The History of the Mathematics
By Juan Tutasi
Prehistoric mathematics (35,000 BC. -20,000 BC.)
The History of the Mathematics
is so extensive that we'll begin since 35,000b.c-20,000b.c when were
found the firsts mathematical ''texts'', which were bones and pieces of
rocks that seems someone had written straight lines on. But why did the
human been feel the necessity of using the mathematics? The
origin of mathematical thought begins with the concepts of number,
magnitude and form. In the Prehistoric age, the mathematics were so
useful -not as nowadays-, for example, in Egypt it was necessary to know
when the river passed across the village to improve agriculture, or
to know how many animals they have. Later the first civilisations
(5,000b.c) incorporated some geometric pictures like the square, circle
and the rectangle.
The ol
dest known possible mathematical
object is the Lebombo bone, discovered in the Lebombo mountains of
Swaziland and dated to approximately 35,000 BC. The first known
mathematics were the Indians (3000bc-2000bc), they used the mathematics
for the construction and they invented the decimal system.
It consists of 29 distinct notches cut into a baboon's fibula.
All of the above is disputed however, the currently oldest undisputed mathematical utilisations are from Babylonian and dynastic Egyptian sources.
First civilisations (3000 BC. -2600 BC.)
When the humans, with knowledge of math
ematics, began building
houses, and living all together with more people. The first
civilisations where in Egypt and India. The Egipcians used the
mathematics for building their famous pyramids, sculptures, and for
knowing when the Nilo was going to overflaw their crops. The Egipcians
created the first number system and a metric system, this was the first
discovery and it has been developing until the modern geometry. In India
the mathematicians created the decimal system which we use nowadays,
this discovery allows us to make mathematic operations that are useful
for technology and other sciences. The first Indian's civilisation
created the number 0 that reduces many calculations, but it was unknown
in Europe until the Roma Empire decadence.
Ancient Orient (1800 BC. -500 BC.)
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In Mesopotamia, nowadays Irak, the mathematics were very useful. The
ancient sumeries created the Mesopotamia's civilisation. In their
discoveries we can find the multiplication table and they began to write
their discoveries in clay rocks, because this rocks were very soft and
you can write on with a stick. But they didn't use the same number
simbology we use, they had a special mark for each number. This rocks
were used in the trades for knowing how much they earned during a week,
or for not to forget if someone had to pay you money that he hadn't paid
you yet. This mathematics weren't written in decimal system, because
they used to write in sixtieh system, it was more difficult but they
didn't know about the decimal system. During this period the Indian
mathematics didn't improve a lot because Indians used them for
cultivation , the spirituality, and meeting the souls. Nevertheless the
mathematics in Egipt improved during the helenistic period, they
combined the mathematics with other sciences and they found the relation
between mathematics and this other sciences. The babilons had a very
short number, they only had six number : 1 ;10 ,100 ; 1,000 ; 100,000
and 1,000,000. The faraons in Egypt order the mathematicians to build the
pyramids, because these were used as tombs,
they also used them for some religious purposes.
Ancient Indian (900BC. -200 AC.)
The oldest mathematic documents from India are the Sulba Sutras, these are religious texts with
simple rules for constructing altars of various shapes, such as squares,
rectangles, parallelograms and others. As Egypt, the Indians were veryworried with religion. In Sutras Sulba, there are methods for constructing
circles with approximately the same area as a square, which approaches
to the number π. Additionally, the Indians obtained the value of the
square root of 2 with a lot of approximation, that belows to the lists of
Pythagorean triples and the statement of the theorem of Pythagoras. All
these results are present in Babylonian mathematics, indicating the strong
influence of Mesopotamia. It is unclear, however, how far the Sutras
Sulba influenced Indian mathematics. But there is a lack of continuity
of the mathematics in India; and there were long periods of inactivity.
Ancient Greece (600BC. - 300 AC.)
Greek mathematicians lived in cities scattered the Eastern Mediterranean, from Italy to North Africa,
but they had a common language and a
common culture. Greek mathematics of the period following Alexander the
Great are called Hellenistic mathematics.
Greek mathematics were more sophisticated than the mathematics that had
been developed before and only the most intelligent people of that
period could learn and teach mathematics.
It
is believed that greek mathematics began with Thalesand Pythagoras.
These mathematics, were probably inspired by Egyptian mathematics,
Mesopotamian and Indian. According to legend, Pythagoras traveled to
Egypt to learn mathematics, geometry and astronomy from Egyptian
priests.
Tales used geometry to solve problems as calculating the height of
pyramids and the distance of ships from the coast. Pythagoras is
credited with the first theorem, the Pythagorean Theorem.
Pythagoras created a school and his members who were called
Pythagoreans proved the existence of irrational numbers. Other
famous mathematicians were Euclid who gave the earliest example of the
mathematical methodology used today. He studied conics and wrote the book
Elements, also did Archimedes of Syracuse who used the method of calculating
the area under the arc of a parabola with the help of the sum of an
infinite series, and gave an approximation of pi.
Roman Empire decadence (300 AC. 450 AC.)
Romans had already conquered Europe
since 27 BC. and put their orders and laws. It is during the period of
decadence, when the war and power became more important than culture. It
was difficult to acquire knowledge, there weren't famous mathematicians
from this period, because to the numerical system which was very bad
for the calculation, women could not study and the men had to go to war.
After the decadence of the Roman Empire, people began to use another
number system, and everyone could study mathematics and others sciences.
Classical China and Japan(500 BC. - 1300 AC.)
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In China, the Emperor Qin Shi Huang gave the order that all books of the
state have to be burned. The order was not obeyed by all the world, but
as a result we know very little about mathematics in ancient China. The
oldest math book that survived from the burning was the I Ching,
trigrams and hexagrams using philosophics, mathematicians and mystics.
These mathematical theorems are composed of lines called yin (female)
and yang (masculine). After the burning of books, the Han Dynasty
produced works mathematics that were burnt. In summary, the mathematical
works of Han astronomer and inventor Zhang Heng contained a formulation
for pi very approximate. Zhang Heng used his formula to find espheric
volumes. Chinese also made use complex combinatorial diagram known as
magic square and magic circle. The Chinese and European mathematics
remained separated, until the exchange between the two cultures between
the sixteenth and XVIII.
The Japanese mathematics of this period was inspired by Chinese
mathematics are essentially oriented to geometric problems. They solved
"geometric puzzles' on wood tables called sangaku where they wrote some
theorems like the Soddy theorem.
Classical India (400 AC. - 1600 AC.)
The advances in Indian mathematics after Sutras are the Siddhantas
Sulba, that are astronomical theory and which shows strong Hellenistic
influence. The Surya-Siddhanta introduced the trigonometric functions of
sine, cosine and inverse sine and established rules to determine the
trajectories of the stars in the positions in the sky. This work was
translated from Arabic into Latin in the Middle Ages. In the V century,
Aryabhata type Aryabhatiya, a muslim volume designed to complement the
rules of calculation where was used in astronomy and mathematical
measure, but certain things, which were later corrected, were wrong. For
the first time Sphuta Brahma-siddhanta, explained clearly the uses of the
number 0. Arab Students exported this knowledge to Europe by the twelfth
century and ended up using the previous numbering systems of the world,
the roman numbers. From the fourteenth century, Madhava, founder of the
Kerala School, computed the value of the number π to 3.14159265359... .
Progress in mathematics and other sciences in India were stopped after the
Muslim conquest of Europe and India.
Medieval Islam (800 AC. -1500 AC.)
The Islamic Empire established across
the Middle East, Central Asia, North Africa, Iberia, and part of India,
made significant contributions to mathematics. But not all of the
texts were written in arabic, some were written in latin and greek.
There weren't only arabian mathematicians, many other important Islamic
mathematicians were Persians. In the ninth century, Al-Khwarizmi wrote
several important books about Arabic numerals and methods of solving
equations. The word algorithm is derived from the Latin of his name,
Algoritmi, and the word algebra from the title of one of his works,
Al-Kitāb fī al-Mukhtasar al-Gabr Hisab wa'l-Muqabala. Al-Khwarizmi is
often nickname "the father of algebra", for their important
contributions to this field. The further development of algebra came
from the hand of Al-Karaji. In his theorem al-Fakhri extends the
methodology to include infinits and unknown quantities. During this
period, many important mathematic theories were discovered . When the
Muslims were expelled from Europe, the advancement of mathematics
increased more after their expultion.
Mathematics in the West (Europe) (1500 AC - 1800 AC)
Medieval Age
During the Middle Ages, people began to use algebra in trade, irrational
numbers were used in some more sciences, a habit that was transmitted
through all Europe. Also
negative solutions were accepted to certain problems and imaginary quantities.
The development of mathematics during the Middle Ages is motivated by
the belief in a "natural order" of arithmetic, geometry, astronomy and
music, and Greek and Arabic mathematical works were improved.
European Renaissance
During the twelfth century, especially in Italy and Spain, were
translated Arabic texts and some Greek texts were rediscovered. Toledo
became a cultural center of translation; European students traveled to
Spain and Sicily in search of scientific literature including the
arabian texts.
The economic and commercial growth that Europe experienced improved use of mathematics in people who were'nt mathematicians.
The new sources gave a boost to mathematics. Fibonacci wrote his Liber
Abaci were he talks about the number Fi or golden number . Thomas
Bradwardine invented some theories of the dynamic movement. The
mathematicians of this period had to use approximate results because
they didn't know the calculus also know as infinitesimal calculus. Until
the late sixteenth century, the mathematicians had a problem with their
solution because mathematicians searched exact answers of some problems
but didn' t know how.
The Scientific Revolution of the XVIIth and XVIIIth
During these centuries, the mathematicians prefered physical and technical
aspects. Isaac Newton and Gottfried Leibniz created calculus, which
opens the era of Mathematical Analysis, the derivative, integration and
differential equations and solve the problem that mathematicians
through all the history had .
The
mathematical universe of this period was dominated by the figure of Leonhard
Euler and his contributions on mathematical functions and numbers
theories. The mathematical function became an object of study with his
own subjects at universities.
In arithmetic, Euler proved Fermat's little theorem, which was difficult
problem of this age, and gave an extended version of the composite
numbers.
XIXth Century (1800 AC. -1900 AC.)
This is one of the most important periods of maths, because most of mathematics we use today were discovered during these years.
The nineteenth century mathematical history is very rich and extense.
Numerous
theories appeared new and some earlier works were complete. The number
of professionals increased a lot and mathematics took a big importance
ever before. The applications of mathematics in other sciences were
developing, making believe that whithout mathematics science can't do
anything, for example, the discovery of a new planet only by calculation,
or the explanation of the creation of the solar system with maths. The
domain of physics, experimental sciences, were completely invaded by
mathematics: heat, electricity, magnetism, fluid mechanics, strength of
materials and elasticity, chemical kinetics, were all
''mathematichzed''. The most important mathematicians of this period
were: Joseph-Louis Lagrange, Augustin Louis Cauchy, Carl Friedrich Gauss
also called the Prince of the Math, Bernhard Riemann, Pierre Laplace,
William Rowan Hamilton and Gottlob Frege.
XXth Century (1900 AC. - 2000 AC.)
During the twentieth century mathematics became one of the greatest professions.
Each year, thousands of doctors graduated, and the job opportunities
were in teaching and industry. Many new disciplines developed with the
work of Poincaré like: topology, differential geometry, logic, algebraic
geometry, Grothendieck's work.In a speech in 1900 in the International
Congress of Mathematicians, David Hilbert proposed a list of 23
mathematical problems. This list, touched several areas of mathematics,
it was a central focus for many mathematicians of the twentieth century.
Until now, 10 have been resolved,7 partially resolved and 2 are still
open and 4 aren't complete enough for knowing if they are resolved or
not. Many conjectures were finally proved . The invention and continued
progress of computers, and electronic machines allowed to work
faster with large amounts of information, . The speed information of
computers also allowed to solve problems that would consume too much
time on calculations using paper and pencil.
XXI Century (2000 AC- ....)
In 2000, the Clay Mathematics Institute announced the seven millennium
problems, and in 2003 the demonstration of the Poincaré conjecture was
solved by Grigori Perelman (who declined the prize). The prize for
solving one of these problems is a Fields Medal (the Oscar of
mathematics) and $ 1,000,000.
Most mathematical excercices and theorems have online version and
printed, also leave many digital publications, so everyone can learn
maths by their own. But this is not the end of way of mathematics, there
are still many things to discover ....
Chromodoris Lochi is a marine gastropod mollusk in the family of Chromorididae.
