id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_7gyy4v6ryvd2jovyltqplr3ydq	Barry Mazur	On mathematics, imagination & the beauty of numbers	2005	8	.pdf	application/pdf	4171	268	66	http://osc.hul.harvard.edu/dash/open-access-feedback?handle=&title=On%20Mathematics,%20Imagination%20and%20the%20Beauty%20of%20Numbers&community=1/1&collection=1/2&owningCollection1/2&harvardAuthors=b7a88f4ba7e143a265c8a195b0ea5d90&departmentMathematics well in your recent book, Imagining Numbers: (particularly the square root of minus think I ever deal with things that are abstract. the word 'abstract' except as a comparative term, even though lots of mathematicians use it in a way that reminds If one is really thinking about this 'abstracted' concept and analogous structure or concept may possibly make sense (say, think of composition of transformations as a kind of multiplication operation). One genre of analogizing in mathematics is to deal with a problem that at number theory, where there is no geometric, hence visual, ½eld, at least at ½rst geometric, hence visual, ½eld at ½rst may seem, the prime numbers are analogous to knots (closed non-self-intersecting loops) in the three-dimensional come from high dimensions, but is already in our three-dimensional space of (or visualizing, if you wish) any geometric object in four-dimensional space in more powerful by mathematical analogies.	./cache/work_7gyy4v6ryvd2jovyltqplr3ydq.pdf	./txt/work_7gyy4v6ryvd2jovyltqplr3ydq.txt