What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.I've often compared maths to music - seeing the theory come together to produce harmony, symmetry, order, unity, that we can at once hear the ensemble and the parts - to which some are 'tone deaf' (though in different proportions to those who appreciate this in music and those who are tone deaf to it).
A scientist worthy of his name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.And on the usefulness of maths:
The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of that beauty that strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that more profound beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp.Now take that thought and instead of ending with the knowledge of the beauty of nature, which is pointless by itself, look along that to see the glory of God. And think of that when you're slogging away on trying to get your epsilons and deltas to befriend each other this side of infinity, and you find joy in appreciating God's glory using the maths he has given us. :D
These views, if I interpret them correctly, are what I have long thought of maths. Even Warwick didn't kill that. Here is the quote that has been used (a little unjustly I think) to embody the anti-religious philosophy which is propagated in some of the universities here:
La pensée ne doit jamais se soumettre, ni un dogme, ni un parti, ni à une passion, ni à un intérêt, ni à une idée préconçue, ni à quoi que ce soit, si ce n'est aux faits eux-mêmes, parce que, pour elle, se soumettre, ce serait cesser d'être.A clumsy translation (no time for better!): "Thought must never submit itself: not to dogma, nor to a party, nor to a passion, nor to a (vested) interest, nor to a preconceived idea, nor to whatever it may be, if it is not to facts themselves, because for thought to submit itself, would be to cease to be."
This is in spirit a rally-cry of modernism, for objective science. But all our science is 'ours', so submits to our individual or collective commitments and preconceptions. It may sometimes suceed in challenging them, but it will never escape them. The only chance we have at 'thought' not submitted to our preconceived ideas is if someone outside of the universe of those preconceived ideas were to directly reveal something.
How would this revelation not be forced into our preconceived ideas and systems as soon as revealed to us? Only by it transforming us internally as well as revealing externally.
"So Jesus said to the Jews who had believed in him, "If you abide in my word, you are truly my disciples, and you will know the truth, and the truth will set you free." [John 8.31-32]