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 Lucas de la Paz on Selfreplication
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Monthly Archives: May 2013
IMO team unveiled
IMO team unveiled After four long exams on contiguous days, the UKMT has selected the IMO team (some of whom are regular readers of this website). For the first time in history, this happens to be identical to the RMM … Continue reading
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Pairwise versus overall
A recurring general theme in mathematics is of a property being true of three objects when considered pairwise, but not true of the entire set. For example, earlier we considered nontrivial mutual friends, and how a simple graph is not sufficient … Continue reading
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The Universe
Some people have recently been discussing Eric Weinstein*, who has proposed a 14dimensional theory of everything known as Geometric Unity. The media attention is possibly as a result of the trivial difference between his surname and that of the patent office clerk responsible … Continue reading
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Sierpinski triangle
The Sierpinski triangle is a surprisingly ubiquitous mathematical object. Rather than describing what a Sierpinski triangle is, I may as well show you a picture of one. Essentially, it consists of three identical copies of itself, scaled by a factor … Continue reading
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Cipher 30: Finale
This is the final cipher of the first season on cp4space. This will be followed by a short period of cp4space aestivation, estimated to be about two or three weeks, before the next season of ciphers commences. Don’t worry; there will still … Continue reading
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HoffmanSingleton graph
I’m not sure exactly how to motivate a discussion of the HoffmanSingleton graph, except perhaps by beginning with the following problem from the October 2011 edition of the Advanced Mentoring Scheme: This problem seems quite innocuous at first, and one would … Continue reading
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Simultaneous proofs
Two open problems about the distribution of the primes have been solved within about 24 hours of each other, namely the ternary Goldbach conjecture and a weakened form of the twin prime conjecture. Let’s look at these in approximate chronological … Continue reading
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Cipher 29: Permutation
This particular ciphertext is 257 characters in length: I ih2 deetnnto nslaitmtm rtxoda r .deeisixtu olfiipfye mno i pa)otruuc ur e sisrsi ifaow auosmsiaas ep loofheltpqbnpu( ttlph imlazafldens heTeeit5elFmr ecrrurntpmfcth7dcseadtcpeant htlcocs eirhcaine tr uhsriiirbeoiaao ,e o dn reopu enefa r … Continue reading
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FRACTRAN
Some of my favourite books were written by Douglas Adams. (Indeed, my forename was actually named after his surname, rather than my Biblical namesake or the Greek word for ‘indestructible’.) Although I personally prefer the Dirk Gently books, I have … Continue reading
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Things that shouldn’t work, but do
There are several mathematical heuristics (it’s difficult to call them proofs), which are nonrigorous in the best of cases and sometimes seemingly insane. For example, Euler’s ‘proof’ that the sum of the reciprocals of the primes diverges at an asymptotic … Continue reading
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