I love to study math because we can discover what God is like. We often think about God creating the physical matter around us, but he also created humor, beauty, music, logic, and math. When we study math we are directly learning what God created. Man does not create math; man discovers math. Man makes up notation, like “+” for addition, but it was God that invented the idea of addition.
Here is one example of math revealing more about God (below is a simple explanation of a complex math concept. I think I have presented it in a way that non-mathy people can understand, but if I did not explain it clearly enough, just skip to the bottom line):
First of all, infinity is a concept, not actually a number. Webster’s defines infinity this way “the quality of having no limits or end”.
If I asked how many whole number (o, 1, 2, 3, …) there are, you would say infinity, because you can always add one more. There is no end.
How many integers (…, -3, -2, -1, 0, 1, 2, 3, …) are there?
It seems like there are more numbers in this list because it includes all of the whole numbers plus other numbers. But we would still say “infinity” because we can find a way to list them all, but once again the numbers will never end.
Listing all of the integers does take a little trick because if you start listing 0, 1, 2, 3, …, you will never get to the negative numbers. However if you list them in this pattern 0, 1, -1, 1, -2, 2, 3, -3, …, then your list will include all of the integers.
Since the set of integers can be put in order, we say that it is “countable”.
However the set of irrational numbers is not countable. There is no possible pattern that you can use which will list all of the irrational numbers. (Irrational numbers are numbers that cannot be written like a fraction: pi, e, square root of 2, …) I won’t go into the proof here because I do not want to get too technical, but the irrational numbers are not countable. They are a higher level of infinity: an infinity of infinities!
In technical math-speak the countable infinity is Aleph-Null and the uncountable infinity is Aleph-One.
The bottom line: There is regular infinity and then there are higher levels of infinity. Anything that can be listed in order is regular infinity, and anything that cannot be listed in order is a higher level of infinity.
(By the way, the line segment above has an infinity (aleph-one) of points)
So what does this have to do with the Almighty?
Think about the “bottom line” and read this verse from Psalms:
New King James Version (NKJV)
5 Many, O Lord my God, are Your wonderful works
Which You have done;
And Your thoughts toward us
Cannot be recounted to You in order;
If I would declare and speak of them,
They are more than can be numbered.
Did you catch it?
There are 2 references to infinity. In the last line, we are told that God’s thoughts toward us “are more than can be numbered”. That speaks of infinity (at least aleph-null, the regular infinity). But earlier in the verse it says that His thoughts toward us “cannot be recounted to You in order”. His thoughts cannot be put in order. This means that God’s thoughts are a higher level of infinity. God is not just infinite, aleph-null, but something higher, at least aleph-one.
The Lord is so much greater than you or me. My brain hurts just trying to understand the most basic level of infinity, and yet He is infinite in a much higher way.
But don’t miss what this verse is saying. The verse is not just speaking about the infinity of God, but of His thoughts toward us. He loves us so much that His thoughts about us are of a higher level of infinity, and He loves us so much that He sent His son to die for us.
I hope that this post and your future math studies help you better understand who God is, or at least helps you be in awe of His greatness.