Read e-book online The Best Writing on Mathematics 2012 PDF

By David Mumford, Mircea Pitici

ISBN-10: 0691156557

ISBN-13: 9780691156552

This annual anthology brings jointly the year's most interesting arithmetic writing from worldwide. that includes promising new voices along the various most well known names within the box, The top Writing on arithmetic 2012 makes to be had to a large viewers many articles no longer simply stumbled on wherever else--and you don't have to be a mathematician to get pleasure from them. those writings supply striking insights into the character, which means, and perform of arithmetic this present day. They delve into the background, philosophy, educating, and daily occurrences of math, and take readers backstage of today's most well liked mathematical debates. the following Robert Lang explains mathematical elements of origami foldings; Terence Tao discusses the frequency and distribution of the leading numbers; Timothy Gowers and Mario Livio wonder whether arithmetic is invented or came upon; Brian Hayes describes what's targeted a few ball in 5 dimensions; Mark Colyvan glosses at the arithmetic of relationship; and lots more and plenty, a lot more.

In addition to proposing the year's so much memorable writings on arithmetic, this must-have anthology encompasses a foreword by way of esteemed mathematician David Mumford and an advent by means of the editor Mircea Pitici. This e-book belongs at the shelf of somebody drawn to the place math has taken us--and the place it really is headed.

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Another argument against the idea that one brings an abstract concept into existence when one invents it is that the concepts that we invent are not fundamental enough: They tend to be methods for dealing with other objects, either abstract or concrete, that are much simpler. For example, the rules of cricket describe constraints on a set of procedures that are carried out by 22 players, a ball, and two wickets. From an ontological point of view, the players, ball, and wickets seem more secure than the constraints on how they behave.

We also drew some more refined, but less important, distinctions within each class. A discovery tends to be more notable than an observation and less easy to verify afterward. And inventions tend to be more general than creations. Do these distinctions continue to hold in much the same form when we come to talk about mathematics? I claimed earlier that the formula for the quadratic was discovered, and when I try out the phrase “the invention of the formula for the quadratic,” I find that I do not like it, for exactly the reason that the solutions of ax2 + bx + c are the numbers (-b !

Doctors depend on homology theory to do brain scans, and cosmologists use it to understand how galaxies form. Mobile-­ phone companies use topology to identify the holes in network coverage; the phones themselves use topology to analyze the photos they take. It is precisely because topology is free of distance measurements that it is so powerful. The same theorems apply to any knotted DNA, regardless of how long it is or what animal it comes from. We don’t need different brain scanners for people with different-­sized brains.

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The Best Writing on Mathematics 2012 by David Mumford, Mircea Pitici

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