A Quote by Vladimir Arnold
The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).
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The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation of it.
Attempts are found in domains of human performance, such as sports, games, artistic domains, professional domains like medicine and the law, and so on. These feature distinctive aims, and corresponding competences. Archery, with its distinctive arrows and targets, divides into subdomains. Thus, competitive archery differs importantly from archery hunting.
I would support peaceful co-existence between religion and science because they concern different domains. Anyone who takes theology seriously knows that it's not a matter of using it to explain things that scientists are mystified by.
Outside speech, the association that is made in the memory between words having something in common creates different groups, series, families, within which very diverse relations obtain but belonging to a single category: these are associative relations.
The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems -- the determination of the diagonal of a square and that of the circumference of a circle -- revealed the existence of new mathematical beings for which no place could be found within the rational domain.
If the resources of different nations are treated as exclusive properties of these nations as wholes, if international economic relations, instead of being relations between individuals, become increasingly relations between whole nations organized as trading bodies, they inevitably become the source of friction and envy between whole nations.
The most rewarding part of my work is the "Aha" moment, the excitement of discovery and enjoyment of understanding something new - the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight. I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.
The existence of common features in different forms of life indicates some relationship between the different organisms, and according to the concept of evolution, these relations stem from the circumstance that the higher organisms, in the course of millions of years, have gradually evolved from simpler ones.
The most striking feature of the perennial philosophy/psychology is that it presents being and consciousness as a hierarchy of dimensional levels, moving from the lowest, densest, and most fragmentary realms to the highest, subtlest, and most unitary ones.
The most striking feature of contemporary culture is the unslaked craving for transcendence.
The broader the chess player you are, the easier it is to be competitive, and the same seems to be true of mathematics - if you can find links between different branches of mathematics, it can help you resolve problems. In both mathematics and chess, you study existing theory and use that to go forward.
Perhaps the most striking feature of the [nonprofit] sector is its relative freedom from constraints and its resulting pluralism.
A decline in courage may be the most striking feature that an outside observer notices in the West today.
Whichever theory we adopt to give a rational explanation of human existence, that theory must take into account and explain the mental nature we see at work in all modern communities.
There is an age-old proverb that really does hold true in every area of life - in relations between nations and right down to the most subtle and sophisticated or must unstable and unsophisticated relations between lovers - and it is this: they took "kindness" for "weakness."
So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bernoulli, Herapath, Joule, Kronig, Clausius, &c., have shewn that the relations between pressure, temperature and density in a perfect gas can be explained by supposing the particles move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure.
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