A History of Mathematics Blog by Tim

If we have learned anything from our mathematical past, it's that the world never splits cleanly into practical problems and abstract problems. A few simple examples of this might be the number  π , which started very simply as a practical relationship between the circumference and diameter of a circle, but can also be calculated in a very abstract way with an infinite series (the Leibniz formula for  π /4). Another example might be the many number theorist who prided themselves in pure abstraction of their field, only for a practical uses for their methods coming with the arrival of computers and the need for encryption techniques.  This article brings up some interesting interplay between practicality and abstraction in ancient Babylonian word problems. Firstly it seems clear, from the examples provided at the beginning and throughout the text, that many word problems were inspired by what was familiar in their everyday lives, so in a sense they have a level of practica...

          For someone taught a primarily Europe-centric math history, such as myself, there was a wealth of new and enlightening information to be gleaned from this chapter. One of the first things to catch me by surprise was the foundational beginning of math originating not in Greece, but in Egypt. The vision I was often presented with was one of famous Greek thinkers coming up with new ideas, as if out of thin air. The intelligence and creativity of the classic Greek thinkers is beyond doubt, but their reliance and debt to even earlier Egyptian mathematicians is essential to understand when trying understand a complete history of mathematical development. What makes this common omission so egregious is that the Greek thinkers themselves attributed the foundation of many of their ideas to Egyptian mathematics.            In the chapter, this neglect of anything mathematical originating prior to ancient Greece was exempli...

I will begin this blog post with some un-researched speculation about why the ancient Babylonians chose to use a base 60 (sexagesimal) number system. It so happens that 60 divides evenly by the first 6 numbers, i.e. 60/1=60, 60/2=30, 60/3=20, 60/4=15, 60/5=12, 60/6=10. This allows quick and accurate calculations of whole numbers when dividing  by 1, 2, 3, 4, 5, or 6 without recurring decimals (or I suppose recurring sexagesimals) showing up.  We see base 60 still present in certain parts of our lives, specifically in how we tell the time as possibly our measurements of degrees. 60 seconds in a minute, 60 minutes in a hour and even the 12 hours of AM and 12 of PM could be seen to be base 60 to some degree, as it's one fifth of 60. Additionally, measuring 360 degrees in a circle might come from 60x6. My guess as to why 360 was chosen is that splitting a circle into 60 parts proved too rough for accurate measurements, whereas splitting a circle into 3600 (60x60) parts proved too ...

          As someone who grew up learning math in the “traditional” way, presented primarily with objective theorems and axioms, math history was often provided as a side-dish not meant to be incorporated with the entrée. If you had already eaten your fill with the main course, you could forget the side-dish, it was interesting, perhaps, but certainly not essential. Additionally, this “side-dish” of math history was inevitably European centric. It lacked the intense spices found in traditional Indian cuisine, the fragrant herbs from Arabic cooking, or the rich flavours of Chinese and other east Asian foods. This, predictably, contributed heavily to my own philosophy around math education but this chapter by Tzanakis, C. et al . has opened my eyes in a number of ways.             Something that jumped out at me immediately, from section 7.3.2 was the idea of integrating history directly into the teaching of math. The idea o...