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.
Fudging the data in any way whatsoever is quite literally a sin against the holy ghost of science. I'm not religious, but I put it that way because I feel so strongly. It's the one thing you do not ever do. You've got to have standards.
'Science in itself' is nothing, for it exists only in the human beings who are its bearers. 'Science for its own sake' usually means nothing more than science for the sake of the people who happen to be pursuing it.
There are always more questions. Science as a process is never complete. It is not a foot race, with a finish line.... People will always be waiting at a particular finish line: journalists with their cameras, impatient crowds eager to call the race, astounded to see the scientists approach, pass the mark, and keep running. It's a common misunderstanding, he said. They conclude there was no race. As long as we won't commit to knowing everything, the presumption is we know nothing.
The conquest of space is not merely a technological project of interest to a handful of select scientists and specialists, valuable though that research and information may be.
I'm not trying to copy Nature, I'm trying to find the principles she's using.
I hope that some day the practice of producing cowpox in human beings will spread over the world - when that day comes, there will be no more smallpox.
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