By Mohammad Khosroshahi

The earliest discovery of humans using math is in a cave in the Czech Republic, where a bone with 55 notches carved into it lies, which dates back approximately 32,000 years. This is the earliest piece of evidence we have to indicate humans started tallying (Suzuki, 2002). And one of the earliest pieces of evidence that humanity would prosper into something great.

Egypt

Moving onto the ancient Egyptians, this is when arithmetic—a type of math that deals with numerical operations like addition, subtraction, multiplication, and division—starts to become popular. It is also the introduction of numerical symbols called hieroglyphs, which were often written on material such as papyrus, leather, and cloth. (Suzuki, 2002).

(O’Connor & Robertson, 2000)

Fractions were also prominent in ancient Egypt. However, unlike modern fractions which can be quite complex, they were in much simpler form using only the digit one in the numerator while utilizing an oval or open mouth symbol over the number they wanted to be the denominator (Suzuki, 2002). It is simply amazing how only a few thousand years ago, humans started to write fractions and basic numerals, and how, through continuous progress, we were able to achieve much greater and astronomical feats in the world of math.

Babylon

In Babylon, we discovered they were more advanced compared to their Egyptian counterparts and utilized place-value notation—which is the way we write numbers in the order of hundreds, tens, ones, which is flipped on the other side of a decimal (e.g. 100.00)—just like how we do today. Their system, however, differs from ours, using base 60 instead of base 10.

The Babylonians were especially successful in their use of mathematics in building canals to improve their city, proving that even thousands of years ago, mathematics changed lives and bettered society.

The Babylonians also were pioneers of geometry. Providing us with formulas that approximated shapes like triangles and isosceles trapezoids. Furthermore, the Babylonians were also knowledgeable of the Pythagorean theorem and were able to calculate square roots accurately (Suzuki, 2002).

Greece

Alongside the other great accomplishments of the Greeks, such as the alphabetic numbering system, is one of the greatest discoveries in human history: the Pythagorean theorem. The theorem states that the squares of two sides of a right triangle are equivalent to the square of the hypotenuse. Made by Pythagoras, an ancient Greek philosopher, the Pythagorean theorem is one of the most important tools in mathematics today (Suzuki, 2002).

Euclid and The Elements

Motivated by his predecessors such as Hippocrates, Euclid wanted to establish his own mathematical treatise, which would be a foundational study of geometry. This treatise is what has come to be known as The Elements. Euclid’s work is still used to this day and has been challenged since the 19th century. Euclid’s Elements include books involving the geometry of circles (book three) to number theory (book seven). The Elements is one of the most important books humanity has to offer to the mathematical world (Suzuki, 2002).

Calculating the Earth’s Circumference with a Stick and Some Mathematics

A few hundred years before Christ, there was a Greek mathematician by the name of Eratosthenes. Eratosthenes read that on the summer solstice, a well in Syene would not cast down a shadow. Wanting to produce the same result, he put a stick in the ground and noticed that a shadow was cast. This was strange as he was expecting the same result. He posited that there was curvature to the earth and that the angle of the shadow can determine what the circumference of the earth is. Measuring the angle to be around 7.2 degrees, he then hired a man to pace from Alexandria to Syene for the distance—5000 Stadia or 800km.

Using this data, he knew that 7.2 degrees is 1/50th of a circle, and with an 800km distance between Syene and Alexandria, it would mean that the earth had a circumference of 40,000 km. Using modern scientific methods today, we know the earth’s circumference is measured at 40,075 km. Considering the rudimentary tools involved, Eratosthenes’ estimation was insanely accurate for his time. Mathematics is truly amazing.

(Did Eratosthenes Really Measure the Size of the Earth?, 2017)

Sources:

Suzuki, J. (2002). A History of Mathematics. Pearson.
O’Connor, J. J., & Robertson, E. F. (2000, December). Egyptian numerals. Maths
History. https://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals/
Did Eratosthenes really measure the size of the earth? (2017, June 29).
The Renaissance Mathematicus.
https://thonyc.wordpress.com/2017/06/29/did-eratosthenes-really-measure-the-size-of-the-earth/