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Part One - The family of minimal principles

Few things are as simple as they seem when you peer below the surface. Take the spinning of a coin...

Srinivasa Ramanujan, (born December 22, 1887, Erode, India—died April 26, 1920, Kumbakonam), Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function. When he was 15 years old, he obtained a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics, 2 vol. (1880–86). This collection of thousands of theorems, many presented with only the briefest of proofs and with no material newer than 1860, aroused his genius. Having verified the results in Carr’s book, Ramanujan...

Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory. It is known, however, that the Pythagoreans (founded c. 525 bce) studied perfect numbers for their “mystical” properties. The mystical tradition was continued by the Neo-Pythagorean philosopher Nicomachus of Gerasa (fl. c. 100 ce), who classified numbers as deficient, perfect, and superabundant according to whether the sum of their divisors wa...

Goldbach conjecture, in number theory, assertion (here stated in modern terms) that every even counting number greater than 2 is equal to the sum of two prime numbers. The Russian mathematician Christian Goldbach first proposed this conjecture in a letter to the Swiss mathematician Leonhard Euler in 1742. More precisely, Goldbach claimed that “every number greater than 2 is an aggregate of three prime numbers.” (In Goldbach’s day, the convention was to consider 1 a prime number, so his statement is equivalent to the modern version in which the convention is to not include 1 among the pr...