Maybe we have become so hung up on looking at the primes from Gauss's and Riemann's perspective that what we are missing is simply a different way to understand these enigmatic numbers. Gauss gave an estimate for the number of primes, Riemann predicted that the guess is at worst the square root of N off its mark, Littlewood showed that you can't do better than this. Maybe there is an alternative viewpoint that no one has found because we have become so culturally attached to the house that Gauss built.
Carl Friedrich GaussRelated topics
alternative built different found hang house looking mark number off root square way worst viewpoint gauss RiemannRelated quotes
Conditions to the north of us, in the Voronezh and Steppe Fronts zone of action, and our offensive on Kharkov demands that we not lose time and we commit all forces so that we can draw off as many divisions as possible from Kharkov. And even if we do not draw them off, at least we will not give Manstein the ability to take any of his units from our part of the front. If we attract one or two German tank divisions - it will be the best contribution to the defeat of the enemy in the south.
Aleksandr Vasilevsky
The history of medicine proves that in so far as man seeks to know himself and face his whole nature, he has become free from bewildered fear, despondent shame, or arrant hypocrisy. As long as sex is dealt with in the current confusion of ignorance and sophistication, denial and indulgence, suppression and stimulation, punishment and exploitation, secrecy and display, it will be associated with a duplicity and indecency that lead neither to intellectual honesty nor human dignity.
Alfred Kinsey
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
If someone offends you, don't tell anyone about it except your elder, and you will be peaceful. Bow to everyone, paying no attention whether they respond to your bow or not. You must humble yourself before everyone and consider yourself the worst of all. If we have not committed the sins that others have, perhaps this is because we did not have the opportunity - the situation and circumstances were different. In each person there is something good and something bad; we usually see only the vices in people and we see nothing that is good.
Ambrose
O death, where is thy sting?
O Hell, where is thy victory?
Christ is Risen, and you, o death, are annihilated!
Christ is Risen, and the evil ones are cast down!
Christ is Risen, and the angels rejoice!
Christ is Risen, and life is liberated!
Christ is Risen, and the tomb is emptied of its dead; for Christ having risen from the dead, is become the first-fruits of those who have fallen asleep.
To Him be Glory and Power forever and ever. Amen!
John Chrysostom