Vol. 10 No 3 - Pi Mu Epsilon

252 PI Mu EPSILON JOURNALcertain. Anyone who has been teaching calculus for a while could, if lockedin a room, supplied with nothing but food, water, and reams of paper and toldthat the door would not be unlocked until a calculus textbook had been written,do the job. It might be excruciatingly tedious, but we could produce anacceptable calculus text because we know calculus.Not everyone is as lucky. In some fields, not only do its practitioners nothave the satisfaction of knowing that they have mastered a body of knowledge,there is a question of whether there is a body of knowledge to be mastered.Mathematicians have the assurance that comes with mastery. This hasbeen widely observed, as by Rebecca Goldstein, a philosopher and novelist, inThe Mind-Body Problem (Random House. 1983, Penguin reprint, 1993, pp.201-202):Observers of the academic scene may be aware that there aredistinct personality types associated with different disciplines. Thetypes can be ordered along the line of a single parameter: the degreeof concern demonstrated over the presentation of self, or "outwardfocus." ...Thus at the end of the spectrum occupied by the sociologists andprofessors of literature, where there is uncertainty as how to discoverthe facts, the nature of the facts to be discovered, and whether indeedthere are any facts at all, all attention is focused on one's peers, whoseregard is the sole criterion for professional success. Great pains aretaken in the development of the impressive persona, with excessiveattention given to distinguished and faultless sentence structure.At the other end, where, as the mathematicians themselves arefond of pointing out, "a proof is a proof," no concern need be given tomaking oneself acceptable to others; and as a rule none whatsoever isgiven.To sum up, mathematics is the best of all possible places to be,intellectually. There is matter, plenty of it, that can be mastered. We cannotmaster all of mathematics, but in the part we have mastered there are problemsto be worked on and solved, no matter what our level of brilliance is. Solvingthe problenls can give satisfaction, and can also advance the subject. Further,the supply of problems will never dry up. We are finite but mathematics isinfinite. Who could ask for anything more? We are lucky.Play the 1995 Game!Though the year is no longer young. there is still time to play the 1995game. Paul S. Bruckmiin challenges you to represent the integers from 1 onup using the digits 1. 9. 9. and 5 in that order. For example.I= -1./9"+9 -5 2= 1+9-1/9'-5- . .-3= 1-9+(/9)! +5 4=-1+9-9+55= 1-9 -9 + 5 6= 1+9-9+5.You may have some dilliculty with 20 and 25 Using various subterfuges, Mr.Bruckman got all the way to 139 before quitting. and closed with a four deforce by noting that1995 = ( l9./9-5).( l + 9 - 5).After the 1995 game there is always the 1996 game to look forward to.though 1 think it may be a bit harder. We should enjoy these games whilecan. since the 2000 game will not be vey rewarding.ErrataWhatever his other virtues, your editor is not very good at proofreading.The Journal always lias errors. too many of them. For example, in the lastissue (p. 103) the sequence was misprinted: as several readers pointed out, itshould have beenwhich makes the next term. 5. obvious if you see the pattern.Rex Wu found three errors in his "A note on an exponential equation" (10(1 994-99) # 1. 22-25): on page 23, line 5. (A-,,. A- ,. , . 4) should have thesubscripts running from 1 to n; on page 23, line 24 in gcd(A-, M) s the termto the right of the divides sign should be (ck - s) ; and on page 24, line 1 1 thefour-tuple of powers of 2 sllould be (2 l3 .2", 236, 2'" ).He also notes that ? + 18' = 3' provides an answer to his last questionin the paper's last paragraph.Corrections generally have a hard time catching up with the original errors,but theJournal will continue to print errata as space permits.