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2700 BCE
Egyptians Develop a Numerical System
Egyptians introduced the earliest fully-developed base 10 numeration system at least as early as 2700 BCE (and probably much earlier.) It was written by used a stroke for units, a heel-bone symbol for tens, a coil of rope for hundreds and a lotus plant for thousands. Other hieroglyphic symbols stood for higher powers of ten up to a million. -
2600 BCE
Sumerian Clay Tablets 1
Clay tablets from this time show multiplication and reciprocal (division) tables, tables of squares, square roots and cube roots, geometrical exercises and division problems. -
2000 BCE
Moscow Papyrus
The Moscow papyrus dates from the Egyptian Middle Kingdom.
It is the oldest known Egyptian Mathematical text discovered. The papyrus was found and kept briefly by Egyptologist Vladimir Golenidenov. Today it is located in the Pushkin State Museum of Fine Arts in Moscow. Measuring in at approximately 18 feet long and varying between 1 1/2 and 3 inches wide, it was divided into 25 problems with tentative solutions by the Soviet Orientalist Vasily Vasilievich Struve in 1930. -
1800 BCE
Sumerian Clay Tablets 2
Later Babylonian tablets cover topics such as as fractions, algebra, methods for solving linear, quadratic and even some cubic equations, and the calculation of regular reciprocal pairs (pairs of number which multiply together to give 60). One Babylonian tablet gives an approximation to √2 accurate to five decimal places.
Others list the squares of numbers up to 59, and the cubes of numbers up to 32. Another gives an estimate for π of 3 1⁄8 (3.125, a reasonable approximation of the real value) -
1800 BCE
Plimpton 332 Clay Tablet
The Plimpton 322 clay tablet suggests that the Babylonians may well have known the secret of right-angled triangles (that the square of the hypotenuse equals the sum of the square of the other two sides) many centuries before Pythagoras and his theorem. It lists 15 Pythagorean triples, but some consider it to be a coincidence rather than deliberate. -
1650 BCE
The Rhind Papyrus
The Rhind Papyrus is a kind of instruction manual in arithmetic and geometry that gives precise demonstrations of how multiplication and division was carried out at that time. It contains evidence of other mathematical knowledge, including composite and prime numbers, and how to solve first order linear equations. The papyrus is named after Alexander Henry Rhind, who bought it from an illegal excavation in Luxor, Egypt. It now belongs to the British Museum, with fragments in Brooklyn. -
1300 BCE
The Berlin Papyrus
The Berlin Papyrus shows that ancient Egyptians could solve second-order algebraic (quadratic) equations. It dates back to the Middle Kingdom. The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902. -
1000 BCE
Vedic Mantras
Mantras from the early Vedic period show use of powers of ten from a hundred all the way up to a trillion, and provide evidence of the use of arithmetic operations such as addition, subtraction, multiplication, fractions, squares, cubes and roots. -
800 BCE
Greek Geometry (800 BC and 600 BC)
Geometry can conceivably lay claim to being the oldest branch of mathematics outside arithmetic, and humanity has probably used geometrical techniques since before the dawn of recorded history. Initially, as with the Egyptians, geometry originated from practical necessity and the need to measure land; the word "geometry" means "Earth Measuring". -
650 BCE
The Lo Shu Square
The Lo Shu Square is a three by three square where each row, column and diagonal adds up to 15, and perhaps the earliest of these dates back to around 650 BCE. The legend of Emperor Yu’s discovery of the the square on the back of a turtle is set as taking place in about 2800 BCE. These squares eventually evolved into complex shapes because many believed that she shapes combined with the numbers had cosmic significance. -
530 BCE
Pythagoras
Greek mathematics was the first attempt to use deductive reasoning to devise theories linking numbers together. Pythagoras was known as the first true mathematician. Pythagoras is generally credited with the theory of the functional significance of attributed to him. For example, the Pythagorean theorem for right triangles were probably developed only later by Pythagoras. -
323 BCE
Hellenistic Greek Mathematics (7th century BC to 4th century AD)
As the Greek empire began to spread its sphere into Asia Minor, Mesopotamia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the societies they conquered. Among the best known and most influential mathematics who studied and taught at Alexandria were Euclid, Archimedes, and Diophantus. Euclid known as "the father of geometry", Archimedes was considered to have been one of the greatest mathematicians of all time, Diophantus known as the "father of algebra". -
300 BCE
Euclid
Euclid enters history as one of the greatest of all mathematicians and he often referred to as the father of geometry. The standard geometry most of us learned in school is called Euclidean Geometry. Euclid gathered up all of the knowledge developed in Greek mathematics at that time and created his great work, a book called "The Elements". This treatise is unequaled in the history of science and could safely lay claim to being the most influential non-religious book of all time. -
250 BCE
Diophantus
Known as the "father of algebra". He was one of the first mathematicians to introduce symbolism into algebra, using an abridged notation for frequently occurring operations. he wrote a collection of books called "Arithmetica", a collection of algebraic problems which greatly influenced the subsequent development if number theory. -
212 BCE
Archimedes (287-212 BCE)
Archimedes is one of the most famous of all the Greek mathematicians, contributing to the development of pure math and calculus, but also showing a great gift for using mathematics practically. With inventions such as the Archimedes Screw and the Archimedes Claw, he showed himself to be a brillant engineer as much as a theorist. -
200 BCE
"Nine Chapters on the Mathematical Art"
The "Nine Chapters" is a mathematical instruction text written by a variety of authors from 200 BCE onward. It became an important tool in the education of civil service, covering hundreds of problems in areas such as trade, taxation, engineering and the payment of wages. One could also use it as a guide to solving complex equations. It also used a complex method of math rediscovered by Carl Friedrich Gauss, called Gaussian elimination -
263
Liu Hui
Liu Hui is a Chinese mathematician who produced a detailed commentary on the “Nine Chapters” in 263 CE. He is also one of the first mathematicians known to leave roots unevaluated, giving more exact results instead of approximations. His research led him to an approximation of π accurate to five decimal places. He developed early forms of calculus as well. -
300
Classical Greek Mathematics (300 BC - 600 BC)
Greek geometry -
300
Unknown Sanskrit Text
This text reports Buddha enumerating numbers up to 10^53, as well as describing six more numbering systems over and above these, leading to a number equivalent to 10^421. Given that there are around 10^80 atoms in the whole universe, this is as close to infinity as the ancient world came. It also describes a series of iterations in decreasing size to demonstrate the size of an atom, which comes very close to the actual size of a carbon atom (about 70 trillionths of a meter). -
600
Brahmagupta
Brahmagupta is the 7th century Mathematician credited with the invention of the zero as a number. He also invented many rules for dealing with zero. -
800
Muhammad Al-Khwarizmi
Muhammad Al-Khwarizmi was an early Director of the House of Wisdom in the 9th Century. His most important contribution to mathematics was his advocacy of the Hindu numerical system (1 - 9 and 0), which he recognized as having the power and efficiency needed to revolutionize Islamic mathematics. The system was soon adopted by the entire Islamic world, and later by Europe. -
900
Muhammad Al-Karaji
Muhammad Al-Karaji was a 10th Century Persian mathematician, who worked to extend algebra still further, and introduced the theory of algebraic calculus. Al-Karaji was the first to use the method of proof by mathematical induction to prove his results, and studied a form of Pascal’s Triangle before it was invented by Blaise Pascal. -
1200
Yang Hui
Yang Hui created large complex shapes akin to the Lo Shu Square. His creations are the most elaborate ever created. His most known creation is a triangle identical to Pascal's triangle. -
René Descartes
René Descartes has been dubbed the "Father of Modern Philosophy", but he was also one of the key figures in the Scientific Revolution of the 17th Century, and is sometimes called the first of the modern school of mathematics. As a young man, he concluded that the key to Philosophy is mathematics. In 1637, he published his ground-breaking mathematical work "Discours de la méthode" (the “Discourse on Method”). One of its appendices, "La Géométrie", is considered a landmark in the history of math. -
Blaise Pascal
Balise Pascal was a prominent 17th Century scientist, philosopher and mathematician. His early work was in the area of applied sciences, and has a physical law named after him. His best known work is for Pascal's triangle, which is a tabular representation of binomial coefficients (each number is the sum of the two numbers directly above it). Pascal also worked with probability, and the Problem of Points. -
Isaac Newton
Isaac Newton was a physicist, mathematician, astronomer, natural philosopher, alchemist and theologian. He is considered by many to be one of the most influential men in human history. His 1687 publication, the "Philosophiae Naturalis Principia Mathematica" (called simply the "Principia"), is considered to be among the most influential books in the history of science. He also pioneered infinitesimal calculus and functions of curved lines, and is credited with the generalized binomial theorem. -
Jacob Bernoulli
Jacob Bernoulli was a member of a prosperous family of traders and scholars from the city of Basel in Switzerland. He was a professor at Basel University, and sided with Newton in the Newton-Leibniz calculus controversy. His brother, Johann, was also a mathematician, as well as his dad. -
Johann Bernoulli
Johann Bernoulli is the brother of Jacob Bernoulli and took Jacob’s position after his death. He published a book based on his son’s Daniel's work, even changing the date to make it look as though his book had been published before his son's, but had his lectures published by his student Guillaume de l'Hôpital
The published lectures contained the famous zero divided by zero rule, called l'Hôpital's Rule. He helped build calculus into the mathematical cornerstone it is today. -
Leonhard Euler
Much of the notation used by mathematicians today - including e, i, f(x), ∑, and the use of a, b and c as constants and x, y and z as unknowns - was either created, popularized or standardized by Euler. He is best known for two formulas, Euler's identity ( e^iπ = -1) and Euler’s Formula (e^ix = cos^x + isin^x). He also "solved" the Seven Bridges of Königsberg Problem (the premise is to not cross the seven bridges in modern-day Kaliningrad once) by determining that it is impossible. -
Nikolai Lobachevsky
Nikolai Lobachevsky had also been working, along very similar lines as Bolyai, to develop a geometry in which Euclid’s fifth postulate did not apply. His work was first published in 1830. Among his other mathematical achievements was a method for approximating the roots of algebraic equations and the definition of a function as a correspondence between two sets of real numbers. Early non-Euclidean geometry is now often referred to as Lobachevskian or Bolyai-Lobachevskian geometry. -
János Bolyai
János Bolyai was a mathematician who lived in the Hapsburg Empire (Hungary). His father and teacher, Farkas Bolyai, was an great mathematician as well, and had been a student of Carl Gauss. Later in life, Bolyai became obsessed with Euclid's fifth postulate. In the 1820s, Bolyai explored what he called “imaginary geometry”(hyperbolic geometry), the geometry of curved spaces on a saddle-shaped plane. The angles of a triangle did NOT add up to 180° and parallel lines were NOT parallel. -
Resources
Taylor Waddell-Smith: https://docs.google.com/document/d/1xkDtlW1OitLG3u7NvHDjMWXK5kQRo4No3MAQjrX4tig/edit
