We open with a simple mathematical puzzle that is easily solved using only elementary reasoning. Imagine a party where some guests are friends while others are unacquainted. Then the following is always true: No matter how many guests there are at the party, there are always two guests with the same number of friends present. … Continue reading Order in the midst of Chaos
Month: April 2020
John Horton Conway: a Charismatic Genius
John Horton Conway was a charismatic character, something of a performer, always entertaining his fellow-mathematicians with clever magic tricks, memory feats and brilliant mathematics. A Liverpudlian, interested from early childhood in mathematics, he studied at Gonville & Caius College in Cambridge, earning a BA in 1959. He obtained his PhD five years later, after which … Continue reading John Horton Conway: a Charismatic Genius
Exponential Growth must come to an End
In its initial stages, the Covid-19 pandemic grew at an exponential rate. What does this mean? The number of infected people in a country is growing exponentially if it increases by a fixed multiple R each day: if N people are infected today, then R times N are infected tomorrow. The size of the growth-rate … Continue reading Exponential Growth must come to an End
The Ross-Littlewood Paradox
A most perplexing paradox appeared in Littlewood's book A Mathematician's Miscellany. It was later analysed in detail by Sheldon Ross in his 1988 book A First Course in Probability. Littlewood wrote: Balls numbered 1, 2, ... (or for a mathematician the numbers themselves) are put into a box as follows. At 1 minute to noon … Continue reading The Ross-Littlewood Paradox
The Mathematics of Fair Play in Video Games
Video games generate worldwide annual sales of about $150 billion. With millions of people confined at home with time to spare, the current pandemic may benefit the industry. At the core of a video game is a computer program capable of simulating a range of phenomena in the real world or in a fantasy universe, … Continue reading The Mathematics of Fair Play in Video Games
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