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1750 BCE
Babylonian mathematics
Most clay tablets dealing with mathematics that were recovered from Mesopotamia date from 1900 BC to 1600 BC and they were inscribed with sideways and downward facing tick marks to represent 10 and 1 respectively. The Mesopotamians were the first advanced society to use a place-value system which was in base 60 (the value in each position was multiplied by factors of 60). Scribes from this culture also worked with simple linear equations and complicated ones that eventually lead to quadratics. -
1650 BCE
Egyptian Mathematics develops--the Rhind Papyrus
Egyptians began using mathematical concepts (some basic arithmetic) as far back as 5,000 BC, and this process continued to develop over the next couple thousand years. The Rhind papyrus, dating back to 1650 BC, shows how Egyptians had a system of numbers based on powers of ten and represented by symbols. They were able to add and double numbers as well as work with many fractions (but only those with 1 in the numerator, known as the "nth part", i.e. 1/4 = the fourth part). -
1000 BCE
The Pythagorean Theorem emerges (well before Pythagoras!)
The first mentions of what we know today as the Pythagorean Theorem came in the first millenium BC in India, but early forms of it were also present in ancient Egypt, China and Mesopotamia! The first semblance of a proof of this theorem may have came from a Chinese source in which pictures of squares were used to prove the result. Even James Garfield, president of the US in 1881, provided a proof for this theorem similar to the ancient Chinese proof (using visuals). -
624 BCE
Thales of Miletus is born
Thales of Miletus was one of the very first Greek mathematicians. Thales did important work in geometry, and one area he studied was how to find the height of objects as well as their distance. While most scholars during his time were using mythology to explain the natural world, Thales was reasoning through the method of deduction to gain information about the world around him. Because of his use of the scientific method he is considered the first "true" mathematician. -
312 BCE
Aqua Appia commissioned
The first Roman aqueduct, the Aqua Appia, is ordered to be built by Appius Claudius, a roman censor (high political official) at the time. This aqueduct was a feat of mathematics and engineering that brought water to the city of Rome from a spring that was 16.4 kilometers away! In order to conserve material, ancient Romans had to understand the concept of arch-building, which is a very efficient way of building strong structures. -
287 BCE
Archimedes is born
Archimedes' was a Greek mathematician who born in modern day Syracuse, Italy. Archimedes discovered the interrelationship between the surface area of a sphere, its volume and the cylinder that is created by elongating the sphere. Archimedes also had the first accurate estimation of pi, which he estimated between 3 10/70 and 3 10/71. He also had the first ideas for a device for raising water (called Archimede's Screw, shown in the picture) which is still in use today in some developing countries! -
207 BCE
Diophantus is born
Diophantus was Greek Mathematician who studied in Alexandria, Egypt. Diophantus is considered the "father of algebra" since he was the first to include the idea of the unknown value in his math writings. He used notations to denote these values which was the only time notation was used for unknown values before the 15th century! In his book Arithmetica, he provides 130 problems and their solutions dealing with determinate (one solution) and indeterminate (more than one solution) equations. -
100 BCE
The Emergence of Modern Fractions from Ancient China
In a book from ancient China titled, "Nine Chapters on the Mathematical Art" we see notation for writing fractions that is very similar to the notation we use today. Before this, most cultures worked solely with unit fractions (where the numerator is always 1). Chinese mathematicians also figured out ways of doing operations with fractions such as adding them, multiplying them and reducing fractions into lowest terms. The only idea that they didn't use was improper fractions (such as 7/3). -
355
Hypatia is born
Hypatia was one of the first prominent female Greek mathematicians of which there is a record but she was also a philosopher and astronomer. She made commentaries on the writing of Appolonius of Perga that dealt with geometric figures and curves that came form them (conic sections) as well as commenting on Diophantus' Arithmetica. During her time, Hypatia was one of the lead mathematicians and astronomers in the world, unfortunately one of the only times that a female has held this distinction. -
525
Aryabhata
Aryabhata was an Indian mathematician and astronomer who lived between 476 AD and 550 AD. Of his vital contributions to the field of mathematics, he introduced the idea of place value and was the first to play with the idea of a ‘zero’ through a dot to denote absence of a number. He also discovered the first 10 decimal places, using 9 symbols to represent the numbers 1 through 9. Also, Aryabhata's approximation of π of 3.1416 was accurate to five significant figures. Not bad for the 6th century! -
598
Brahmagupta is born
A famous Indian mathematician as well as astronomer, Brahmagupta headed the astronomical observatory in a city called Ujjain, the most important city for mathematics in India at the time. He wrote a book which included a table of values for the sine function as well as rules for arithmetic when dealing with positive and negative numbers. Most importantly, Brahmagupta is also credited with introducing the concept of negative numbers and being the first to do calculations with zero. -
830
Muhammad ibn Musa al-Khwarizmi formalizes algebra
Muhammad ibn Musa al-Khwarizmi was an Arabic mathematician who lived between 780-850 AD and he was the first mathematician to present a systematic way of solving linear and quadratic equations. He showed how to solve these quadratic equations by completing the square and his justification was based in geometry. Al-Khwarizmi also introduced the idea of performing mathematical calculations in a very specific way with a specific method which could be more easily followed called an algorithm. -
Francois Viete introduces the concept of constants to algebra
Francois Viete lived in France in the 16th century. Although not strictly a mathematician, he contributed to math knowledge. Viete was a lawyer and also cryptographer, which meant he broke secret codes. It was this latter profession which lead him to introduce the idea of using consonants (e.g. b, d, h etc...) to indicate known numbers in an equation (constant terms). So, Viete was the first to write something similar to: ax^2+bx = c, transforming algebra to the modern form we recognize today. -
Decimals start to get credibility! (In the West)
In a book published in 1585 titled "The Tenth" published by a Flemish mathematician and engineer, Simon Stevin, the argument is made that doing basic arithmetic with non-whole numbers is much easier with decimals than with fractions. This is because decimal operations can be treated as though they are whole numbers. And so, from this point on decimals began to be used much more widely than before in European mathematical activity. -
Descartes publishes Le Geometrie
Rene Descartes, famous for being a philosopher, was also a prominent mathematician. In his book, he introduced our modern algebraic notation of using lower case letters at the end of the alphabet (x, y, z) for variables and lower case letter at the beginning for constants (a, b, c) as well as our modern coordinate system (hence the name "Cartesian" plane). With other mathematicians, he also brought together algebra and geometry to begin the exploration of coordinate geometry. -
Calculus is born!
Two towering figures in the field of mathematics, Isaac Newton and Gottfried Wilhelm Leibniz, independently invented calculus towards the end of the 17th century. This early form of calculus was based on the idea of an infinitesimal, or measuring a infinitely small increase or decrease in the value of a variable. This later lead to the ideas of limits, integrals and derivatives which are common today. -
Maria Gaetana Agnesi publishes "Instituzioni Analitiche"
Maria Gaetana Agnesi lived from 1718 to 1799 and she is considered to be the first female mathematician to gain popular appeal in academic circles. In this book she describes a lot of the work of mathematicians of her day such as Newton, Leibniz and Descartes and discussed integrals and differential calculus. Because of her hard work, Pope Benedict XIV appointed her a math professor at the University of Bologna, a remarkable feat for a woman considering they were discouraged from learning math.
