Mathematicians deal with numbers by which the general public understands positive integers (also called natural numbers) like 7. Of course, as people versed in the matter know perfectly well, there are other kinds of numbers. But the general public is right in its own way too, because natural numbers form the basis of mathematics. 'God created integers, the rest was the work of mankind', the great German mathematician Leopold Kronecker said. Some 2,500 years ago, students of the Ancient Greek mathematician, Pythagoras believed that everything could be explained with the help of integers and their ratios. Eventually it became clear that this was not exactly the case, which threw orthodox Pythagoreans into despair. According to legend, the first man to recognise the existence of irrational numbers (any number that can be expressed as the ratio of two integers) was thrown overboard by his horrified fellow Pythagoreans, who vowed to keep the discovery a secret.