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Ivor Grattan-Guinness

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Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists.
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Ivor Grattan-Guinness

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Mathematics occupies a peculiar position in cultural life today. 'Everybody knows' that it is one of the most basic, and also ancient, types of knowledge; yet it is not part of normal cultural discourse, and few people know much about its historical development, or even that it has a history.

 
Ivor Grattan-Guinness
 

I advocate an alliance of democratic states, with a dual purpose. One, to promote what I call open society. I talk about an alliance of open societies which would first foster the development of open societies within individual countries, because there's a lot that needs to be done in that effort. And secondly, to establish basic international law and international institutions that you need for a global, open society. So that's my sort of broad concept. Now, I have not worked out the details, because I don't think it's for me to work out the details. It's for them to work out the details.

 
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In our time of ever-increasing specialization, there is a tendency to concern ourselves with relatively narrow scientific problems. The broad foundations of our present-day scientific knowledge and its historical development tend to be forgotten too often. This is an unfortunate trend, not only because our horizon becomes rather limited and our perspective somewhat distorted, but also because there are many valuable lessons to be learned in looking back over the years during which the basic concepts and the fundamental laws of a particular scientific discipline were first formulated.

 
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Although much remains obscure, and will long remain obscure, ... I am convinced that Natural Selection has been the main but not exclusive means of modification.

 
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Where speculation ends — in real life — there real, positive science begins: the representation of the practical activity, of the practical process of development of men. Empty talk about consciousness ceases, and real knowledge has to take place. When reality is depicted, philosophy as an independent branch of activity loses its medium of existence. At the best its place can only be taken by a summing-up of the most general results, abstractions which arise from the observation of the historical development of men. Viewed apart from real history, these abstractions have in themselves no value whatsoever. They can only serve to facilitate the arrangement of historical material, to indicate the sequence of its seperate strata. But they by no means afford a recipe or schema, as does philosophy, for neatly trimming the epochs of history. On the contrary, our difficulties begin only when we set about the observation and the arrangement — the real depiction — of our historical material, whether of a past epoch or of the present.

 
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