These are some external pages on mathematics in general, mathematical philosophy, culture and society of mathematics, etc. See also this discussion at mathoverflow.net that mentions many of the papers.
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Terry Tao’s career advice has very useful information. The undergraduate, graduate, and postdoctoral sections, as well as miscellanous links at the bottom, are particularly relevant for people studying and researching mathematics.
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Some of Timothy Gowers’ writings can be accessed here. His famous writings/speeches include: Does mathematics need a philosophy?, Two cultures of mathematics and the importance of mathematics (slides)(transcript).
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On proof and progress in mathematics by William Thurston.
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Two articles/speeches by Freeman Dyson: Birds and Frogs, and Missed Opportunities.
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Articles by Yuri Manin: Truth as value and duty: lessons of mathematics and Mathematical knowledge: internal, social and cultural aspects, among many others.
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The Princeton University Press’s section on advice to younger mathematicians.
What Is Research? 
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