Since prehistoric times, people have been finding different ways to count and measure things in the world. In most cultures, mathematics soon developed far beyond basic counting, and historical artifacts such as books, drawings, and tools have helped us track the evolution of these mathematical ideas.
Ancient tallies (30,000 BCE)
Before written numbers are invented, prehistoric people make marks in wood, clay, bone, or stone to count things such as passing days or animals in their herds.
First numbers (3500 BCE)
People in the Sumerian civilization in Mesopotamia (modern-day Iraq) devise the first system to use symbols to stand for the numbers of objects. The system is sexagesimal, meaning that it uses 60 as its base. This is based on the Sumerian method of counting on their hands. They count each finger segment on one hand to reach 12, and multiply that by five (the number of fingers on the other hand) to reach 60.
Piece of Pi (3000 BCE)
The Babylonian people in Mesopotamia calculate that a circle’s circumference is about three times the size of its diameter. This ratio is important as it applies to any circle of any size. We now know that this number is 3.141592..., with the numbers after the decimal point continuing forever. This number is represented by the Greek symbol pi (π).
Ancient fractions (3000 BCE)
Ancient Egypt is one of the first civilizations to use fractions. This advancement is referred to in the Rhind Papyrus, an ancient mathematics textbook written around 1550 BCE that won’t be discovered until thousands of years later in a tomb in Thebes in Egypt.
Building the Great Pyramid (2560 BCE)
Ancient Egyptians’ knowledge of right angles helps them to build the Great Pyramid, an architectural wonder whose construction involves precise measurements and the perfect alignment of at least 2.5 million stones. Present-day mathematicians are amazed by how complex the Egyptians’ calculations are.
The golden ratio (500 BCE)
The ancient Greeks are fascinated by a ratio, known as the golden ratio, which they discover can be used to draw attractive patterns of rectangles. They build temples using this ratio, as it is said to create shapes that are pleasing to the eye.
Triangle theory (500 BCE)
Ancient Greek mathematician Pythagoras presents a theory of right-angled triangles, which can be used to work out the length of any unknown sides, and is used in many other math problems. It is known by the formula a² + b² = c², where the letters refer to the length of each side of the triangle.
Zero (630 CE)
The idea of zero to represent nothing is introduced in a manuscript by Indian mathematician Brahmagupta, written around 630 CE. The creation of zero is one of the greatest breakthroughs in math, as it allows us to write huge numbers without the need to create new digits.
Known numbers (800 CE)
Persian mathematician Al-Khwarizmi adapts a number system in which Hindu-Arabic symbols stand for the number of objects, to create the system most used today. In this, the numerals 0 to 9 are used to represent all numbers. In 300 years, these numbers will be introduced to Europe.
Fibonacci sequence (1202)
Italian mathematician Fibonacci devises a special sequence of numbers in which each number is found by adding together the two numbers before it: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. This sequence can be used to draw a perfect spiral pattern, and will go on to be used to write computer programs, too.
Artistic mathematics (1415)
Renaissance artists discover they can use math to make pictures look more three-dimensional by drawing distant objects smaller. This geometrical approach, known as perspective, is first adopted by Italian designer and artist Fillipo Brunelleschi.
To infinity (1655)
The concept of a number going on forever, known as infinity, has been discussed since ancient times. However, British mathematician John Wallis is the first person to come up with a symbol for infinity. ∞ is still used to represent infinity today.
US mathematician Edward Kasner asks his nine-year-old nephew what to call the number 1 followed by 100 zeros, and he suggests "googol". The number 1 followed by a googol of zeros is a googolplex, and 1 followed by a googolplex of zeros is a googolplexian, the biggest named number to date.