Mathematics has been traced to exist as a knowledge among peoples of Indus
Valley Civilization with Harappan culture as
has been proved by continuing archeological excavations in lands presently known
as bhaart or India and Pakistan. Indus Valley Civilization is acknowledged as
the oldest civilization on this planet earth. The continuing archeological
research indicates that this civilization included well planned and engineered
cities, towns and villages integrated with extensive Harappan urban and
rural cultures around dating back to at least 6500 BC and continued to dominate
the region for at least 700 years, from 2600 to 1900 B.C. It was only in the
1920's that the buried cities and villages of the Indus valley were recognized
by archaeologists as representing an undiscovered civilization. The buildings,
artifacts and special seals found in Harappan culture sites indicates that the
culture practiced veDik lifestyles.
This Harappan culture of veDik lifestyle
is proved to have extended to east Europe as proved by archeological
research in areas around present day Turkey. The Babylonians and Egyptians who
have an history dating back to 3500 BC also has evidence of interaction with
Harappan culture. The war of mHaa-bhaart
was fought around 5000 years ago (3000 BC) and included the entire lands
of Asia, Africa and Europe as can be deduced from the description of the armies
of different peoples who took part in the 18-day war which killed about 1.7
billion peoples. In all these different lands the history of mathematics is
traced by the following events:
- circa 3000 BC:
The Babylonians of ancient Mesopotamia and
the ancient Egyptians left the earliest records of
organized mathematics. Well-preserved Babylonian clay tablets show wedge-shaped
writing known as cuneiform.
The earliest tablets date from about 3000 BC.
Arithmetic and algebra dominated their mathematics for commerce to exchange
of money and merchandise, to compute
simple and compound interest, to calculate taxes, and to allocate shares of a harvest
to the state, temple, and farmer. The building of canals, granaries, and other
public works also required using arithmetic and geometry.
Calendar reckoning,
used to determine the times for planting and for religious events, was another
important application of mathematics.
- To circa 31 BC: The Greeks
adopted elements of mathematics from the Babylonians and the Egyptians
in circa 600 BC
with through the development of mathematics by Thales and Pythagoras.
Greek mathematicians invented abstract mathematics based on deductive proof
based on logical, axioms and proofs of the mathematical concepts. The mathematics that had existed
before their time was a collection of conclusions based on observation of the
nature and natural phenomenon. The development of Greek mathematic ended
in 31 BC with Roman conquest of Egypt, the last of
Greek Alexander’s kingdoms.
- To circa 476 AD: Nothing mathematically
significant was accomplished by the Romans. The Roman numeration system was
based on Roman numerals, which were cumbersome for calculation. Roman orator
Cicero boasted that the Romans were not dreamers like the Greeks but applied
their study of mathematics to the useful.
- TO circa 800 AD: After the decline of Greece and Rome, mathematics flourished in India. Mathematics in India was largely a tool
for astronomy, yet Indian mathematicians discovered a
number of important concepts. The current Western numeration system, for example, is
based on the Indian system which was conveyed to Western world by Arabs and is
generally known as the
Hindu-Arabic system.
The system of numbers in current use with each number having an absolute
value and a place value (units, tens, hundreds, and so forth)
originated in India. Indian Mathematicians were the first to recognize
zero as both an integer and a placeholder.
Mathematics existed in veDik lifestyle
as is shown in science of jyotiSH
which is one of the 6 veDNg meaning
limbs of veD.
veD contains all the sciences of knowledge of creation and
life. As per NaarD puraaAN, Chapter
54 the science of jyotiSH was relayed
by pRjaapti BRH`maao,
to Daevtaaoo,
RUSHioo and munioo
for the use by humans for the fulfillment of their duties as per their
DHARmo. The science of
jyotiSH was expounded by in 400,000 s`lok
(aphorisms in verse forms) which are divided into 3 categories:
1. gNit =
mathematics and astronomy
2. jaatk =
horoscopy
3. sMhitaa =
astrology
The above means that knowledge of mathematics is encoded in all creations but
is manifested as knowledge in individual creations as per the needs of the
individual creation in the "space-time continuum"
and as warranted by the occurrence of intersections of
"world lines" as per the relativity theory developed by Albert
Einstein in his science discoveries of 1905 to 1915. To date only
parts of veD texts have been
deciphered with the SNskrut grammar
knowledge developed by pANiANi
in circa 500 BC. And even with this limited deciphering of the
veDik texts in
sNskrut language the concepts in these texts are still very
hard to understand. But the veD texts
deciphered to date has numbers everywhere explaining space in multiple
dimensions, time in various reckonings as per the location in space of the
domains of various existences of various creations, quantities of all materials
in creation and also natural processes in the universe for which the
veD text is meant for. We will share
with each other more knowledge on this after knowing the history of development
of mathematics as humans know in 2000 AD.
- ( pRjaapti BRH`maa, per
veD, is the creator, as empowered
by creator BRH`m, of all that
exists in a universe. Daevtaao
are all entities who are which are manifestations of
creator BRH`m's powers and forces in
nature). RUSHio and
munio are sages who were versed in
veD and whose function is to look after the welfare of all
creations through their powers obtained through
tps and yGN. tps
means totally focused meditation on creator
BRH`m resulting in the meditative mode
called smaaDHi whereby the
meditator is blessed by creator BRH`m
with the powers to be sub-creator and/or sub-sustainer and/or
sub-re-creator in birth-death cycles called
sNsaar in BRH'm's
stead. yGN is a process and a
rite prescribed in veD in which oblation is offered to
creator BRH`m or any of His
manifestations. It is
stated in veD that
tps and
yGN is what creates, sustains and recycles the created
through a process called ly a
universe and everything in that universe. DHARm
is the laws, rules and regulations in nature and among the created that
empowers the harmonious co-existence of all created in a universe.)
It is not known when
the Indian numeration system as is in current existence around the world was developed.
But digits similar to
the Arabic numerals used today have been found in a Hindu temple built about 250
BC.
In circa 500 AD, Indian mathematician and astronomer
Aryabhata expounded beyond the Greek mathematician in his
use of fractions as opposed to whole numbers to solve indeterminate equations
(equations that have no unique solutions). The mathematical development by Aryabhata
has already been outlined in the previous serial titled "veDik MATHEMATICS -
What does it mean".
In circa 630 AD Indian
mathematician Brahmagupta expounded the
concept of negative numbers in
mathematics for the first time in the history of current mathematics. He presented rules for them in terms of
fortunes (positive numbers) and debts (negative numbers). Brahmagupta’s
understanding of numbers exceeded that of other mathematicians of the time. He
also made full use of the place system in existence in India in his method of multiplication. Brahmagupta wrote two
treaties on mathematics and astronomy dealing with topics such as
eclipses, risings and settings, and conjunctions of the planets with each other
and with fixed stars.
In circa 900 AD, Jain mathematician Mahavira stated rules for
operations with zero.
In circa 1200 AD Bhaskara supplied the correct answer for division
by zero as well as rules for operating with irrational numbers. Bhaskara wrote
six treaties on mathematics, including Lilavati
meaning The Beautiful, which summarized
mathematical knowledge existing in India up to his time, and
Karanakutuhala, meaning “Calculation of Astronomical Wonders.”
- 800 AD TO 1400: In 800 AD,
Indian mathematics reached
Baghdaad, a major early center of Islam
culture. Mathematical masterpieces of
Indians and those of the Greeks were translated into Arabic in centers of
Islamic learning, where mathematical discoveries continued during the period
known in the West as the Middle Ages.
In circa 800 AD Arab mathematician
al-Khwaarizmī wrote a systematic introduction to
algebra called Kitaab al-jabr w’al Muqabalah
meaning Book of Restoring and
Balancing. The English word algebra comes from al-jabr
in the title of this mathematical treatise.
Al-Khwaarizmī’s algebra was founded on Brahmagupta’s work, which he duly
credited, and showed the influence of Babylonian and Greek mathematics as well.
A 12th-century Latin translation of al-Khwaarizmī’s treatise was crucial for the
later development of algebra in Europe. Al-Khwaarizmī’s name is the source of the
word algorithm.
In 900 AD Arab
scholars completed the acquiring of all Indian and Greek mathematics in
existence at that time and began further development.
From 900 AD to 1000 AD Alhazen,
who was an outstanding Arab
scientist, developed algebraic solutions of
quadratic and cubic equations. Al-Karaji
continued development of the algebra of polynomials (mathematical expressions that are the sum
of a number of terms) of al-Khwaarizmī with polynomials with an infinite
number of terms. Geometers such as Ibrahim ibn Sinan
continued Archimedes’s investigations of areas and volumes, and Kamal al-Din and
others applied the theory of conic sections to solve problems in optics.
In circa 1100 AD, Persian mathematician Omar Khayyam and other Arab
mathematicians, solved certain cubic equations geometrically by using conic
sections. Arab astronomers contributed the tangent and cotangent to
trigonometry.
In circa 1200, Arab astronomer Nasir al-Din
al-Tusi created the mathematical disciplines of plane and spherical trigonometry
and separated trigonometry as a stand-alone from
astronomy. Arab mathematicians made important discoveries
in the theory of numbers and also developed a variety of numerical methods
for solving equations.
The Arab mathematicians through translations in Arabic preserved many of the
Greek mathematics in existence to 1500 AD when civilization in Europe was in
stagnation after the destruction of Roman empire. Europe re-acquired much of this
translated Greek mathematics along with the Indian mathematics when mathematics
was re-translated
into Latin which was the written language of educated Europeans starting
sometime 1100 AD.
With the blessing of creator BRH`m
we will continue reviewing the history of the development of mathematics
spearheaded in Europe in the Enlightenment Age (from circa 1500 AD) after the
completion of Middle Ages. Through mathematics Europe started making a
fast headway in understanding the veD = SCIENCES
OF CREATION AND LIFE in the universe the Europeans and the
rest of humankind knew....
om tt st......om bRH`myae
nmH......
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