The question is not whether or not mathematics is useful. Obviously it is. The question is this; does it exist only in the mind or does it have a reality independent of mind? If the former, it could be argued that it is no more real than, for example, beauty. "Beauty is in the eye of the beholder" and all that trite nonsense. If it is the latter, it existed prior to the human mind or any mind. It has a substantive reality and is both self-contained and independent. It is eternal.

I was reading an article on the Fibonacci spiral today. I happened to come across a photo of a woman. To be tactful, the photo was disturbingly familiar. I have seen it here. I never expected that math could lead to a discovery of this nature.

Here are some questions. There are no correct answers. They might just be important things to think about.

1. Is zero a number?
2. Do members of Congress in the USA know anything about math?
3. How do you feel about negative numbers? It is easy to "visualize" positive numbers. Can you "visualize" negative ones? Or, to put it yet another way, how can you HAVE less than zero?
4. How to banks manufacture money out of thin air?

You can choose a number now or look for something you like and be that number.

0 is the additive identity.
1 is the multiplicative identity.
2 is the only even prime.
3 is the number of spatial dimensions we live in.
4 is the smallest number of colors sufficient to color all planar maps.
5 is the number of Platonic solids.
6 is the smallest perfect number.
7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass.
8 is the largest cube in the Fibonacci sequence.
9 is the maximum number of cubes that are needed to sum to any positive integer.
10 is the base of our number system.
11 is the largest known multiplicative persistence.
12 is the smallest abundant number.
13 is the number of Archimedian solids.
14 is the smallest even number n with no solutions to f(m) = n.
15 is the smallest composite number n with the property that there is only one group of order n.
16 is the only number of the form xy = yx with x and y being different integers.
17 is the number of wallpaper groups.
18 is the only positive number that is twice the sum of its digits.
19 is the maximum number of 4th powers needed to sum to any number.
20 is the number of rooted trees with 6 vertices.
21 is the smallest number of distinct squares needed to tile a square.
22 is the number of partitions of 8.
23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.
24 is the largest number divisible by all numbers less than its square root.
25 is the smallest square that can be written as a sum of 2 squares.
26 is the only positive number to be directly between a square and a cube.
27 is the largest number that is the sum of the digits of its cube.
28 is the 2nd perfect number.
29 is the 7th Lucas number.
30 is the largest number with the property that all smaller numbers relatively prime to it are prime.
31 is a Mersenne prime.
32 is the smallest non-trivial 5th power.
33 is the largest number that is not a sum of distinct triangular numbers.
34 is the smallest number with the property that it and its neighbors have the same number of divisors.
35 is the number of hexominoes.
36 is the smallest non-trivial number which is both square and triangular.
37 is the maximum number of 5th powers needed to sum to any number.
38 is the last Roman numeral when written lexicographically.
39 is the smallest number which has 3 different partitions into 3 parts with the same product.
40 is the only number whose letters are in alphabetical order.
41 is a value of n so that x2 + x + n takes on prime values for x = 0, 1, 2, ... n-2.
42 is the 5th Catalan number.
43 is the number of sided 7-iamonds.
44 is the number of derangements of 5 items.
45 is a Kaprekar number.
46 is the number of different arrangements (up to rotation and reflection) of 9 non-attacking queens on a 9×9 chessboard.
47 is the largest number of cubes that cannot tile a cube.
48 is the smallest number with 10 divisors.
49 is the smallest number with the property that it and its neighbors are squareful.
50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.
51 is the 6th Motzkin number.
52 is the 5th Bell number.
53 is the only two digit number that is reversed in hexadecimal.
54 is the smallest number that can be written as the sum of 3 squares in 3 ways.
55 is the largest triangular number in the Fibonacci sequence.
56 is the number of reduced 5×5 Latin squares.
57 = 111 in base 7.
58 is the number of commutative semigroups of order 4.
59 is the number of stellations of an icosahedron.
60 is the smallest number divisible by 1 through 6.
61 is the 3rd secant number.
62 is the smallest number that can be written as the sum of of 3 distinct squares in 2 ways.
63 is the number of partially ordered sets of 5 elements.
64 is the smallest number with 7 divisors.
65 is the smallest number that becomes square if its reverse is either added to or subtracted from it.
66 is the number of 8-iamonds.
67 is the smallest number which is palindromic in bases 5 and 6.
68 is the 2-digit string that appears latest in the decimal expansion of p.
69 is a value of n where n2 and n3 together contain each digit once.
70 is the smallest weird number.
71 divides the sum of the primes less than it.
72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimensions.
73 is the smallest multi-digit number which is one less than twice its reverse.
74 is the number of different non-Hamiltonian polyhedra with a minimum number of vertices.
75 is the number of orderings of 4 objects with ties allowed.
76 is an automorphic number.
77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
78 is the smallest number that can be written as the sum of of 4 distinct squares in 3 ways.
79 is a permutable prime.
80 is the smallest number n where n and n+1 are both products of 4 or more primes.
81 is the square of the sum of its digits.
82 is the number of 6-hexes.
83 is the number of strongly connected digraphs with 4 vertices.
84 is the largest order of a permutation of 14 elements.
85 is the largest n for which 12+22+32+ ... +n2 = 1+2+3+ ... +m has a solution.
86 = 222 in base 6.
87 is the sum of the squares of the first 4 primes.
88 is the only number known whose square has no isolated digits.
89 = 81 + 92
90 is the number of degrees in a right angle.
91 is the smallest pseudoprime in base 3.
92 is the number of different arrangements of 8 non-attacking queens on an 8×8 chessboard.
93 = 333 in base 5.
94 is a Smith number.
95 is the number of planar partitions of 10.
96 is the smallest number that can be written as the difference of 2 squares in 4 ways.
97 is the smallest number with the property that its first 3 multiples contain the digit 9.
98 is the smallest number with the property that its first 5 multiples contain the digit 9.
99 is a Kaprekar number.

I have briefly mentioned perfect numbers in an earlier blog. The best way to understand is to give an example. 6 is a perfect number because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. At the same time, 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6.

A few other perfect numbers are 28, 496 and 8128.

These, as are all known perfect numbers, are also even.

Once again, there is a relationship to the divine and the cosmos. For example, God created the universe in 6 days and there are about 28 days in the lunar cycle (that varies). Research will show you that all the perfect numbers (that I have managed to check) have some significance outside themselves.

The largest known perfect number has 1,791,864 digits, so I won't put it here.

There are no known perfect numbers that are odd.

1, 9, 45, 55, 99, 297, 703, 999 , 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 17344, 22222, 38962, 77778, 82656, 95121, 99999, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170, ...

Thank you to those who have supported my blogs about math. I appreciate the comments here, in emails and in chat. I am working on some new stuff and it is pretty cool.

Just wanted those few who are interested to know I have not given up.

Whenever we think of the end of the world we must remember the words of Louise B. Young. "Whatever can be done once, can always be repeated." Consequently, there is no end to the universe, but only to the world as we know it.

Having said this, we know the formula for the end of the world as outlined by:

W = 1492n - 1770n - 1863n + 2141n [n is in superscript]. A very detailed proof can be found in the American Mathematical Monthly, January 1945.

The proof depends on x-y being a divisor of xn-yn for n= 0,1,2 . . .

Please note that the numbers are all divisible by 1492 and that, significantly, they all have profound historical importance. Consequently 2141 will have profound historical significance.

Gods are free of form and material change. They are therefore pure. However they have being in the ideal of numbers, since that is the only concept relevant to them. We can easily see, therefore that numbers are gods.

Meditation on numbers helps us transcend our own materiel being and commune with the gods. Meditation on numbers is therefore prayer.

This is all put forward clearly by the prophet Pythagoras.

That is a brief introduction to the formula:
Pure + Mathematics = God

A formula containing everything about infinity, God and the end of the world.
Pure + Mathematics = God
I will unravel that as I am able to.