How to write a proof Export

@article{citeulike:791402, abstract = {In their <em> The mathematical experience</em> \ref[Birkh\"{a}user, Boston, MA, 1980; <A HREF="/msnmain?fn=105\&fmt=doc\&r=1\&pg1=CNO\&s1=601591\&loc=fromrevtext">MR0601591 (82i:00020)</A>], P. J. Davis and R. Hersh are right to point out that "In being exposed to the scrutiny and judgement of a new audience, the proof is subject to a constant process of criticism and revalidation. Errors, ambiguities, and misunderstandings are cleared by constant exposure" (p. 151). However, the most illuminating aspect of their discussion of the role of proving theorems in mathematics is that theorem proving, in the best instances, increases "understanding by revealing the heart of matter" (p. 151). To the author of this paper, Leslie Lamport, "structured proofs", if not written appropriately, may fail to become more rigorous than conventional ones even though they communicate better messages. Reading very carefully through the paper several times, I remain unconvinced that the structured proof, say the one applied to the irrationality of the square root of 2, is a "good" one. My reason is simple: the standard of rigor for a mathematical proof evolves over time. Of course, a "good" proof should be as rigorous as possible. Yet it is not good enough unless it is able to convey as many messages as possible in an acceptable length. Nonetheless, the author should not be blamed for telling us how to write a good proof in terms of his perspectives. I gather sometimes that the different views of proof for a mathematician and for a computer scientist may lie in their different perception of what mathematics should be all about.}, address = {1529 Eighteenth St. NW, Washington DC 20036}, author = {Lamport, Leslie}, citeulike-article-id = {791402}, citeulike-linkout-0 = {http://www.ams.org/mathscinet-getitem?mr=1349872}, editor = {Ewing, John H.}, journal = {The American Mathematical Monthly}, keywords = {mathematics, methodology}, mrnumber = {MR1349872}, number = {7}, pages = {600--608}, posted-at = {2006-08-10 13:37:43}, priority = {4}, publisher = {American Mathematical Society}, title = {How to write a proof}, url = {http://www.ams.org/mathscinet-getitem?mr=1349872}, volume = {102}, year = {1995} }

TY - JOUR ID - citeulike:791402 L3 - citeulike-article-id:791402 N2 - In their <em> The mathematical experience</em> \ref[Birkhäuser, Boston, MA, 1980; <A HREF="/msnmain?fn=105&fmt=doc&r=1&pg1=CNO&s1=601591&loc=fromrevtext">MR0601591 (82i:00020)</A>], P. J. Davis and R. Hersh are right to point out that "In being exposed to the scrutiny and judgement of a new audience, the proof is subject to a constant process of criticism and revalidation. Errors, ambiguities, and misunderstandings are cleared by constant exposure" (p. 151). However, the most illuminating aspect of their discussion of the role of proving theorems in mathematics is that theorem proving, in the best instances, increases "understanding by revealing the heart of matter" (p. 151). To the author of this paper, Leslie Lamport, "structured proofs", if not written appropriately, may fail to become more rigorous than conventional ones even though they communicate better messages. Reading very carefully through the paper several times, I remain unconvinced that the structured proof, say the one applied to the irrationality of the square root of 2, is a "good" one. My reason is simple: the standard of rigor for a mathematical proof evolves over time. Of course, a "good" proof should be as rigorous as possible. Yet it is not good enough unless it is able to convey as many messages as possible in an acceptable length. Nonetheless, the author should not be blamed for telling us how to write a good proof in terms of his perspectives. I gather sometimes that the different views of proof for a mathematician and for a computer scientist may lie in their different perception of what mathematics should be all about. IS - 7 JF - The American Mathematical Monthly AD - 1529 Eighteenth St. NW, Washington DC 20036 EP - 608 TI - How to write a proof PB - American Mathematical Society VL - 102 SP - 600 KW - mathematics KW - methodology AU - Lamport, Leslie A2 - Ewing, John PY - 1995/// UR - http://www.ams.org/mathscinet-getitem?mr=1349872 ER -