Behold the Ages of Math...
Math (Before 1000 B.C.E.)
Like most of our knowledge of ancient times, our knowledge
of the oldest math has faded with
the millennia, although we can guess as to its nature. Before arithmetic,
before numbers themselves, there was counting.
A Shepard needed to know that they ended the day with as many animals as
when they had set out.
In order to solve this problem, in truly ancient times it
was common to mark numbers with pebbles or tallies, even fingers.
These simple, even crude systems were enough to ensure that two numbers
were equal without ever defining the concept of number.
However, even in the most ancient times recorded math was already highly developed. Although the "Pythagorean Theorem" was named for the Greek philosopher Pythagoras, it was already well known to the Chinese, the Hindu, and the Babylonians. The ancient Egyptians, with their highly developed architecture had an equally evolved geometric system. Yet our knowledge of these times remains broken and fragmented. Any conjectures about earlier math will, for now, remain merely conjectures.
Less) Ancient Chinese Math (1000 B.C.E.- 1650 C.E)
Although separate from most Western theories of math at the
time, the Chinese had a highly sophisticated number theory.
A full thousand years before European civilization the Chinese had
approximated pi to sixteen digits. They
had even developed a method for solving systems of equations that was related to
modern linear algebra.
Arithmetic in Nine Sections.
A collection of 246 problems dating from the Han dynasty, including a
rough estimation for arc length that presents a value of 3 for pi.
text of an age with the Arithmetic in Nine Sections.
It contains the beginnings of elementary number theory.
Important People: Chu Shi-kie. Understood the properties of what is commonly referred to as "Pascal's Triangle." He also created a method of advanced matrix manipulation.
Greek Math (600 B.C.E. - 450 C.E.)
The Greeks were some of the best mathematicians of the
ancient world. Their geometry
continues to impress and challenge math students of all ages. They came up with ingenious
solutions to some very famous problems. Their
meticulous nature and careful proofs greatly advanced the science of math, and
they successfully gathered many of the discoveries of other cultures.
Their use of the compass and straightedge in geometry continues to
influence high school classes today.
Elements. This is
Euclid's masterpiece that set the foundation for much of geometry until the
modern age. Its name suggests that
its focus was on an elementary level of geometry, implying that it represented
only the beginning of the author's true mastery of the art.
Pythagoras. The man whose name was bestowed upon the famous
Pythagorean Theorem, was both a philosopher and a mathematician.
Although he was not the first to discover the basic properties of right
triangles, he founded a branch of philosophy and mathematics that effected Greek
society long after his death. They
believed that the basic properties of number theory (whole numbers, perfect
numbers, ratios, etc.) reflected the true nature of the universe.
of the greatest geometers ever. Euclidian
geometry bears his name, and he is responsible for compiling its fundamental
list of postulates.
Archimedes. Perhaps the greatest mathematician of the time period. He expanded on the Greek art of geometry, working out many of his problems in three dimensions.
Math (200 B.C.E. - 1250 C.E.)
The caste system restricted the study of mathematics to the
priesthood during this time, but many important discoveries were made in the
region that is currently called India. Unlike
the more rigorous Greeks, the Hindus favored calculation over the more artful
study of geometry. As in many
civilizations, the majority of the most famous Hindu mathematicians were
astronomers by profession, and because of this very few works were published
whose focus was truly mathematics.
work is the source of much of our knowledge of Hindu arithmetic.
It highlights their system for writing equations.
From this work, we know that the Hindu's had already discovered
irrational and negative numbers, understood some of the more basic properties of
Brahmagupta. The most
prominent Hindu mathematician of the seventh century his work in the field of
astronomy gives us insight into the advanced state of mathematics in the region
during this time. Bhaskara.
Rose to fame around the year 1150 C.E.
Despite writing almost half a millenium after Brahmagupta the work shows
only marginal advances in the field of math.
Srinivasa Ramanujan. In 1913, this astounding mathematician met the eminent British theorist G. H. Hardy. Ramanujan possessed amazing intuitive prowess and made a significant contribution to modern number theory.
Math (650 C.E. - 1200 C.E.)
The Arabs have been an important group throughout the
history of mathematics. They
adopted and adapted the Hindu system of numerals and developed the system used
worldwide today. During the Dark
Ages of Western Europe, the Arabs preserved many of the discoveries made by
Greek scholars. Although they
lacked the rigorous proofs of the Greeks the Arabs also made many discoveries of
their own in the field of Algebra.
Fakhri. Written by
al-Karki, it is a very disciplined and professional study of algebra.
by Omar Kayyam, it is very highly regarded in intellectually circles in the
Important People: Omar Kayyam was one of the first mathematicians to solve cubic equations. He used a geometric solution that he also used to find roots of special quartic equations.
Math (450 - 1500)
The less said about European mathematics during this time period the better. The Dark Ages had set in, and many of the advances developed and spread during the Classical period were lost and forgotten in the region. Almost all discoveries were simply rediscoveries made from older Greek texts or communication with other cultures. Little original work was accomplished during this stagnant period.
Early Modern Math (1500 C.E. - 1700C.E.)
Development was much faster and thorough from the
Renaissance on. Through stronger
nations, more formalized relations, and better communication across cultures
math began to awaken from its slumber. Calculus
was developed, and most of the fundamental parts of modern math were developed
first in this time.
Principia. Newton's most
famous publication. It marked the
beginning of a new age in physics and applied math. It illustrated the true genius of Newton and paved the way
for many of his most important discoveries.
Important People: Renee Descartes. His most famous work involves analytic geometry. By using Cartesian coordinates Descartes finally succeeded in advancing geometry beyond the discoveries of the ancient Greeks.
Math (1700 C.E.- 2000 C.E.)
At this point, the advances and discoveries race ahead too
fast for justice to be done to them here. Calculus
thrived and flourished, giving birth to a whole new species of applied math that
remains important in the present day. The
Industrial Revolution created a new need for the unification of math and
science. As always, math advanced.
Matrix theory in its present form was created leading to a new set of
important discoveries. The modern
standards of proof were implemented, and communication between mathematicians
increased leading to the sharing of ideas and discoveries.
Proceedings of the St. Petersburg Academy. This is a journal rather than a single work, and its most
important period was during the eighteenth century when it had the honor of
publishing Euler's manuscripts. Euler,
besides contributing to the theory of math in general, is respected for
standardizing the notation used by mathematicians in the present day.
The metric system.
A very important advancement, although not a published work.
The metric system was the standardization and organization of measurement
that marked the success of the scientific method and the general advancement of
scientific procedure. Disquisitiones
arithmeticae. The masterwork of
Charles Gauss represents yet another great leap in number theory.
Important People: To mention a person here by name is to disregard the dozens of other great mathematicians who could not be named. Truly, as much has happened to the field of math in the last three hundred years as had happened in all the time before. Among the greatest of the great are Charles Gauss, an extraordinary scholar of the nineteenth century whose potential as a child prodigy was truly realized as an adult, and Albert Einstein the revolutionary physicist. Among these great names were new tools, more powerful than any before. Modern mathematicians are aided tremendously by computer, calculator, and communication. Each year it becomes more difficult to keep abreast of the truly amazing discoveries. Each year, more names are added to the list of great mathematicians.