Struik: A Concise History of Mathematics: The Beginnings
by Carson Reynolds
Struik begins with the Paleolithicum (the old stone age). He paints primitive peoples transitioning from gathering to production. Modern encounters with primitive people provide so information about the development of mathematics.
The first occurrence of quantitative reasoning Struik sees was a qualitative distinction between one and two-or-more. Interesting, many languages first formed higher numbers through addition. Citing Australian tribes, he shows that 4 is formed by 2 and 2 (in Kamilaroi 2=bulan while 4=bulan bulan). As craft improved so did the number concept. By using fingers to count, numbers were bundled into larger units. This led to numeration to 5 and then 10 as a base. Sometimes systems were 20 base (toes being used), but in a survey of native American tribes, the good majority were decimal. Tally sticks were used to record numbers. Struik refutes the old saying “counting started as finger counting” by asserting that a certain amount of development was first required. Crude multiplication and division were used, almost always starting with the notion of 1/2. There was also a curious love of VERY large numbers, witness the bible.
Mensuration often from parts of the human body led to the beginnings of geometry. The etymology of straight and line has to do with measuring instruments. Geometric patterns were used for decoration and sacred acts. Magical figures and patterns from the neolithic and even paleolithic era are linked to the development of numerology.
The reckoning of time and the motion of the stars helped with the development of the understanding of the sphere, angular directions, and the circle.
The historical development does not follow the logical development we now teach. E.g. knots and patterns were only recently studied by modern mathematics.