【Hacker News搬运】鄂尔多斯问题汇编

[hackernews]

Title: Erdos Problems Collection

鄂尔多斯问题汇编

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hn link

Url: https://www.erdosproblems.com/

Erős问题网站是一个关于数学问题的地方，这些问题是数学家Paul Erős在他的一生中选择的。网站上有589个问题，其中159个已经被解决。Erős认为，一个好的问题可以揭示一个特定领域的核心困难，成为衡量该领域进展的基准。这些问题可能像“棉花糖”，提供短暂的享受，也可能像“橡子”，需要深刻的和新颖的洞察力，从而产生更普遍的结果和新的问题。Erős在1997年的著作《我的一些最喜欢的问题和结果》中提到了这些问题的多样性，他不能保证所有问题都是“橡子”，但因为这些问题已经阻碍了最好的数学家几十年的努力，并且经常为解决这些问题提供现金奖励，这可能表明需要新的想法，这些想法可以反过来导致更一般的结果，自然而然地，也会产生新的问题。这样，数学生命的循环永远继续。

Post by: dargscisyhp

Comments:

skinner_: The question of what is an Erdős problem and what is not is not black and white. My team has managed to solve a problem that's sort of an Erdős problem. In the early sixties, Leo Moser asked about the value of some quantity. In a 1985 paper, Erdős commented that the quantity “seems likely” to be less than 1/4. It was known to be at most 2/7. After a long line of improvements by several teams, we were the first ones to go below 1/4.<p>For those who are interested, <a href="https://www.sfu.ca/~vjungic/RamseyProjects/section-11.html" rel="nofollow">https://www.sfu.ca/~vjungic/RamseyProjects/section-11.html</a> describes the question. Our answer is at <a href="https://arxiv.org/abs/2207.14179" rel="nofollow">https://arxiv.org/abs/2207.14179</a>, and a popsci account of our result is at <a href="https://www.quantamagazine.org/mathematicians-break-bounds-in-coloring-problem-20230719/" rel="nofollow">https://www.quantamagazine.org/mathematicians-break-bounds-i...</a> .

skinner_: 什么是埃尔德问题，什么不是埃尔德问题的问题不是非黑即白的。我的团队已经设法解决了一个问题；这有点像埃尔德的问题。在60年代初，Leo Moser询问了一些数量的价值。在1985年的一篇论文中，埃尔德斯评论说，这个数量“似乎很可能”小于1/F；4.已知其至多为2/F；7.经过几个团队的一长串改进，我们是第一个低于1/F的团队；4.<p>对于感兴趣的人，<a href=“https://；&#x2F；www.sfu.ca&#x2F！~vjungic&#x2F：Ramsey Projects&#x2F&section-11.html”rel=“nofollow”>https://&#x2F；www.sfu.ca&#x2F~vjungic；拉姆齐项目；第11.html</a>节描述了这个问题。我们的答案在<a href=“https://；&#x2F；arxiv.org/#xx2F；abs&#x2F！2207.14179”rel=“nofollow”>https://上&#x2F；arxiv.org/x2F；abs；2207.14179</a>，我们的结果的popsci说明位于<a href=“https://；&#x2F；www.quantamagazine.org/x2F；mathematicians-break-bounds-in-coloring-problem-20230719&#x2F”rel=“nofollow”>https://&#x2F；www.quantamagazine.org/x2F；数学家们-健全人-我…</a>。

readyplayernull: > Ron Graham bet him $500 that he could not stop taking the drug for a month. Erdős won the bet, but complained that during his abstinence mathematics had been set back by a month: 'Before, when I looked at a piece of blank paper my mind was filled with ideas. Now all I see is a blank piece of paper.' After he won the bet, he promptly resumed his amphetamine use.<p><a href="http://en.wikipedia.org/wiki/Paul_Erdős" rel="nofollow">http://en.wikipedia.org/wiki/Paul_Erdős</a>

readyplayernull: &gt；罗恩·格雷厄姆和他打赌500美元，说他一个月都不能停止服药。埃尔德斯赢得了赌注，但抱怨在禁欲期间，数学被推迟了一个月：；以前，当我看着一张白纸时，我的脑海里充满了想法。现在我看到的只是一张空白的纸&#x27；在他赢得赌注后，他立即恢复使用苯丙胺<p> <a href=“http://x2F；&#x2F；en.wikipedia.org&#x2F！wiki&#x2F：Paul_Erd%C5%91s”rel=“nofollow”>http://x2F&#x2F；en.wikipedia.org&#x2F；wiki&#x2F；Paul_Erd%C5%91s</a>

pnielsen2: One of my friends from undergrad solved an erdos problem a couple years ago during the first year of his PhD... Absolutely insane.

pnielsen2: 几年前，我的一个本科生朋友在读博士的第一年解决了一个erdos问题。。。简直疯了。

johnthescott: if you like the "book", you may like the scottish book.<p><pre><code> https://en.wikipedia.org/wiki/Scottish_Book
</code></pre>
eastern european mathematics ...

johnthescott: 如果你喜欢“；书”；，你可能喜欢这本苏格兰书<p> ＜pre＞＜code＞https:&#x2F&#x2F；en.wikipedia.org&#x2F；wiki&#x2F；苏格兰图书</code></pre>东欧数学。。。