The document provides a timeline of key developments in mathematics from 6000 BCE to the present. Some of the highlights include: - The earliest written Egyptian numbers dating back to 2700 BCE which used symbols for units, tens, hundreds, and thousands. - Babylonian mathematics from 1800 BCE which had multiplication tables and worked on solving quadratic and cubic equations. - Early Chinese mathematics from 1600 BC which included the use of an efficient decimal place value system using bamboo rods. - Indian mathematics from 1000 BCE which developed concepts like zero, negative numbers, and trigonometry that were later transmitted worldwide. - Classical Greek mathematics from 624 BC which included theorems attributed to Thales and Euclid's Elements textbook.

1. Reporter JONA GREGORIO

2. > The Early Egyptians
6OOO BCE
> (GREEK) Hellenistic
547 BC
> Written Egyptian Numbers
2700 BCE
> Babylonian Mathematics
539 BC
> Babylonians have multiplication
tables
1800 BCE
> Islamic Middle Ages
632-1258
> Early Chinese Mathematics
1600 BC
> Renaissance 16th, 17th, 18th Century
1501- 1800
> Indian Mathematics
1000 BCE
> 19th, 20th,21st Century Math
1801 - Present
>(GREEK) Classical Mathematics
624 BC- 548 BC
> Father Of Mathematics

3. > The Pharaoh’s surveyors used measurements
based on body parts (a palm was the width of
the hand, a cubit the measurement from elbow
to fingertips) to measure land and buildings very
early in Egyptian history, and a decimal numeric
system was developed based on our ten
fingers. The oldest mathematical text from
ancient Egypt discovered so far, though, is the
Moscow Papyrus, which dates from the
Egyptian Middle Kingdom around 2000 – 1800
BCE
The Early Egyptians - 6OOO BCE
Moscow Papyrus

4. Ancient Egyptian Number System
It is thought that the Egyptians introduced the earliest fully-developed
base 10 numeration system at least as early as 2700 BCE .Written
numbers used a stroke for units, a heel-bone symbol for tens, a coil of
rope for hundreds and a lotus plant for thousands, as well as other
hieroglyphic symbols for higher powers of ten up to a million. However,
there was no concept of place value, so larger numbers were rather
unwieldy although a million required just one character, a million minus
one required fifty-four characters.

5. The Rhind Papyrus, dating from around
1650 BCE, is a kind of instruction manual in
arithmetic and geometry, and it gives us
explicit demonstrations of how multiplication
and division was carried out at that time.
Written Egyptian Numbers
This happens to be around the time that the Rhind Mathematical Papyrus (RMP)
was written. The RMP is basically a huge scroll detailing many mathematical
problems and solutions. Its design suggests that it was intended to be used by a
teacher to assign problems to students. It was written near 1550BC..

6. Many of the mathematical tablets are "problem texts:" they contain
problems or sets of problems, sometimes with solutions.
"Old Babylonian" refers here to the civilization that flourished some four
thousand years ago (around 2000 B.C.) in what is present-day Iraq.
Documents at the time were written in cuneiform ("wedge-shaped")
characters on clay tablets, most of them rectangular and of a size to be
held comfortably in the hand (about
5 × 8cm or 2 × 3 inches).

7. BABYLONIAN MATHEMATICS
SEXAGESIMAL NUMERALS
IN CUNEIFORM
*Sumerians had multiplication and division
tables, geometric exercises
* Babylonians developed pre-calculated
tables for solutions of quadratic and cubical
equations
* Calculations of growth (e.g. for loans)
*Calculations of ephemeris into astronomical
tables
* Extensive metrological system

8. Origins of Babylonian mathematics
Babylonian mathematics is a range of numeric
and more advanced mathematical practices in
the ancient Near East, written in cuneiform script.
Study has historically focused on the Old
Babylonian period in the early second millennium
BC due to the wealth of data available. There has
been debate over the earliest appearance of
Babylonian mathematics, with historians
suggesting a range of dates between the 5th and
3rd millennia BC.
Babylonian mathematics was primarily written on
clay tablets in cuneiform script in the Akkadian or
Sumerian languages.

9. > One of the oldest surviving mathematical
works is the Yi Jing, which
greatly influenced written literature during the
Zhou Dynasty (1050–256 BC). For
mathematics, the book included a
sophisticated use of hexagrams. Leibniz
pointed out, the I Ching contained elements of
binary numbers.
Early Chinese
Mathematics
> Simple mathematics on Oracle bone script
date back to the Shang Dynasty (1600–
1050 BC).

10. The simple but efficient ancient Chinese numbering system, which
dates back to at least the 2nd millennium BCE, used small bamboo
rods arranged to represent the numbers 1 to 9, which were then
places in columns representing units, tens, hundreds, thousands,
etc. It was, therefore, a decimal place value system, very similar to
the one we use today – indeed it was the first such number system,
adopted by the Chinese over a thousand years before it was
adopted in the West – and it made even quite complex calculations
very quick and easy.
The Chinese
Number System

11. Lo Shu magic square
Chinese magic square
There was a pervasive fascination with numbers and mathematical patterns in
ancient China, and different numbers were believed to have cosmic significance. In
particular, magic squares – squares of numbers where each row, column and
diagonal added up to the same total – were regarded as having great spiritual and
religious significance.
Lo Shu magic square, with its traditional
graphical representation

12. > Mantras from the early Vedic period
(before 1000 BCE) invoke powers often
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.
The evolution of Hindu-Arabic
numerals

13. Earliest Recorded Usage of a Circle Character as
Number Zero
The use of zero as a number which could be used in calculations and
mathematical investigations, would revolutionize mathematics.Brahmagupta
established the basic mathematical rules for dealing with zero: 1 + 0 = 1; 1 – 0 = 1;
and 1 x 0 = 0 (the breakthrough which would make sense of the apparently non-
sensical operation 1 ÷ 0 would also fall to an Indian, the 12th Century
mathematician Bhaskara II)

14. Indian mathematics emerged in the Indian subcontinent from 1200 BCE
until the end of the 18th century.
In the classical period of Indian mathematics (400 CE to 1200 CE),
important contributions were made by scholars like Aryabhata,
Brahmagupta, Bhaskara II, and Varāhamihira. The decimal number
system in use todaywas first recorded in Indian mathematics.
Indian mathematicians made early contributions to the study of the concept
of zero as a number,negative numbers, arithmetic, and algebra. In addition,
trigonometry was further advanced in India, and, in particular, the modern
definitions of sine and cosine were developed there.
These mathematical concepts were transmitted to the Middle East,
China, and Europe and led to further developments that now form the
foundations of many areas of mathematics.

15. (GREEK) Classical Mathematics
Attic or Herodianic numerals
The ancient Greek numeral system, known as Attic or Herodianic numerals, was
fully developed by about 450 BCE, and in regular use possibly as early as the
7th Century BCE. It was a base 10 system similar to the earlier Egyptian one
(and even more similar to the later Roman system), with symbols for 1, 5, 10,
50, 100, 500 and 1,000 repeated as many times needed to represent the
desired number.

16. > Thales's theorem states that if
A, B, and C are distinct points on
a circle where the line AC is a
diameter, the angle ABC is a
right angle.
> Thales's theorem is a special
case of the inscribed angle
theorem and is mentioned and
proved as part of the 31st
proposition in the third book of
Euclid's Elements. It is generally
attributed to Thales of Miletus,
but it is sometimes attributed to
Pythagoras.
Thales’ theorem: if AC is a
diameter and B is a point
on the diameter's circle, the
angle ABC is a right angle.

17. Renaissance 16th
Century
1501 - 1600 An important person in the early 16th century
was an Italian Franciscan friar named Luca
Pacioli.He is referred to as the father of
accounting and bookkeeping and he was the
first person to publish a work on the double-
entry system of book-keeping on the continent
> SUMMA DE ARITHMETICA (1996)
a textbook for use in the schools of Northern
Italy. It was a synthesis of the mathematical
knowledge of his time and contained the first
printed work on algebra written in the vernacular
(i.e., the spoken language of the day).

18. 16TH --CENTURY
MATHEMATICS
The Supermagic Square
It is a tribute to the respect in which
mathematics was held in
Renaissance Europe that the famed
German artist Albrecht Dürer
included an order-4 magic square in
his engraving “Melencolia I“. In fact,
it is a so-called “super magic
square” with many more lines of
addition symmetry than a regular 4 x
4 magic square (see image at right).
The year of the work, 1514, is
shown in the two bottom central
squares.
The supermagic square shown in Albrecht
Dürer’s engraving “Melencolia I”

19. During the 16th and
early 17th Century, the
equals, multiplication,
division, radical (root),
decimal and inequality
symbols were gradually
introduced and
standardized.

20. Logarithms were invented by John
Napier, early in the 17th Century
The invention of the logarithm in the
early 17th Century by John Napier
and later improved by Napier and
Henry Briggs contributed to the
advance of science, astronomy and
mathematics by making some
difficult calculations relatively easy. It
was one of the most significant
mathematical developments of the
age, and 17th Century physicists like
Kepler and Newton could never have
performed the complex calculatons
needed for their innovations without
it.
17TH CENTURY MATHEMATICS

21. The 20th Century continued
the trend of the 19th towards
increasing generalization and
abstraction in mathematics, in
which the notion of axioms as
“self-evident truths” was
largely discarded in favour of
an emphasis on such logical
concepts as consistency and
completeness.
20TH CENTURY
MATHEMATICS

22. > Here in the present, we learn from our
history to then discover new branches of
math.
> Our math will evolve more in time, as in
more formulas and answers.
21st Century Math
2001 - PRESENT

23. Father of Mathematics
Archimedes is considered the Father of Mathematics
for his significant contribution to the development of
mathematics. His contributions are being used in great
vigour, even in modern times.
From his childhood, Archimedes took an interest in
studying science, mathematics, and politics. Throughout his
entire life, Archimedes was fascinated with mathematical
equations and problem-solving.
Archimedes's family also supported him in getting a
proper education. This was probably the reason for which
he joined the School of Mathematics, which is in Egypt.

24. > There are many excellent reasons to study the history of mathematics.
> It helps students develop a deeper understanding of the mathematics they
have already studied by seeing how it was developed over time and in various
places.
> It encourages creative and flexible thinking by allowing students to see
historical evidence that there are different and perfectly valid ways to view
concepts and to carry out computations. Ideally, a History of Mathematics
course should be a part of every mathematics major program.
> Mathematics is essential to our world, so its knowledge is transferable to
many situations. Engineering, Science, and Technology contribute to great
inventions in the world, with all experts in all those fields having outstanding
math skills.
Why is it significant to study the “HISTORY
OF MATHEMATICS”?

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