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5000 BCE
Writing first developing
Around 5000 B.C. writing was first originating in the Ancient Near East, as centralized government was arising in society. -
Period: 5000 BCE to
History of Mathematics
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3000 BCE
Hieroglyphic numerals were used in Egypt
The Hieroglyphic numeral system was an improvement from the Egyptian's previous tally system. This new hieroglyphic system was more efficient that the prior tally system, and it consisted of various symbols that were strung together to represent numbers. Such symbols included the stroke to represent 1, the heel bone to represent 10, the coiled rope to represent 100, the lotus flower to represent 100, and etc. -
2400 BCE
Postitional system of notation in Mesopotamia
In Mesopotamia, a sexagesimal positional notation system was created, which was based on the number 60. They used symbols known as "cuneiform" that resemble arrow/wedge-like shapes that were carved into soft clay tablets. The downward pointing arrows represented 1 and the left pointing arrows represented 10. These symbols were used repetitively and added together to express numbers between 1-59. Larger numbers were expressed by grouping the symbols, separating them, and multiplying by 60. -
1650 BCE
Rhind Papyrus
The Rhind Papyrus is the most detailed source of information regrading the mathematics of Egypt, and it was named after 19th century archeologist Henry Rhind. -
518 BCE
Pythagorean arithmetic and geometry popularized
Pythagoras founded a semi-religious society and Brotherhood in which his followers were known as Pythagoreans. They believed in number mysticism, a belief that numbers possess a symbolic portrayal of reality. Pythagoras had many contributions to mathematics in both the study of arithmetic and geometry. In arithmetic, he studied whole numbers and the study of ratios (which can be applied to music). In geometry, his major contribution was the Pythagorean Theorem (a^2 + b^2 = c^2). -
400 BCE
Maya civilization had a numeration system based on 20
The Mayan civilization in Central America created a numeration system similar to the Babylonian system in which they used groupings of basic symbols to portray larger numbers. Their positional number system was based on 20. -
334 BCE
Alexander the Great conquered much of the Near East
Alexander the Great's goals were to create a cosmopolitan city that was the center of knowledge, and commerce. This centralized source of knowledge and emphasis on learning, had positive implications on the importance of mathematics. -
300 BCE
Euclid's Elements
Some of the earliest exposure to Greek mathematics comes from Euclid's 13 book series, "The Elements." -
250
Diophantus of Alexandria wrote "Arithmetica"
Diophantus of Alexandria was a Greek mathematician who lived around 200-284, and "Arithmetica" is a study of number theory problems in which the solutions are rational numbers. This book consists of a list of algebraic problems and solutions and includes information on the theory of numbers. -
400
Hypatia's contributions to mathematics
Hypatia, daughter of Theon of Alexandria, was the first women to make contributions to the field of mathematics. In around 400, she taught mathematics and philosophy, and she became the head of the Platonist School at Alexandria. -
1200
Fibonacci Series discovered
Italian mathematician 1175, Leonardo Fibonacci discovered the properties of a unique number series, known as the Fibonacci Series or the Fibonacci Sequence. The Fibonacci Sequence is an infinite series of numbers that follows a pattern in which each subsequent number is the sum of the previous two numbers; i.e., {1, 1, 2, 3, 5, 8, 13, 21, 34,...}. -
1202
Fibonacci's "Liber Abbaci" ("Book of Calculation")
Leonardo of Pisa (also known as Fibonacci) published his first book, Liber Abbaci, in 1202 and revised it in 1228. In this book, he discussed Hindu-Arabic numeration, as well as a diverse selection of problems covering a variety of mathematical topics. -
1225
Fibonacci's "Liber Quadratorum" ("The Book of Squares")
This is another of Fibonacci's works that describes equations involving squares, and the solutions must be whole numbers. -
1440
The first European printing press was developed
The innovation of printing in Europe led to many opportunities in the field of mathematics because information could easily be recorded, printed, preserved, and transported. Printing allowed for the discoveries and mathematical knowledge to spread over seas and to reach more people. -
1498
Da Vinci's Last Supper Painting
Leonardo Da Vinci's famous painting of the Last Supper was painted in 1498, utilizing the golden proportion, also known as the "golden section." The golden section was used to accentuate the focal points of the painting. Many Renaissance artists, such as Da Vinci, implemented the golden proportion into their art to add a sense of beauty. -
1503
Da Vinci's Mona Lisa
The famous Mona Lisa painting was painted in around 1503-1504. This painting is another example of a piece of art that uses precise mathematics, including the golden proportion. There are many golden rectangles (rectangles with dimensions of the golden ratio) that can be identified throughout the painting. For example, the dimensions of the outline of Mona Lisa's head demonstrate the golden ratio proportion, as well as the location of her eyes in relation to the top of her head. -
1504
Michelangelo's David Sculpture
The sculpture David, in Florence Italy, is one of the most beautiful pieces of Renaissance art illustrating the beauty of the human body, which possesses the beautiful proportions of the golden ratio. -
1509
Luca Pacioli published dissertation, "De Devina Proportione"
"De Devina Proportione" was published in 1509 by Luca Pacioli, in which the term "Divine Proportion" was first used in literature. Illustrations for this mathematical dissertation were provided by Renaissance artist Leonardo da Vinci, including the famous sketch of the human body inscribed in a circle, "Virtruvian Man," demonstrating the proportions of the human body. Da Vinci was perhaps the first to call this proportion, the "sectio aurea" translating to the golden section. -
1512
Sistine Chapel finished
Michelangelo's paintings in the Sistine Chapel use over two dozen applications of the golden proportion, which may be the reason the painting has a breathtaking beauty. Michelangelo emphasizes significant portions of the painting with the use of the golden section. For example, in the painting "Creation of Adam," he paints Adam's finger touching the finger of God precisely at the golden section. -
1527
Pascal's Triangle published
Peter Apian published an arithmetic book in 1527 that contained the first printed version of Pascal's Triangle. Pascal's Triangle has many applications to the Fibonacci Sequence, such as the diagonals adding up to the numbers in the Fibonacci sequence. -
1535
Tartaglia
Mathematician Niccolo Fontana, also known as Tartaglia, claimed that he was able to solve cubic equations. However, he would not tell anyone how he could solve these equations. -
1540
Robert Recorde's textbook "The Grounde of Artes"
English mathematician Robert Recorde wrote the textbook, "The Grounde of Artes," in 1540 and this book covers topics such as operations with arabic numerals, computation with counters, proportions, fractions, and also the "rule of 3." -
1557
The first use of + and - in an English book
Robert Recorde's algebra text, titled "The Whetstone of Witte," introduces the + (plus) and - (minus) sign, as well as an elongated = sign to represent equality. -
1563
Cardano's "Liber de ludo aleae"
Cardano's "Liber de ludo aleae" was the first study of the theory of probability. -
1579
Viete's "Canon mathematicus" published
French mathematician, Francois Viete, had many contributions to mathematics in the topics of arithmetic, geometry, and trigonometry. In his text, "Canon mathematicus," he proposed the use of decimal fractions rather than sexagesimal fractions. -
Kepler's "Astronomia nova"
German mathematician and astronomer Johann Kepler, established the laws of planetary motion. In this book, he provided the first two laws of astronomy, regarding the planets' motion around the sun following an elliptical orbit, and regarding the radius vector of the planets and the sun. -
Napier's Invention of logarighms
John Napier was a Scottish theologist who explored the study of mathematics and came up with the calculations to invent the logarithm. Today in mathematics, logarithms are specified to be of a particular base, however, Napier's logarithms do not specify a particular base. -
Rene Descartes' treatise "Discours de la methode"
French philosopher and mathematician, Rene Descartes, made huge strides in mathematics by applying algebra to geometry. This achievement was so significant because it led to Cartesian Geometry, which made the study of mathematics more accessible to people. Cartesian Geometry allowed people of less academic skill and less knowledge of advanced formal geometry, to understand the study of mathematics. -
Leibniz' published first paper on calculus
Leibniz published his description on differential calculus, including his rules for finding derivatives of powers, products and quotients, utilizing the notation (d). -
Greek letter was used to represent pi
British mathematician William Jones first used the Greek letter we know as pi to represent the irrational number 3.14159... -
French Revolution
The French Revolution had many influences to the field of mathematics in Europe. One of the implications of the revolution was a new emphasis on education, establishing schools such as the Ecole Polytechnique in Paris, thus creating an outlet to share and teach mathematics. -
Gauss' "Disquisitiones Arithmeticae" ("Arithmetical Investigations")
Gauss' first significant book, in which he discussed whole numbers and their properties. -
Term "Golden Ratio" coined
Martin Ohm published "Die reine Elementar-Mathematik" ("The Pure Elementary Mathematics") in 1815, and this book is famous for using the term "goldener schnitt" (translating to "golden section") for the first time. -
Hilbert's Problems
"Hilbert's Problems" are 23 extremely difficult, nearly-unsolvable, problems that challenge mathematicians of the 20th and 21st century. Some of the questions have indeed been solved to date. -
"Phi" used to designate the golden ratio
It was not until the 1990's that "phi" was designated to represent the golden ratio. The golden ratio and golden proportion were established and well known by this time in history, however, it was not until the 1990's that American mathematician Mark Barr assigned the ratio to the Greek letter "phi" and Theodore Andrea Cook included this in his book, "The Curves of Life," in 1914. "Phi" is the first letter of Phidias, the Greek sculptor and mathematician that used the golden ratio in his art. -
Female mathematician Emmy Noether proves "Noether's Theorem"
Emmy Noether is a significant female mathematician who proved two theorems in 1918, including "Noether's Theorem." She has also contributed to the field of mathematics with her research in ring theory and number theory, which has been beneficial to physicists as well as mathematicians. After she died, Albert Einstein referred to her as, "the most significant creative mathematical genius thus far produced since the higher education of women began." -
Godel's Incompleteness Theorem
Godel's Incompleteness Theorem states that when dealing with any consistent formulation of number theory, there will be statements that can not be proven or disproved. Basically, this prove shows that it is not possible to prove absolutely everything. -
Composer Bela Bartok's Sonata for two Pianos and Percussion
Bartók’s works utilize the golden section in proportions of lengths of movements, main divisions of a composition, and even chordal structures. His piece, Sonata for two Pianos and Percussion use the golden section to accentuate the start of the recapitulation of the sonata, thus emphasizing a significant formal break in the composition. -
First women to be elected to the National Academy of Sciences
Julia Robinson was the first women to be elected to the National Academy of Sciences in 1975. This is a significant event because it highlights and recognizes the accomplishments of women in mathematics . -
Fermat's Last Theorem was proved
Andrew Wiles proved Fermat's Last Theorem in 1994. Wiles' work is a proof of the modularity theorem for semi-stable elliptic curves. -
21st Century Mathematical Challenges Released
Similar to "Hilbert's 23 Challenging Problems" in 1900, a team of mathematicians assembled a set of new mathematical challenges in 2000 for today's mathematicians to study and attempt. This is significant because it shows that mathematical inquiry never dies and currently, mathematical discoveries are still being explored and proven. Mathematics is an ever-growing field that builds upon the discoveries of the past.
