Ben G's Math History Blog

For me, practicality in math has three requirements: one, the math involved should be relatively simple, even if the problem is not; two, the problem being considered should be non-mathematical in nature; three, the problem should be quotidian. I don’t believe that my interpretation relies on my familiarity with contemporary algebra, beyond the fact that being able to represent the situation in algebra rather than words makes it more tractable. Babylonian mathematics appears to have been developed, at least initially, to address real-world problems in farming, accounting, and surveying, and in that sense, Babylonian math was often practical. As Susan Gerofsky notes, however, sometimes the “impractical nature of [Babylonian word problems] […] casts doubt upon the serious practicality of even those most plausible problems” (Gerofsky 2004).  My notion of abstraction, on the other hand, is heavily reliant on contemporary algebra. For me, math is abstract when it is one degree removed f...

I generally consider myself decently knowledgable about the history of mathematics, for someone with no previous formal training or coursework in the area. Nevertheless, I was surprised to find the lengths that Western (meant to denote Europe, Canada, the US, New Zealand and Australia; Joseph prefers the term European) historians and writers went to in order to devalue the mathematical contributions of non-Western societies. Reading Joseph, this makes sense, since one of the implicit goals in writing these histories is to “[Ignore and devalue] the contributions of the colonized people … as part of the rationale for subjugation and dominance” (Joseph 2011, p. 5).  Nevertheless, it was surprising to me that it was known, at least by some, that there was “full acknowledgement given by the ancient Greeks themselves of the intellectual debt they owed the Egyptians” (Joseph 2011, p.5). I don’t know the exact timeline in which these acknowledgements were discovered, but it strikes me as v...

 Speculative Phase I will admit, I did spoil my speculative phase somewhat by discussing with my group in-class why we thought that Babylonians used a sexagesimal system. Tim suggested that one of the driving factors for the use of the sexagesimal system is that 60 is divisible by many of the smallest numbers, including 2,3,4,5,6, and 10. The power of this, as Tim pointed out, is that it is very easy to reduce a quantity by a half, or a third, or a quarter in the sexagesimal system. As far as I know (pre-research), Babylonians primarily used their number system for commerce and accounting, where it would be useful to be able to, say, figure out how much of your grain stock would remain if you lost a quarter to a mold infestation, or had to pay a tenth of it in taxes.  I imagine the fact that we still use 60 for time (60 seconds in a minute, 60 minutes in an hour) is a result of the Babylonians utilizing the sexagesimal system. I think I recall learning at some point that they ...

 I am a little embarrassed to say, my pre-reading thinking on the utility and value of the history of mathematics for mathematical education was a little unsophisticated and narrow. Before reading this week’s article, I viewed the role of history in the math classroom mostly as something to contextualize the actual math being learned. I felt that, by sprinkling historical blurbs throughout a semester, students would  (a) be better able to appreciate the way that many different types of people, not just European and American men, made deep and original contributions to mathematics. I believed that doing this would foster a more inclusive classroom environment, which would make more students feel confident about  (b) be better able to see math as a human endeavour, by exposing the creativity, passion, debates, mistakes and paradigm shifts that accompany human intellectual and creative activity I was pleased to see the article touch on the second point, emphasizing that...