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I believe that faith is a precursor of all our ideas. Without faith, there never could have evolved hypothesis, theory, science or mathematics. I believe that faith is an extension of the mind. It is the key that negates the impossible. To deny faith is to refute oneself and the spirit that generates all our creative forces. My faith is in the unknown, in all that we do not understand by reason; I believe that what is beyond our comprehension is a simple fact in other dimensions, and that in the realm of the unknown there is an infinite power for good.
I had a feeling once about Mathematics, that I saw it all—Depth beyond depth was revealed to me—the Byss and the Abyss. I saw, as one might see the transit of Venus—or even the Lord Mayor's Show, a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable: and how the one step involved all the others. It was like politics. But it was after dinner and I let it go!
No one is without Christianity, if we agree on what we mean by that word. It is every individual's individual code of behavior by means of which he makes himself a better human being than his nature wants to be, if he followed his nature only. Whatever its symbol — cross or crescent or whatever — that symbol is man's reminder of his duty inside the human race. Its various allegories are the charts against which he measures himself and learns to know what he is. It cannot teach a man to be good as the textbook teaches him mathematics. It shows him how to discover himself, evolve for himself a moral codes and standard within his capacities and aspirations, by giving him a matchless example of suffering and sacrifice and the promise of hope.
But as I considered the matter carefully it gradually came to light that all those matters only were referred to Mathematics in which order and measurement are investigated, and it makes no difference whether it be in numbers, figures, stars, sounds or any other objects that the question of measurement arises.
We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science.
Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.