If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.
David HilbertRead
The further a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.
Interpretation
Mathematics reveals deeper connections as it develops further.
David Hilbert suggests that as mathematical theories advance, they tend to become more coherent and interconnected, unveiling unexpected relationships between different areas of mathematics. This reflects the inherent unity of mathematical concepts and the way that progress in one domain can illuminate understanding in another.
In practice
A mathematician might use this quote to inspire students at a seminar about the beauty of mathematical connections.
If one were to bring ten of the wisest men in the world together and ask them what was the most stupid thing in existence, they would not be able to discover anything so stupid as astrology.
The art of doing mathematics consists in finding that special case which contains all the germs of generality.
Wir mussen wissen. Wir werden wissen. We must know. We will know. Inscribed on his tomb in Gilttingen.
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
No one shall expel us from the paradise that Cantor has created for us.
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts.
A black hole really is an object with very rich structure, just like Earth has a rich structure of mountains, valleys, oceans, and so forth. Its warped space whirls around the central singularity like air in a tornado.
Math is the language of the universe. So the more equations you know, the more you can converse with the cosmos.
It is now widely realized that nearly all the 'classical' problems of molecular biology have either been solved or will be solved in the next decade. The entry of large numbers of American and other biochemists into the field will ensure that all the chemical details of replication and transcription will be elucidated. Because of this, I have long felt that the future of molecular biology lies in the extension of research to other fields of biology, notably development and the nervous system.
[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory.
No one knows the diversity in the world, not even to the nearest order of magnitude. ... We don't know for sure how many species there are, where they can be found or how fast they're disappearing. It's like having astronomy without knowing where the stars are.
We cannot even predict what kinds of emergent properties would appear when animals begin interacting as part of a brain-net. In theory, you could imagine that a combination of brains could provide solutions that individual brains cannot achieve by themselves.
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