Why learn the history of maths?
Maths was not made by one person or one country. It grew step by step, in Africa, Asia, Europe and the Americas, as people solved real problems: counting animals, measuring fields, building temples, tracking stars and trading goods.
Knowing this history shows that everyone can do maths. Ideas moved between cultures and each one added something. In class, this means respecting every classmate's way of thinking, sharing ideas and helping each other.
Counting and the first numbers
Old bones with notches (for example the Ishango bone from Central Africa, about 20,000 years old) show early tally marks. Later, people grouped marks in 5s and 10s because we have 5 fingers on each hand.
Different numeral systems appeared: Egyptian hieroglyph numerals, Roman numerals (I, V, X), the Maya system (base 20, with a shell for zero) and the Babylonian base-60 system.
Egypt and Mesopotamia
After the Nile floods, Egyptians had to mark fields again. "Rope stretchers" used ropes with equal knots. A loop of 12 knots pulled into sides 3, 4 and 5 makes a right angle.
Babylonians (in today's Iraq region) wrote on clay tablets in base 60. They solved equations, knew many Pythagorean triples, and their 60 is still in our 60 seconds, 60 minutes and 360° in a circle.
Origins of geometry: Thales and Pythagoras
Thales of Miletus (about 600 BCE) is called the first Greek mathematician. He found the height of a pyramid from its shadow: at the same moment, a stick and the pyramid have the same ratio height ÷ shadow. This is the idea of similar triangles (Thales' theorem on proportional segments).
Pythagoras (about 530 BCE) and his school are linked to the rule a² + b² = c² for right triangles. The same fact was known earlier in Babylon and in India's Baudhayana Shulba Sutra, but the Greeks gave a general proof.
Euclid and Hypatia
Euclid (about 300 BCE, Alexandria) wrote the Elements, 13 books that build geometry from a few simple axioms (statements accepted as true) using step-by-step proofs. It was used to teach geometry for over 2,000 years.
Hypatia (about 370–415 CE, Alexandria) was a leading teacher of maths, astronomy and philosophy. She wrote commentaries on geometry and on conic sections (circle, ellipse, parabola, hyperbola) and is one of the first women mathematicians we know by name.
Zero, algebra and the journey of ideas
- India: place value with 10 digits including zero. Aryabhata (499) used place value and a good value of π; Brahmagupta (628) wrote rules for zero and negative numbers.
- Baghdad: al-Khwarizmi (about 820) wrote a book whose title gave us the word algebra; "algorithm" comes from his name.
- Europe: Fibonacci (1202) spread Hindu-Arabic numerals; later Newton and Leibniz built calculus.
- China: counting rods, negative numbers and the "Nine Chapters" methods for equations.
Women in mathematics
For centuries girls were kept out of schools and universities, yet many still did great maths:
- Sophie Germain (France) studied in secret and used a man's name to send her work.
- Ada Lovelace (England) wrote the first published computer program (1843).
- Emmy Noether (Germany) founded modern algebra and linked symmetry to the laws of physics.
- Katherine Johnson (USA) calculated space flight paths for NASA.
- Maryam Mirzakhani was the first woman to win the Fields Medal (2014).
- Shakuntala Devi (India) became famous for mental calculation.
Try it
Make a rope with 12 equal knots (or 13 marks on a string). Pull it into a 3-4-5 triangle and check the corner with the corner of a book. Then measure a tree's height with a stick and shadows, like Thales.
Key formulas and definitions
- 3² + 4² = 5² → 9 + 16 = 25 (Egyptian rope triangle)
- Thales: height of object ÷ its shadow = height of stick ÷ its shadow
- Base 60: 1 hour = 60 minutes = 3,600 seconds
- Place value: 205 = 2 × 100 + 0 × 10 + 5 × 1
- Axiom = a starting statement accepted without proof
- Theorem = a statement proved from axioms
Worked examples
1. At the same time, a 1 m stick casts a 1.5 m shadow and a tower casts a 30 m shadow. How tall is the tower?
Height ÷ shadow is equal. Tower ÷ 30 = 1 ÷ 1.5. Tower = 30 ÷ 1.5 = 20 m.
2. Show that a rope triangle with sides 3, 4 and 5 has a right angle.
3² + 4² = 9 + 16 = 25 = 5². The sides fit a² + b² = c², so the angle opposite 5 is 90°.
3. Why does the number 307 need a zero?
307 = 3 hundreds, 0 tens, 7 ones. Without the 0 the digits would be 37, a different number. Zero holds the empty tens place.
Common mistakes
- Thinking maths was invented in one place. It grew in Africa, Asia, Europe and the Americas, and ideas travelled between them.
- Thinking Pythagoras was the first to know a² + b² = c². Babylon and India knew triples earlier; the Greeks gave a general proof.
- Calling our digits 'Arabic' only. They began in India and reached Europe through Arab scholars, so we say Hindu-Arabic numerals.
- Believing there were no women mathematicians. Hypatia, Germain, Lovelace, Noether and Mirzakhani are just a few.