The so-called Golden Number or phi defines a ratio that appears repeatedly in nature, for example in the way many flowers’ petals are formed.
Some claim it is also associated with beauty, although leading mathematicians insist this is not true.
via Jitze Couperus
Known in maths as Tau, this number is the ratio of a circle’s circumference to its radius. It is double the value of pi, 3.14..., which is ratio of a circle’s circumference to its diameter. Mathematicians appear to be split over which one is better.
The ultimate answer to the meaning of Life, the Universe and Everything, according to fictional super computer Deep Thought in Douglas Adams’ The Hitchhiker’s Guide to the Galaxy. Attempts to discover what the question was produced the disappointing: “What is six times nine?” Six times nine is 54.
In 1918, Cambridge professor GH Hardy visited Srinivasa Ramanujan, who was sick in a nursing home in Putney, and travelled in taxi number 1729. Hardy told Ramanujan it was rather a dull number, but the Indian maths genius immediately replied it was “very interesting” as the smallest number that could be expressed as the sum of two cubes in two different ways. It appears repeatedly in Futurama in honour of Ramanujan.
The lowest uninteresting number, according to mathematicians. However, writer and comedian Sandi Toksvig pointed out on the BBC’s QI programme that this meant it was actually quite interesting.
Six is the first perfect number, which means it is the sum of all its divisors (3, 2, 1), and the only number that is both the sum and product of the same three consecutive positive integers (1, 2, 3).
It's also the atomic number of carbon, the biological basis of all known life. Six-sided shapes (hexagons) are everywhere in nature...
via Alexey Kljatov
Is considered a sacred number in Dharmic religions (Hinduism, Buddhism and Jainism); Hindu deities have 108 names and Buddhist temples in Japan chime bells 108 times to bring in the new year, while many Buddhist temples have 108 steps. In martial arts, there are 108 pressure points in the body, while the number is also the final number of 'forms' in karate.
Not so much a beautiful number as a beguiling one. The 23 enigma belief is that most things that happen in life are related to the number 23. Jim Carrey even starred in a film about it in 2007.
What more evidence do you need?
With thanks to this Quora thread