I discovered the works of Euler and my perception of the nature of mathematics underwent a dramatic transformation. I was de-Bourbakized, stopped believing in sets, and was expelled from the Cantorian paradise. I still believe in abstraction, but now I know that one ends with abstraction, not starts with it. I learned that one has to adapt abstractions to reality and not the other way around. Mathematics stopped being a science of theories but reappeared to me as a science of numbers and shapes.
Alexander StepanovRelated topics
abstraction believing believe mathematics nature now numbers paradise perception reality science stop transformation way works euler endsRelated quotes
The man who has struggled bravely with the passions of the body, has fought ably against unclean spirits, and has expelled from his soul the conceptual images they provoke, should pray for a pure heart to be given him and for a spirit of integrity to be renewed within him (cf. Ps. 51:10). In other words, he should pray that by grace he may be completely emptied of evil thoughts and filled with divine thoughts, so that he may become a spiritual world of God, splendid and vast, wrought from moral, natural and theological forms of contemplation.
Maximus the Confessor
No matter how much we may study, it is not possible to come to know God unless we live according to His commandments, for God is not know by science, but by the Holy Spirit. Many philosophers and learned men came to the belief that God exists, but they did not know God. It is one thing to belief that God exists and another to know Him. If someone has come to know God by the Holy Spirit, his soul will burn with love for God day and night, and his soul cannot be bound to any earthly thing.
Silouan the Athonite
If you are remembering evil against someone, then pray for him; and as you remove through prayer the pain of the remembrance of the evil he has done, you will stop the advance of the passion. And when you have attained brotherly love and love for mankind, you will completely cast this passion out of your soul. Then when someone else does evil to you, be affectionate and humble toward him, and treat him kindly, and you will deliver him from this passion.
Maximus the Confessor
In 1915 Sophie Taeuber and I carried out our first works in the simplest forms, using painting, embroidery and pasted paper [without using oil colors to avoid any reference with usual painting]. These were probably the first manifestations of their kind, pictures that were their own reality, without meaning or cerebral intention. We rejected everything in the nature of a copy or a description, in order to give free flow to what was elemental and spontaneous.
Jean Arp
Three principles - the conformability of nature to herself, the applicability of the criterion of simplicity, and the "unreasonable effectiveness" of certain parts of mathematics in describing physical reality - are thus consequences of the underlying law of the elementary particles and their interactions. Those three principles need not be assumed as separate metaphysical postulates. Instead, they are emergent properties of the fundamental laws of physics.
Murray Gell-Mann
