Home / Maths around the world
Mathematics belongs to everyone. People in every part of the world have counted, measured, calculated and proved things, and they often learned from one another along the way.
Follow the line from the earliest counting marks to maths today.
About 43,000 years ago
Lebombo Mountains, southern Africa
A small baboon bone found in Border Cave, on the border between Eswatini and South Africa, has deliberate notches cut into it. It is about 43,000 years old, which makes it one of the oldest known marked bones. Some researchers think it may have been a tally stick used for counting.
About 20,000 years ago
Ishango, Central Africa
A bone found near the Semliki River in the Democratic Republic of the Congo has rows of carefully cut notches in groups. Some people think it is one of the oldest records of counting. Others think the notches may show patterns in the numbers. Nobody can be sure, which is part of what makes it fascinating.
About 3300 BCE
Uruk, Sumer
In the Sumerian city of Uruk, people pressed marks into soft clay with a reed to keep track of grain, sheep and beer. This was some of the earliest writing in the world, and numbers came first. Later scribes used a wedge-shaped tip, which gave cuneiform its name, and wrote on clay tablets that survive to this day.
About 3000 BCE
Ancient Egypt
Ancient Egyptians counted in tens with picture symbols: a stroke for 1, a cattle hobble for 10, a rope coil for 100, a water lily for 1,000, a finger for 10,000 and a tadpole for 100,000. They repeated symbols to make bigger numbers, so 3,000 was three lilies. They had no place value system.
About 2600 BCE
Indus Valley
People of the Indus Valley civilisation planned cities on a grid. They made stone weights in regular ratios, with the smaller ones in a ratio of 5:2:1, and decimal divisions for measuring. The same measures were used across a huge region, from Pakistan to western India.
About 1850 BCE
Ancient Egypt
The Moscow Papyrus is an Egyptian scroll with 25 problems. In Problem 14 a scribe finds the volume of a pyramid with its top cut off, called a frustum, with a base of 4, a top of 2 and a height of 6. The answer, 56, is correct, and the steps are the same as the formula we use today.
About 1800 BCE
Babylon, Mesopotamia
Babylonian scribes wrote numbers in clay with a base 60 system, using only two kinds of wedge mark, and the position of a mark gave its value, just like our place value. That is why an hour has 60 minutes and a circle has 360 degrees. A famous tablet called Plimpton 322 lists number patterns that match right-angled triangles, more than a thousand years before Pythagoras.
About 1700 BCE
Babylon, Mesopotamia
A Babylonian tablet known as YBC 7289 shows a square with its diagonals. The scribe wrote the length of the diagonal as 1;24,51,10 times the side, which is the square root of 2 correct to about six decimal places, around 3,700 years ago.
About 1550 BCE
Ancient Egypt
The Rhind Papyrus is a scroll of practical problems, including sharing loaves, working out the areas of fields and finding the slope of a pyramid. Egyptian scribes wrote most fractions as sums of unit fractions, such as 1/2 + 1/4.
About 1300 BCE
Shang dynasty, China
In ancient China, numbers up to tens of thousands were scratched on animal bones and turtle shells in a base 10 system. Later, from about the Han dynasty, people calculated with small rods laid out on a board so that the position of a rod gave its value, an early place value system that was used for centuries.
About 800 BCE
India
The Sulba Sutras are Indian texts that teach how to build the fire altars used in Vedic rituals, with exact shapes and sizes. They state the Pythagorean theorem, list Pythagorean triples and give good approximations for the square root of 2, hundreds of years before Pythagoras is thought to have lived.
About 300 BCE
Ancient Greece
Euclid collected geometry into a book called the Elements, built up from a few simple ideas by careful proof. It was used to teach geometry for more than two thousand years.
About 250 BCE
Syracuse, Sicily
Archimedes trapped the value of pi between two numbers by drawing shapes with 96 sides inside and outside a circle. He showed that pi is between 3 10/71 and 3 1/7, the fraction many of us still use.
About 240 BCE
Alexandria, Egypt
Eratosthenes noticed that the Sun's shadow was different in two cities at the same moment. Using geometry, he worked out the size of the whole Earth, and his answer was close to the real one.
196 BCE
Rosetta, Egypt
The Rosetta Stone carries the same decree in three scripts, including Greek and Egyptian hieroglyphs. When Jean-François Champollion worked out how to read hieroglyphs in 1822, scholars could finally read Egyptian texts, including the maths papyri, and understand how the ancient Egyptians counted and calculated.
Over 2,000 years ago
China
The Nine Chapters on the Mathematical Art is a collection of problems on farming, trade, building and taxes. It shows how to solve several equations at once, with a method very like the elimination method students learn today.
About 250 CE
Alexandria, Egypt
Diophantus wrote a book called Arithmetica about solving equations. He used a symbol for the unknown number, an early step towards the letters we use in algebra.
Over 1,500 years ago
The Maya, Central America
The Maya wrote numbers in base 20, using dots for ones, bars for fives and a shell shape for zero. Maya priests used these numbers to run a sacred calendar of 260 days that meshed with a 365-day year, like two gears. The two cycles line up again every 52 years, or 18,980 days, and they also predicted the movements of Venus.
About 359 CE
Jewish communities
The Jewish calendar follows both the Moon and the Sun. Its months are 29 or 30 days long, so 12 months are about 11 days short of a solar year. To fix this, an extra month is added in 7 out of every 19 years. This 19-year cycle is called the Metonic cycle, and the fixed rules for it are traditionally credited to Hillel II around 359 CE.
About 400 CE
Alexandria, Egypt
Hypatia taught mathematics and astronomy in Alexandria and was known across the Mediterranean as a brilliant teacher. She wrote a commentary on the Arithmetica of Diophantus, a book of equations, and another on the Conics of Apollonius, about curves made by slicing a cone. She also helped to edit Ptolemy's Almagest, a book of astronomical calculation.
499 CE
India
Aryabhata wrote a book on astronomy and mathematics when he was only 23. In it he gave pi as about 3.1416, and he worked with a table of sines to study the movement of the planets.
For many centuries
Africa and Asia
Mancala games are played in many forms across Africa and Asia, such as oware in Ghana, gebeta in Ethiopia and pallanguzhi in India. Players sow seeds one by one around the board, so they must count ahead to plan their moves and captures. Boards from Ethiopia and Eritrea are about 1,400 years old.
628 CE
India
Indian mathematicians developed the place value system with a digit for zero. The Sanskrit word for zero, shunya, means empty. Brahmagupta wrote rules for calculating with zero, including adding, subtracting and multiplying, as a number in its own right.
683 CE
Sambor, Cambodia
A stone inscription found near Sambor in Cambodia has the number 605 in the Khmer script, which corresponds to the year 683 CE. It is the oldest firmly dated example of zero used as a digit in a number, and it shows how Indian ideas about zero travelled across Asia.
725
Jarrow, England
Easter falls on the Sunday after the first full moon on or after 21 March, so it moves every year. Working out the date, called computus, was a big task for monks. The English monk Bede explained a full method in 725. In 1800, Carl Friedrich Gauss wrote a short algorithm that calculates the date of Easter for any year.
Around 820
Baghdad
Al-Khwarizmi worked in the House of Wisdom in Baghdad. His book on balancing and completing equations gave algebra its name, and it included methods for sharing out an inheritance fairly, which was an important question under Islamic law. A Latin version of his name gave us the word algorithm. He also helped spread the Indian number system.
About 850 CE
Karnataka, India
Jain scholars in India were fascinated by very large numbers and by infinity. Their texts sorted numbers into those that can be counted, those that are too many to count and those that are infinite, and described five different kinds of infinity. The Jain mathematician Mahavira wrote a textbook on arithmetic called the Ganita Sara Sangraha around 850.
For many centuries
Yoruba, West Africa
The Yoruba language counts in twenties, and uses subtraction a lot. For example, the word for 15 means 20 take away 5. It is a good reminder that our base 10 way of counting is not the only way to say numbers.
Over many centuries
Marshall Islands, Pacific Ocean
Marshallese navigators made charts from coconut fronds and shells to show how ocean swells bend around islands. Navigators memorised the charts before a voyage and then felt the swells through the canoe to find their way across the open sea.
Passed on for generations
Warlpiri and Yolŋu, Australia
Aboriginal peoples such as the Warlpiri and the Yolŋu have kinship systems that work like mathematical cycles. Among the Yolŋu, everything belongs to one of two halves, Dhuwa or Yirritja, and a child is always in the opposite half to their mother. Eight skin names are arranged in cycles with strict rules about relationships. Researchers have found that the Warlpiri pattern matches a group of symmetries called the dihedral group of order 8, even though the idea of a group is much newer than the system.
Over many generations
The Chokwe, Central Africa
The Chokwe and Luchazi peoples of Angola, Zambia and the Democratic Republic of the Congo draw sona in sand. They press a grid of dots into the sand and connect them with one continuous line, while telling a story or proverb. About 80% of the designs are symmetric. The mathematician Paulus Gerdes found six different rules for building them.
Before European contact
The Yuki, California
The Yuki people of northern California counted using the spaces between their fingers instead of the fingers themselves. Because we have four gaps on each hand, that gives a base 8 number system, not base 10.
Recorded in the 1880s
The Wotjobaluk, Australia
The Wotjobaluk people of Victoria counted up the body, starting with the little finger of one hand, then up the arm to the shoulder, neck, ear and head, so the number 15 sat at the top of the head. Aboriginal communities also sent message sticks with notches to show how many moons and how many camps away an event was.
Over many generations
Māori, Aotearoa New Zealand
Traditional Māori carving, tattoo and weaving use patterns that repeat, reflect and rotate. Researchers have found that the carvings in a meeting house use all seven of the types of strip pattern that mathematicians recognise, which are called the frieze groups.
About 1100
Persia
Omar Khayyam, a poet as well as a mathematician, showed how to solve cubic equations using geometry. He also helped design a calendar that was remarkably accurate.
1202
Pisa, Italy, and Béjaïa, Algeria
Fibonacci grew up in Béjaïa, in what is now Algeria, where he learned the Hindu-Arabic numbers. His book Liber Abaci showed European merchants how much easier they were than Roman numerals. The Fibonacci sequence appears in the same book, in a problem about rabbits.
1300s
Kerala, India
Madhava and the mathematicians of the Kerala school found infinite series for sine, cosine and pi, about 250 years before similar results were found in Europe.
1437
Samarkand, Uzbekistan
Ulugh Beg was a prince and a mathematician who built a great observatory in Samarkand. He and his team measured the positions of stars and created a star catalogue in 1437. They also calculated tables of sines and tangents correct to at least eight decimal places, which is better than most calculators needed in the days before computers.
1400s
The Inca, South America
The Inca recorded numbers on bundles of knotted cords called khipu. The position and type of each knot showed ones, tens, hundreds and more, so the cords worked like a written decimal system.
1453
Isfahan, Iran
Islamic art uses geometry, instead of pictures of people or animals, to decorate mosques and shrines. Some patterns were designed using five tile shapes, called girih tiles. In 2007 the physicists Peter Lu and Paul Steinhardt showed that a 1453 shrine in Isfahan has patterns that never exactly repeat, like quasicrystals, which scientists only studied centuries later.
1400s and 1500s
Timbuktu, West Africa
Timbuktu was a famous centre of learning. Scholars there copied and wrote thousands of manuscripts on subjects including astronomy, law and mathematics, and many are still looked after by local families.
1600s and 1700s
Japan
During the Edo period, Japan developed its own style of mathematics called wasan, with mathematicians such as Seki Takakazu. People hung wooden tablets with beautiful geometry problems in Shinto shrines and Buddhist temples as offerings and challenges. These are called sangaku, and some are still there today.
1703
China and Germany
The I Ching, an ancient Chinese book used for divination and wisdom, has 64 symbols called hexagrams, each made of six lines that are either broken or unbroken. In 1703 the German mathematician Leibniz noticed that they look like the binary numbers he was developing, with 0 and 1. Binary is now the language of every computer.
1711
Cambridge, England
Nicholas Saunderson lost his sight to smallpox as a baby, yet he became Lucasian Professor of Mathematics at Cambridge, the same chair once held by Isaac Newton and later by Stephen Hawking. He taught with a pegboard that let him calculate by touch, and he wrote a textbook of algebra, which was published after he died.
1700s
Basel, Switzerland
Leonhard Euler was born in Basel and became one of the most productive mathematicians ever. He learned from a member of the Bernoulli family, which produced several famous mathematicians over generations. Euler gave us notation such as e, i and f(x).
1763
Tunbridge Wells, England
Thomas Bayes was a Presbyterian minister who loved maths. After he died, his friend Richard Price published his essay in 1763. It showed how to work backwards from what we observe to the chance of what caused it. This idea, Bayes' theorem, is now used in medicine, science and artificial intelligence.
From 1766
St Petersburg, Russia
Cataracts left Leonhard Euler almost completely blind by 1766. He kept working for another 17 years, doing long calculations in his head and dictating his results to his assistants and family. In that time he wrote a famous algebra textbook and worked on how the Moon moves.
About 1787
Brunswick, Germany
A famous story says that when Carl Friedrich Gauss was a schoolboy, his teacher asked the class to add up the numbers from 1 to 100. Gauss paired them up, 1 + 100, 2 + 99 and so on, and quickly wrote 5050.
Early 1800s
Paris, France
Women were not allowed into the École Polytechnique, so Sophie Germain borrowed the lecture notes and sent her work to the professors under a man's name. When Gauss learned who she really was, he praised her talent. She proved a first result about Fermat's Last Theorem for a whole family of prime numbers, now called Germain primes, and she won a prize from the Paris Academy for a theory of vibrating elastic surfaces.
1824
Paris, France
Louis Braille was blind from childhood. He was only 15 when he developed a code of six raised dots, and he published it in 1829. Braille has no separate digits. Instead, a number sign is placed in front of the first ten letters, so a to j mean 1 to 9 and 0. For example, ⠼⠁⠃⠉ is 123.
1843
London, England
Ada Lovelace studied Charles Babbage's design for a mechanical computer. She wrote down a step-by-step method for it to calculate Bernoulli numbers, which many people call the first computer program.
1880s
Stockholm, Sweden
Women could not go to university in Russia, so Sofya Kovalevskaya studied abroad, and in 1874 she earned a doctorate at Göttingen. She proved a key theorem about when differential equations, which describe how things change, must have solutions, now called the Cauchy–Kovalevskaya theorem. She also solved the motion of a spinning top in a new case, which won the 1888 Bordin Prize. In 1889 she became a professor at Stockholm University, one of the first women in modern Europe to hold a full mathematics professorship.
1913
Tamil Nadu, India to Cambridge
Srinivasa Ramanujan taught himself maths from books and filled notebooks with astonishing results about numbers, infinite series and ways of splitting numbers into sums. He was a devout Hindu who said his ideas came from his family goddess, Namagiri. In 1913 he wrote to the mathematician G. H. Hardy in Cambridge, who recognised his genius and invited him to England. Hardy once said his taxi number 1729 was dull, and Ramanujan replied that it is the smallest number that is a sum of two cubes in two different ways.
1931
Beijing, China
Hua Luogeng left school early. At 18 he caught typhoid fever, which left his left leg partly paralysed for the rest of his life. He taught himself maths from the few books he had, and when he spotted an error in a published paper, a professor at Tsinghua University invited him to join the department. He became famous for number theory, including how numbers can be written as sums of powers, and later used maths to improve factory planning.
1933
Göttingen, Germany to Pennsylvania, USA
Emmy Noether had already overcome many barriers for women in German universities. In 1933 the Nazi government stopped her from teaching because she was Jewish, and she moved to the United States. She showed that every symmetry in a physical system gives a conserved quantity, such as energy. This is Noether's theorem, one of the most important ideas in modern physics. She also shaped modern algebra, in particular the study of rings and ideals.
1938
Budapest, Hungary to the United States
Paul Erdős left Hungary in 1938 when it had become dangerous for Jewish people, and several members of his family were later killed in the Holocaust. For the rest of his life he lived out of a suitcase, travelling from one mathematician to the next. He asked questions about prime numbers and about networks of dots and lines, and wrote about 1,500 papers with more than 500 different collaborators. That is why mathematicians still talk about their Erdős number.
1938 onwards
France
Alexander Grothendieck was born in Berlin and came to France as a refugee at the age of ten. His father was murdered at Auschwitz. He grew up without a country, travelling for many years with a stateless person's passport. He rebuilt algebraic geometry, the study of shapes defined by equations, with an idea called schemes. He won the Fields Medal in 1966 and is considered one of the greatest mathematicians of the 20th century.
1952
Manchester, England
In 1936 Alan Turing described an imaginary machine, now called a Turing machine, to explore what can and cannot be calculated by following rules. This idea became the foundation of computer science. In the Second World War he led the team at Bletchley Park that helped break German naval codes. In 1952 he was convicted because he was gay, which was then a crime in Britain. He was pardoned in 2013, and his face appears on the £50 note.
1952
United States
Abraham Nemeth, a blind mathematician, wrote a braille code for maths and science in 1952. It allows blind students and mathematicians to read and write fractions, powers, square roots and long equations by touch, using the same six dots.
1962
NASA, United States
Katherine Johnson, Dorothy Vaughan and Mary Jackson were Black women mathematicians at NASA when workplaces and schools in much of the United States were still segregated. Johnson used geometry and trigonometry to calculate the path and the launch window for Alan Shepard's 1961 flight, the first American in space. Before John Glenn orbited the Earth in 1962, he asked her to check the computer's numbers by hand.
1960s and 1970s
Strasbourg, France
Bernard Morin lost his sight as a child and became a famous topologist, a mathematician who studies shapes that can be stretched and bent. He was part of the team that first showed how to turn a sphere inside out without cutting, tearing or creasing it, something that sounds impossible. The surface he found along the way is called the Morin surface, and it is still used to study the problem.
1968
California, United States
Lynn Conway was a brilliant computer scientist at IBM, where she worked on how computers decide which instructions to run next. She was fired in 1968 when she told the company she planned to transition. She rebuilt her career, and with Carver Mead she wrote the 1980 textbook Introduction to VLSI Systems, which showed engineers how to design chips with huge numbers of tiny components. Chips are designed this way today, and she shared her story publicly many years later.
1977
Brazil
The Brazilian mathematician Ubiratan D'Ambrosio introduced the word ethnomathematics, meaning the mathematics practised by particular cultural groups. It reminds us that people everywhere count, measure, build patterns and solve problems, in ways that do not always look like school maths.
1994
Kaktovik, Alaska
In 1994, students at a school in Kaktovik, in northern Alaska, noticed that the Iñupiaq language counts in twenties, and that our digits did not fit it well. Led by their teacher, nine students invented a base 20 number system where each digit is drawn from strokes that show its value, and zero looks like crossed arms. It is now taught and officially recognised in Alaska and has been recommended for use in Canada.
From the 2000s
Indonesia
Indonesian batik, the fabric patterns made with wax and dye, often repeat the same shape at smaller and smaller sizes. The Indonesian researcher Hokky Situngkir analysed the geometry of batik and used maths to design new batik patterns, called fractal batik.
2010
Vietnam and France
Ngô Bảo Châu grew up in Vietnam and won a Fields Medal in 2010 for proving a deep result called the Fundamental Lemma, which had been blocking progress for decades in a big web of ideas linking numbers and symmetry, the Langlands programme. He was the first Vietnamese mathematician to win the medal.
2014
Stanford, United States
Maryam Mirzakhani was born in Tehran. She studied hyperbolic surfaces, curved shapes where the usual rules of triangles change, and showed how the number of simple closed loops on such a surface of a given length grows. In 2014 she became the first woman and first Iranian to win the Fields Medal. She called herself a slow mathematician and liked to doodle on huge sheets of paper while she thought. She died in 2017 aged 40.
2014
Rio de Janeiro, Brazil
Artur Ávila grew up in Rio de Janeiro in Brazil. He studies dynamical systems, which describe how things change over time, from the orbit of a planet to the way a pendulum swings, and he won the Fields Medal in 2014. He was the first mathematician from Latin America to win it.
2016
Lausanne, Switzerland
Maryna Viazovska was born in Kyiv in Ukraine. In 2016 she solved the problem of the best way to pack spheres in 8 dimensions, which people had been trying to solve for a long time, and showed that a pattern called the E8 lattice is the densest possible. She works in Switzerland, at EPFL in Lausanne, and in 2022 she became the second woman to win the Fields Medal.
2022
Seoul, South Korea
June Huh grew up in Seoul and wanted to be a poet. He only began to study maths seriously at university. He proved that the numbers that count the ways to colour a map or network with different colours never dip in the middle, a puzzle called Read's conjecture. In 2022 he won the Fields Medal for this and related work.
These stories are only a taste. Dates are approximate, and many ideas were found more than once, in different places. If you know a story from your own country or family, please tell Ms B in class.