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 non-trivial 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 14-dimensional 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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Hoffman-Singleton graph

I’m not sure exactly how to motivate a discussion of the Hoffman-Singleton 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 he-Teeit5elFmr ecrrurntpmfcth7dcseadtcpeant htlcocs eirhcaine  tr uhsriiirbeoiaao ,e  o  dn reopu enefa r … Continue reading

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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 non-rigorous 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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