history, which I only vaguely know by the way!

1 weekectn
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15. Top Mathematician
euca

About the paper itself, it really does look like a complicated ad hoc kind of inductive argument, almost completely elementary. Lots of one-variable inequalities to keep track of parameters. However no use of any tools such as quasirandomness, probabilistic method, entropy.....

Has it been posted? Links?

1 weekeuca
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16. Top Mathematician
gqfn

Has it been posted? Links?

It is on arXiv, check recent postings in mathCO

1 weekgqfn
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17. Top Mathematician
ipge

About the paper itself, it really does look like a complicated ad hoc kind of inductive argument, almost completely elementary. Lots of one-variable inequalities to keep track of parameters. However no use of any tools such as quasirandomness, probabilistic method, entropy.....

Has it been posted? Links?

Look to put it bluntly if you don't already know this, or if you don't immediately know where to look, you really should be on reddit or quora. Ideally to participate in this thread you should be looking at the more technical estimates in the paper at this point

1 weekipge
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18. Top Mathematician
zglb
[...]

Has it been posted? Links?

Look to put it bluntly if you don't already know this, or if you don't immediately know where to look, you really should be on reddit or quora. Ideally to participate in this thread you should be looking at the more technical estimates in the paper at this point

Shut up you nerd

1 weekzglb
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19. Top Mathematician
qomb
[...]

Has it been posted? Links?

Look to put it bluntly if you don't already know this, or if you don't immediately know where to look, you really should be on reddit or quora. Ideally to participate in this thread you should be looking at the more technical estimates in the paper at this point

Thank you for wasting five minutes of your time by writing this paragraph and wasting five minutes of my time by making me go to the arxiv. Here

https://arxiv.org/abs/2303.09521

1 weekqomb
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