Guide to the History of Mathematics



The history of mathematics is a long and detailed one. With the earliest records older than 3,000 B.C., there is much information on the development of modern day math. A great deal of information has been lost during wars, religious changes and other disasters but most of it has been preserved. Every region of the ancient world from China to Europe and Africa holds records of the progress of mathematics.

The MacTutors History of Mathematics Archive: A website dedicated to the history of math with a number of interesting indexes
Mathematics: Ancient science and modern facts about math
History of Math: The history of math sorted by culture and topics

Math Around the World

Ancient East: Mesopotamia, which is modern Iraq, is also known as the era of Babylonian mathematics. A complex system of metrology was developed around 3000 B.C. After 2,500 B.C. multiplication tables were recorded on clay tablets along with forms of geometry and division. Topics which were included in the clay tablets ranged from fractions, algebra, quadratic and cubic equations. They used the base 60 numeral system from which our modern day 60 seconds in a minute, 60 seconds in an hour and 360 degrees in a circle have been derived.

Egyptian: The most popular record of mathematics in Egypt is in the form of the Rhind papyrus which was most likely a copy of texts from about 2000 B.C. It is actually an instruction manual for students in math and geometry. The information in this manual ranged from area formulae, composite and prime numbers, how to solve linear equations, along with other theories. Other popular papyruses of the time include the Moscow papyrus and the Berlin papyrus. The first contained mathematical word problems and the second proved that Egyptians could solve second order algebraic equations.

African: The knowledge of fractal geometry arose from the African continent. This permeated all forms of life including art, design structures, architecture and even religious systems. The Nubians also used a trigonometric method similar to the Egyptians.

Greek: The mathematics of the Greeks rose to a level above that of previous cultures. Famous Greek mathematicians included Thales who was known for using geometry in calculating distances and height, and Pythagoras who established a school responsible for the actual study of math. In fact, the Pythagoreans were the ones who developed the term mathematics and created the Pythagorean Theorem. Aristotle created the laws of logic. Another famous mathematician from the area was Euclid who compiled the book Elements, including the irrationality of the concept of the square root of two and the existence of infinite prime numbers.

Oriental: The Chinese developed the most advanced number system being able to represent large numbers. From the difference between Chinese math and the rest of the world it is clear that the Chinese developed their mathematics independently of other regions. The oldest math records from China are dated at approximately 300 B.C. The Chinese developed algebra in the 13th century. Recorded work of the time explains Pascal's Triangle. However, after this period mathematical ideas began to be exchanged between Europe and Chinese mathematical ideologies declined rapidly.

Indian: The first use of numbers is shown in India to be around 3000 B.C. with the usage of counting tokens. Around the same time weights using the base 10 system were also used. After the invasion of Indo-Europeans mathematicians were aware of the idea of infinity by 1800 B.C. Because of an interest in astronomy, geography was usually a favorite subject and by 1300 an Indian astronomer called Lagadha wrote a book of rules for the movement of the sun and moon.

Islamic: Around 630 A.D. numbers were brought into the region that would soon become the Islamic Empire. This was the beginning of numbers as we know them today. Algebra followed shortly with the writing of numerous book by Muhammad ibn Musa-al-Khwarizmi. Mathematical proofs were created around 1000 AD by Al-Karaji. Other significant advancements included the decimal point, trigonometric functions, analytical geometry, algebraic geometry and algebraic notation.

European Middle Ages: The major developments of the time included the translation of Greek writings and implementation of formal schooling. People believed that math would unlock the secrets of creation and that God ordered things in measure, number, and weight. The study of arithmetic, geometry, astronomy, and music were brought into the curriculum by a philosopher named Boethius.

The History of Mathematics: Information on mathematics divided by geographical regions
Archeology Online: History of mathematics in India
Kidipede: The history of ancient Greek mathematics

Famous Mathematicians
There were numerous mathematicians throughout history all of whom contributed to our modern day math. Even facts and formulas that may have contained errors became a factor of learning as they were corrected in later times.
Pythagoras

  • Born in Greece, 578 to 505 B.C
  • Major Areas of Contribution: Pythagorean theorem, discovered that a harmony of strings is possible if the length of the strings are whole numbers, diagonal of a square was not an integral multiple of its sides, irrational numbers

Aryabhata

  • Place of Birth Unkown, 476 B.C. to unknown
  • Major Areas of Contribution: Approximate value of Pi, formula to calculate the value of a triangle, method to solve the first order of Diophantine equations

Euclid

  • Born in Egypt, 300 B.C. to unknown
  • Major Areas of Contribution: Plane geometry, number theory, theory of irrational numbers, solid geometry, theory of five regular polyhedrons

Archimedes

  • Born in Greece, 287 to 212 B.C.
  • Major Areas of Contribution: Area of plane figures, areas and volumes of curved surfaces, and integral calculus

Muhammed Al-Khwarizmi

  • Born in Persia, 780 to 850 AD
  • Major Areas of Contribution: systematic approach to solving linear and quadratic equations, wrote On the Calculation with Hindu Numerals which was responsible for spreading of the Indian system of numbering, introducing Arabic numerals

Leonardo Fibonacci

  • Born in Italy, 1170 to 1250 AD
  • Major Areas of Contribution: Spread of the Hindu-Arabic numeral system to Europe, creation of the Fibonacci series

Blaise Pascal

  • Born in France, 1623 to 1662 AD
  • Major Areas of Contribution: Pascal's triangle, created the mechanical calculator, projective geometry, probability theory and economics

Sir Isaac Newton

  • Born in England, 1643 to 1727 AD
  • Major Areas of Contribution: differential and integral calculus to finding areas, the length of a curve, areas, maxima and minima.

Collections of Mathematicians: A view of math history from the eyes of the people
Top 10 Greatest Mathematicians: Details of the greatest mathematicians with photos
Grade a Math Help: Details on famous math personalities

History of Mathematics Timeline
2450 BC - Egypt, first method for approximate calculation of the circle using the sacred Triangle
530 BC - Pythagoreans study the vibrating lyre strings and discover the irrationality of the square root of two
260 BC - Archimedes computes pi to two decimal places
140 BC - Hipparchus develops the bases of trigonometry
450 - The Chinese compute pi to six decimal places
1030 - Ali Ahmed Nasawi develops the division of days into 24 hours, hours into 60 minutes, and minutes into 60 seconds
1202 - Leonardo Fibonacci uses Arabic numerals in his Book of the Abacus
1424 - Ghiyath al-Kashi computes pi to sixteen decimal places
1596 - Ludolf van Ceulen computes pi to twenty decimal places
1665 - Isaac Newton invents calculus
1722 - Abraham De Moivre states a theorem connecting trigonometric functions and complex numbers
1811 - Carl Friedrich Gauss discusses the meaning of integrals with complex limits
1903 - Edmund Georg Hermann Landau provides simpler proof of the prime number theorem
1983 - A collaboration of about 100 mathematicians classifying finite simple groups, is completed after 30 years
2000 - The Seven Millennium Prize Problems, a list of unsolved important math questions are established by the Clay Institute

A Time Line for the History of Mathematics: A list showing advancements in math alongside the advancements of mankind
From Cave Paintings to the Internet: Mathematics and logic timeline
History of Mathematics Timeline: A graphical depiction of the history of math

Other Resources for the History of Mathematics

History of Mathematics: A brief introduction with links to books and other resources
National Center for Excellence in the Teaching of Mathematics: A brief history of mathematics
Epact: Medieval and renaissance mathematical arts and sciences
Recovered Science: Ancient creation stories told by numbers
The British Society for the History of Mathematics: A society dedicated to promote research into the history of mathematics

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