In most areas, the important problems are the ones the community feels are important, the ones which are obviously natural, or perhaps the ones that bigshots in their prime say are important.
Why then does combinatorics decide the importance of problems according to the pronouncements of Erdos?
every community values highly conjectures and problems posed by bigshots at any time and independently of how much time has passed since. Actually, the more times passes, the more the problem becomes classical, the more it’s usually valued. It seems pretty obvious to me.
In most areas, the important problems are the ones the community feels are important, the ones which are obviously natural, or perhaps the ones that bigshots in their prime say are important.
Why then does combinatorics decide the importance of problems according to the pronouncements of Erdos?
If a number theorist solves a problem that Gauss wasn't able to, the result will get into Annals of Mathematics. It seems fair that if a combinatorialist solves a problem that Erdos wasn't able to, then the result should get into a top combinatorics journal.
every community values highly conjectures and problems posed by bigshots at any time and independently of how much time has passed since. Actually, the more times passes, the more the problem becomes classical, the more it’s usually valued. It seems pretty obvious to me.
In most areas, the important problems are the ones the community feels are important, the ones which are obviously natural, or perhaps the ones that bigshots in their prime say are important.
Why then does combinatorics decide the importance of problems according to the pronouncements of Erdos?
They don't. But he asked a lot of straightforwardly interesting questions some of which are benchmarks for progress in particular areas.
In most areas, the important problems are the ones the community feels are important, the ones which are obviously natural, or perhaps the ones that bigshots in their prime say are important.
Why then does combinatorics decide the importance of problems according to the pronouncements of Erdos?
They don't. But he asked a lot of straightforwardly interesting questions some of which are benchmarks for progress in particular areas.
Seconded. It seems to me that quite a few people on MJR have never tried actually talking to friendly combinatorists (they do exist) about what they think, and merely get their information 2nd-hand based on internet-shorthand.
If a number theorist solves a problem that Gauss wasn't able to, the result will get into Annals of Mathematics.
Are there really such problems? Gauss was no Hilbert. If he couldn’t answer a question himself he just kept the failure to himself. The closest thing I know is:
https:// en. wikipedia. org/wiki/Class_number_problem
but I suspect Gauss didn’t explicitly pose it as a conjecture.
If a number theorist solves a problem that Gauss wasn't able to, the result will get into Annals of Mathematics.
Are there really such problems? Gauss was no Hilbert. If he couldn’t answer a question himself he just kept the failure to himself. The closest thing I know is:
https:// en. wikipedia. org/wiki/Class_number_problem
but I suspect Gauss didn’t explicitly pose it as a conjecture.
My understanding is that there wasn't as much of a culture of posing conjectures and problems in pre-Hilbert days anyway. Most things we would reasonably call conjectures of Fermat or Euler, for example, were just things they wrote down in letters but either didn't prove or explicitly said they weren't able to prove.
In that sense Gauss was more reticent than contemporaries, but the prime number theorem is a good example of a statement he said he believed but wasn't able to prove.
In most areas, the important problems are the ones the community feels are important, the ones which are obviously natural, or perhaps the ones that bigshots in their prime say are important.
Why then does combinatorics decide the importance of problems according to the pronouncements of Erdos?
Why were the conjectures of some 17th century amateur given so much attention in algroid number theory?
Why were the conjectures of some 17th century amateur given so much attention in algroid number theory?
They were and are marginal (sorry) except for the one that was related to a central technical question about the machinery. Similarly the Goldbach conjecture is just a test case for progress on central technical questions in analytic number theory such as proving predictions based on the density of primes, understanding what sieves can and cannot do, and so on.
In most areas, the important problems are the ones the community feels are important, the ones which are obviously natural, or perhaps the ones that bigshots in their prime say are important.
Why then does combinatorics decide the importance of problems according to the pronouncements of Erdos?
Because of the lack of any other metrics in the field. Also with the mythology around Erdos, it gives the field some much-needed credibility to try to ride on his coattails. Both are very damning facts about the field though.
Why were the conjectures of some 17th century amateur given so much attention in algroid number theory?
They were and are marginal (sorry) except for the one that was related to a central technical question about the machinery. Similarly the Goldbach conjecture is just a test case for progress on central technical questions in analytic number theory such as proving predictions based on the density of primes, understanding what sieves can and cannot do, and so on.
Thank you for (serious) reply to flippant question. I'm (geometer here) still struggling to get beyond Kummer level algebraic number theory.
In most areas, the important problems are the ones the community feels are important, the ones which are obviously natural, or perhaps the ones that bigshots in their prime say are important.
Why then does combinatorics decide the importance of problems according to the pronouncements of Erdos?
If a number theorist solves a problem that Gauss wasn't able to, the result will get into Annals of Mathematics. It seems fair that if a combinatorialist solves a problem that Erdos wasn't able to, then the result should get into a top combinatorics journal.
Does this mean the Annals of Mathematics is a top number theory journal?
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