Free Republic

This map is one of the most important surviving examples of 13th-century map-making. It tells us much about the way English men and women viewed the world at this time. Jerusalem is in the centre of the map, and the whole world is looked upon by Christ who is attended by angels. This shows that medieval people looked at geography in relation to the Bible and to earth’s creation by God. But the map also shows an interest in local places: you can see the British Isles, and the rivers Thames and Severn. London is marked with a gold dot....

Professional biologist and amateur mathematician Aubrey de Grey has partially solved the Hadwiger-Nelson problem, which has vexed mathematicians since 1950. He has published a paper describing the solution on the arXiv preprint server. The Hadwiger-Nelson problem came about when Edward Nelson and Hugo Hadwiger wondered about the smallest number of colors necessary to color all of the points on a graph, with no two connected points using the same color. Over the years, mathematicians have attacked the problem, and have narrowed the possibilities down to four, five, six or seven. Now, de Grey has eliminated the possibility of four colors...