- Let's
see four amazing properties of number 5: a) It is the hypotenuse of the smallest Pythagorean
triangle. b) There are five Platonic solids. c) It is the smallest automorphic
number. Automorphic numbers are those whose square ends in the
number. d) It is probably the only odd untouchable number.
Untouchable numbers are those that are not equal to the sum of the proper
divisors of any other number.
- Champernowne's
number:
0.1234567891011121314… Can you see how it is formed? Would you know how to
continue the figures? This number is transcendental, and possibly
normal, like e and π, which means that its digits meet all the conditions usually used to determine if a number is random or not. However,
it is obvious that it is not random, also like e and π.
- What
makes number 1729 famous?
While the mathematician G.H. Hardy was visiting the famous Indian
mathematician Srinivasa Ramanujan, he mentioned that the taxi that had
brought him had the number 1729 which, he said, is a rather boring number.
Ramanujan immediately replied: No, it is very interesting, because it is the smallest number
that can be expressed as the sum of two positive cubes in two different
ways: 1729 = 13+123
= 93+103.
- Erdös conjecture: In this set of equalities:
the only one that has a solution is the trivial equation: 11+21=31, which is obtained for m=3, n=1. The conjecture has been proven up to m<1.485×109321155, but until now it has not been possible to prove it.
- The Tegmark number: The distance that would have to be traveled to meet a copy of oneself in a homogeneous and infinite universe would be
- meters. I find this highly doubtful, as discussed in this article.
- The number of possible chess games: The mathematician G.H. Hardy estimated it at
And these are the quotes:
- The
knowledge we have of mathematical truths is not only certain, but real knowledge;
and not the bare empty vision of vain, insignificant chimeras of the brain. (John Locke, An
essay concerning human understanding,
1690).
Arthur Eddington I believe there are 15,747,724,136,275,002,577,605,653,961,181,555,468,044,717,914,527,116,709,366,231,425,076,185,631,031,296 protons in the universe and the same number of electrons. (Arthur Eddington, The philosophy of physical science, 1939).
- The
enormous usefulness of mathematics in natural sciences is something
bordering on the mysterious, and there is no rational explanation for it.
It is not at all natural that ‘laws of nature’ exist, much less that man is able to
discover them. The miracle of the appropriateness of the language of mathematics for the formulation
of the laws of physics is a wonderful gift which we neither understand nor deserve. (Eugene P. Wigner, The
Unreasonable Effectiveness of Mathematics in the Natural Sciences, 1960).
- A [mathematician]
often experiences the discomforting feeling that his pencil surpasses him
in intelligence. (Howard E. Eves, Mathematical circles,
1969).
- Science
in its everyday practice is much closer to art than to philosophy. When I
look at Gödel’s proof of his undecidability theorem, I do not see a
philosophical argument. The proof is a soaring piece of architecture, as
unique and as lovely as a Chartres cathedral. (Freeman Dyson, introduction to book Nature’s imagination,
1995).
- Is
God a mathematician? Certainly, the world, the universe, and nature can be
reliably understood using mathematics. Nature is mathematics. The arrangement
of seeds in a sunflower can be understood
using Fibonacci numbers. Sunflower heads, like other flowers, contain two
families of interlaced spirals—one winding clockwise, the other counter clockwise.
The numbers of seeds and petals are almost always Fibonacci numbers. (Clifford Pickover, The
Loom of God, 1997).
- Our brains evolved so that we could survive out there in the jungle. Why in the world should a brain develop for the purpose of being at all good at grasping the true underlying nature of reality? (Brian Greene, quoted by Susan Kruglinski in her article When even mathematicians don’t understand the math, New York Times, 25-5-2004).
Manuel Alfonseca
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