I will never again say that picking a number between 43 and 48 is ridiculously easy. And this is just two dimensions. I guess the ultimate aim would be to generate generalized pattern-finding (or clique-finding) formulae for n-dimensions, which I imagine might help us learn more about the nature of space and hyperspace, but I am not too sure. Would be glad if anyone could enlighten me further on this.
Progress in mathematics is often slow and difficult, and breakthroughs in even minor seeming problems can take years. Results in my field may require new tools, new inspiration, or new computational power to achieve. Sometimes it takes all of these to push the subject forward.
Last week, it was announced in a paper posted on arXiv that the fifth Ramsey number R(5) is at most 48. Before this, it was known to be at most 49. To a random person, the response to this announcement would be a resounding “big deal”. But this is a breakthrough and I will explain why.
Have you ever looked up at the night sky and seen a pattern in the stars, one that doesn’t fit one of the known constellations? That is Ramsey theory at work, with your brain connecting the dots to find new patterns. What the math tells us is that patterns are truly…
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