2008-03-10 16:20MATH 880 PROSEMINAR JT SMITHOUTLINE 20 SPRING 20081. Assignmenta. Have we neglected anything for the in-class outline?b. Are there further questions about the social organization of mathematics?c. Continue reading Gillman 1987 and prepare to discuss it.d. Example proofs. I’d hoped to find a neat proof that any two bases of a vectorspace are equinumerous, which used Zorn’s lemma directly, without treatingthe finite case separately. But my attempt failed. Instead I crafted a combina-tion of proofs for the finite and infinite cases that are the neatest I found. Theproof sketches are posted on the website under “Readings”. Posted also arethe original versions. Please familiarize yourself with them. We’ll use themas an exercise for writing a literate proof later.2. Gillman 1987, chapter 3, continued.a. We celebrated the emphasis Gillman places on reader-friendliness.b. First person plurali. Gillman favors use of first person plural: “Next we show ... .” There iscontroversy about this.ii. I prefer to say I when I don’t mean you and I. But many readers andwriters seem embarrassed by such personal references.iii. Gillman probably regards his we as portraying his leading the reader.OK, that’s not bad.iv. But in many cases, the writer obviously is traveling solo: we means me,myself, and I.v. I believe Churchill once quipped that the only writers really entitled touse we that way were Queen Victoria, the Pope, and writers with tape-worms.c. Second personi. Gillman uses second person: “Keep the reader informed of what you aredoing.” I like that and have used it in my books about programming.But many of my colleagues and certainly my academic publisher wouldobject to any use of second person, probably as being too direct. Theymight write in third person, “The writer should keep the reader in-formed of what he is doing.” But that causes lots of problems.d. Third person.i. That gender-specific wording could be eliminated by pluralizing: “Writ-ers should keep the reader informed of what they are doing.”ii. Almost all unnecessarily gender-specific references can be avoided bypluralization or use of second person.iii. But this is not necessarily good. It sounds like a bunch of writers areganging up on one reader. How about unisex singulars: “One shouldkeep readers informed of what one is doing.” Yucch! Milquetoast! Howabout “Writers should keep readers informed of what they are doing”?Page 2 MATH 880 SPRING 2008 OUTLINE 202008-03-10 16:20That sounds ok until you begin wondering how writers are supposed toknow what readers are doing. Pay attention to what you write!iv. Students wondered whether Q.E.D. is passé. Probably, but in any caseit’s too language-specific. Would you understand the German W.Z.B.W.in place of the Latin? Clearly, Gillman prefers the diamond ‚ to callattention to the crystal clarity of your proof, or the tombstone  to