One of the most interesting, but troubling and confusing concepts in mathematics and sciences is infinity. Probably arts and religion embraces it with much more ease. The operations of infinity and other numbers has confused the students. You encounter infinitesimally small and infinitely large things.
When I was listening to a video recently, there was another insight on infinity from an interesting mathematician called Dr. Steven Strogatz based on the interesting mathematical concept called ‘pi’. The sequence is extremely unpredictable, disorderly and it moves like this infinitely. There is an infinite amount of information. But this infinite amount of information is captured by an orderly circle, whose area or perimeter has the value of pi enshrined in it. So the scientist would speak of that extremely interesting combination of unpredictable infinity and predictable order in pi/circle. Many other fractions like 1/3 or 2/3 is extremely predictable, but if you go for the exact value, it is never ending. Again the combination of finiteness and infinity.
Another interesting description could be given by an ant moving on the surface of a sphere. In one way the area on the surface is measurable. But ant can keep on moving. It would have never have to turn around; moving on and on. Probably art is another medium where the infinity is captured beautifully.
Another interesting and powerful arena for believers in God is the idea/concept/person called God. Most religions equate God with infinity. We are time-bound; God is eternal (timeless). Yet many of our experiences of God are capturing that infinite God in our finite world. Most importantly the mystical experiences of several people of different religions have an deep and powerful encounter with the infinite God. They struggle to explain it in words, but it is again a moment of encountering infinity. When we have great and beautiful concepts of infinity in sciences and art, let us not be satisfied by our finite images and understandings of God (though they are significant) and constantly seek to understand and experience the mystery of mysteries, God.
The entire reality and each humans have the smell of infinity within. They have infinite possibilities, potentials and options. Friendships, love and other intimate relationships are attempts to capture that infinitude within the other person. They are the encounter of two infinities. The categories and judgments are important, but let us not fully capture the other or the reality in those categories of mine. They are beyond it.