A Quote by Alexander Markovich Polyakov
We know that nature is described by the best of all possible mathematics because God created it. So there is a chance that the best of all possible mathematics will be created out of physicists' attempts to describe nature.
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We know that nature is described by the best of all possible mathematics because God created it.
What I realized is that if we're going to be able to have a theory about what happens in, for example, nature there has to ultimately be some rule by which nature operates. But the issue is does that rule have to correspond to something like a mathematical equation, something that we have sort of created in our human mathematics? And what I realized is that now with our understanding of computation and computer programs and so on, there is actually a much bigger universe of possible rules to describe the natural world than just the mathematical equation kinds of things.
All our surest statements about the nature of the world are mathematical statements, yet we do not know what mathematics "is"... and so we find that we have adapted a religion strikingly similar to many traditional faiths. Change "mathematics" to "God" and little else might seem to change. The problem of human contact with some spiritual realm, of timelessness, of our inability to capture all with language and symbol-all have their counterparts in the quest for the nature of Platonic mathematics.
One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.
Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.
I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.
Knowledge, in so far as it is directed to practical matters, has only to enumerate the principal possible attitudes of the thing towards us, as well as our best possible attitude towards it. Therein lies the ordinary function of ready-made concepts, those stations with which we mark out the path of becoming. But to seek to penetrate with them into the inmost nature of things, is to apply to the mobility of the real a method created in order to give stationary points of observation on it.
God created the world; the laws of nature were created by God. True science tries to find out what God put in the world. The trouble is where scientists speculate about theology and they don't know what they're talking about because they weren't there. They can't speculate about the origins of life because they weren't there.
Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought.
I admit that I do not recall the speeches of Comrades [Earl] Browder and [Samuel] Darcy. I do not even recall of what they spoke. It is possible that they said something of this nature. But it was not the Soviet people who created the American Communist Party. It was created by Americans.
One cannot inquire into the foundations and nature of mathematics without delving into the question of the operations by which the mathematical activity of the mind is conducted. If one failed to take that into account, then one would be left studying only the language in which mathematics is represented rather than the essence of mathematics.
Without doubt, God is the universal moving force, but each being is moved according to the nature that God has given it. God directs angels, men, animals, brute matter, in sum all created things, but each according to its nature: and man having been created free, he is led freely.
Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos [mathematics], where pure thought can dwell in its natural home.
Do not feed children on a maudlin sentimentalism or dogmatic religion; give them nature. Let their souls drink in all that is pure and sweet. Rear them, if possible, amid pleasant surroundings ... Let nature teach them the lessons of good and proper living, combined with an abundance of well-balanced nourishment. Those children will grow to be the best men and women. Put the best in them by contact with the best outside. They will absorb it as a plant absorbs the sunshine and the dew.
Why does mathematics describe nature. That's a deeper question than most.
In your nature, eternal Godhead, I shall come to know my nature. And what is my nature? It is fire, because you are nothing but a fire of love. And you have given humankind a share in this nature, for by the fire of love you created us.
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