The history of mathematics begins 33,000 years ago Africa, when a woman made 29 notches in a baboon’s fibula to record the days between her menstrual cycles. This record shows that as far back as prehistoric times, humans have had a concept of numbers and have been using this concept to improve their lives as well as their understanding of the universe.
Among ancient civilizations, Mesopotamia and Egypt developed the highest level of mathematical understanding. We currently have more than 400 tablets of Sumerian Cuneiform writing showing that the Mesopotamian understood not only basic times tables, but quadratic and linear equations. In Egypt, mathematicians developed the first “word problems” such as are the terror of students even today, although they were thought of as more of an amusing pastime. And this is to say nothing of the advanced level of mathematical and scientific understanding that was required to build the pyramids.
The Greeks were the next the systematically study the science of numbers. Among Greek mathematicians, the chief two are Pythagoras and Euclid. Pythagoras first proposed what came to be known as the Pythagorean Theory, that the square of the hypotenuse of any right triangle is equal to the sum of the squares of its two other sides. Euclid developed the axioms that formed the basis of all geometry until the early 20th century. Indeed, standard geometry is still referred to as Euclidean geometry after the man who codified it.
The next major advance in mathematics occurred, as it had at the dawn of civilization, in the Middle East. Medieval Islamic scholars working from translations of Euclid made major strides in the study of algebra—indeed, the word “algorithm” comes from the Latinized name of the Persian mathematician Al-Khwarizmi. The scholar and poet Omar Khayyam’s critiques of Euclid lead him to forms the theories at the base of modern analytic geometry.
It was in part the work of Al-Khwarizmi and others like him that mathematics flourished as it did in the Renaissance. With the rise of an interest-based economy, calculations involving complex algebra became more important than ever, and furthermore lead to the development of the decimal system. The era also marked some of the first developments in Trigonometry, from example Bartholomaeus Pitiscus’s “Trigonometria”, which was published in 1595. Rene Descartes also formally began the study of analytical geometry, which studies planar surfaces using points on a graph or Cartesian Coordinates.
From the 19th Century on, mathematics has become increasingly abstract. Russian Nikolai Ivanovich Lobachevsky and Hungarian Janos Bolyai simultaneously developed a new kind of non-Euclidean geometry, Hyperbolic geometry, which dispensed with many of Euclid’s basic theories in order to study more complex surfaces. In the late 19th century, George Cantor developed Set Theory, which took more note of the concept of infinity than had ever previously been done, and so changed the way scholars view mathematics even now.
From the twentieth century to today, the study of mathematics has grown ever deeper. Some mathematicians, however, have tried to show there is a limitation to what mathematics can say about the universe, as Kurt Gödel with his Incompleteness Theorem. Nevertheless, mathematicians continue to rigorously study numbers and how they can be used to improve our lives, just as the African woman with the baboon’s fibula did 33,000 years ago.