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— Nikolai Lobachevsky"In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid. As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain."
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Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas.
— Jean Dieudonne
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When I first began studying philosophy, a good deal of what went on in analytic epistemology was focused on addressing the Gettier problem. At first, I became quite caught up in it, and the kind of analytical ingenuity required for the work appealed to me. After a while, however, I started to lose interest.
— Hilary Kornblith
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