Paulos Essays
Beyond Numeracy: Ruminations of a Numbers Man
By John Allen Paulos
Algebra – Some Basic Principles
I always liked elementary algebra partly because my first teacher of it had been recruited (dragoonedV1 might be a better word) into teaching the subject even though she didn’t know a quadratic formula from an upper leg regimen. Being honest, however, she didn’t try to hide this fact, and being near retirement, she depended on her better students to help her out of any mathematical difficulties. She often found some pretext to have one of us come to her classroom after school, at which time she always managed to rehearse the next day’s lesson. Happily (and necessarily) she stressed a few basic principles and left most of the details to us. Despite knowing some mathematics, I’ll try to follow her sound pedagogicalV2 example of sketching the broad picture and avoiding technicalities as much as possible. This is especially important in algebra, whose mere mention brings back for many people miserable memories of trying to determine Henry’s age when told that he is 5 times as old as his son, but will in 4 years time be only 3 times as old.W1 There are many reasons for this distaste, but I sometimes wonder if one of them might not be traceable to algebra’s discovery by Al-KhowarizmiQ1 in the early ninth century. This Al-Khowarizmi, from whose name the English word “algorithmV3” is derived and from whose influential book Al-jabr wa’l Muqabalah we get our word “algebra,” was one of the preeminentV4 mathematicians of a most impressive era in Arabic learning. His book deals with the solving of various simple sorts of equations, but true to what algorithm has come to mean, Al-Khowarizmi concentrated almost exclusively on recipes, formulas, and procedures. To my mind, his text has little of the elegance or logical appeal of Euclid’s ElementsQ2, but like the latter it was the standard work in its field for a very long time. Although Al-Khowarizmi did not
By John Allen Paulos
Algebra – Some Basic Principles
I always liked elementary algebra partly because my first teacher of it had been recruited (dragoonedV1 might be a better word) into teaching the subject even though she didn’t know a quadratic formula from an upper leg regimen. Being honest, however, she didn’t try to hide this fact, and being near retirement, she depended on her better students to help her out of any mathematical difficulties. She often found some pretext to have one of us come to her classroom after school, at which time she always managed to rehearse the next day’s lesson. Happily (and necessarily) she stressed a few basic principles and left most of the details to us. Despite knowing some mathematics, I’ll try to follow her sound pedagogicalV2 example of sketching the broad picture and avoiding technicalities as much as possible. This is especially important in algebra, whose mere mention brings back for many people miserable memories of trying to determine Henry’s age when told that he is 5 times as old as his son, but will in 4 years time be only 3 times as old.W1 There are many reasons for this distaste, but I sometimes wonder if one of them might not be traceable to algebra’s discovery by Al-KhowarizmiQ1 in the early ninth century. This Al-Khowarizmi, from whose name the English word “algorithmV3” is derived and from whose influential book Al-jabr wa’l Muqabalah we get our word “algebra,” was one of the preeminentV4 mathematicians of a most impressive era in Arabic learning. His book deals with the solving of various simple sorts of equations, but true to what algorithm has come to mean, Al-Khowarizmi concentrated almost exclusively on recipes, formulas, and procedures. To my mind, his text has little of the elegance or logical appeal of Euclid’s ElementsQ2, but like the latter it was the standard work in its field for a very long time. Although Al-Khowarizmi did not