University of Madras.
In 1914 Ramanujan joined Hardy at Cambridge University and remained in England for five years, in which time he became one of the youngest ever members of the Royal
Society, had work published and finally gained a degree. However, Ramanujan was often ill.
During one bout of illness, Hardy visited him and mentioned that the number of his taxi, 1729, was ‘rather dull’. Ramanujan replied instantly that 1,729 was
the lowest number that could be written as the sum of two cubes in two different ways, and as such, was actually quite interesting:
1 3 + 12 3 = 1 + 1728 = 1729
9 3 + 10 3 = 729 + 1000 = 1729
There are lower numbers that can be written as the sum of two cubes, but 1,729 is the lowest number that can be written like this in two ways, and Ramanujan’s
instant recognition of this was nothing short of miraculous.
In his short life Ramanujan came up with nearly 4,000 theorems, equations and identities that still inspire mathematical research to this day.
If you find half the perimeter of the quadrilateral (let’s call it ‘s’) then the area of the shape can be found using Brahmagupta’s
formula:
√(s-a)(s-b)(s-c)(s-d)
Although the Indians were clearly excellent mathematicians, when the British began to take control of the country in the 1700s they assumed the backward pagan Hindus had nothing
of worth to contribute beyond vast natural resources and cheap labour. It has only been in the last hundred years that we have come to appreciate the mathematical heritage of the sub-continent.
I SLAMIC M ATHEMATICS
Mohammed, the founder of Islam, was born in AD 570. In the two centuries following Mohammed’s birth the Islamic Empire came to dominate all of the
Middle East, Central Asia, North Africa and what would become Spain and Portugal. This Islamic Golden Age saw much important mathematical progress emerge from the countries in the empire, while
Europe remained still in its Dark Ages.
The Islamic religion itself is particularly open to the idea of science, which contrasted strongly with the ideas prevalent in medieval Europe, where it was often considered heretical to
question or investigate the workings of a world made by God.
The Islamic Empire too was committed to gathering the knowledge of the ancient world. Texts in Classical Greek and Latin, Ancient Egyptian, Mesopotamian, Indian, Chinese
and Persian were all translated by Islamic scholars, broadening their availability to the empire’s scientists and mathematicians.
A L -K HWARIZMI (
c.
790–
c.
850)
Mathematician Al-Khwarizmi hailed from an area situated in present-day Uzbekistan, and he is credited with providing several significant contributions to mathematics. Although
some of his original works have survived, he is familiar to us through editions of his work translated into Latin for use later in Europe.
The new number system
One of Al-Khwarizmi’s significant legacies was what is now known as the Hindu-Arabic numeral system, which we still use to this day. Derived from his
Book of Addition
and Subtraction According to the Hindu Calculation
, Al-Khwarizmi’s system of numbers, developed over time in India from
c.
300 BC and passed through into
Persia, revolutionized arithmetic.
Up to this point, no culture had a system of numerals with which it was really possible to use in arithmetic. Numbers would always be converted into letters or symbols (either mentally or using
counters, abacuses or other such tools), the calculationperformed and the result reconverted back into numerals. Lots of symbols were often needed to show a number, many of
which were difficult to decipher at a glance.
The Hindu-Arabic system contains just ten symbols – 0 1 2 3 4 5 6 7 8 9 – that could be used to write any number. It is important to note that these symbols were exactly that –
they were not associated with the value they represented through stripes or dots. The zero (from the Arabic
zifer
, meaning ‘empty’)
In 1914 Ramanujan joined Hardy at Cambridge University and remained in England for five years, in which time he became one of the youngest ever members of the Royal
Society, had work published and finally gained a degree. However, Ramanujan was often ill.
During one bout of illness, Hardy visited him and mentioned that the number of his taxi, 1729, was ‘rather dull’. Ramanujan replied instantly that 1,729 was
the lowest number that could be written as the sum of two cubes in two different ways, and as such, was actually quite interesting:
1 3 + 12 3 = 1 + 1728 = 1729
9 3 + 10 3 = 729 + 1000 = 1729
There are lower numbers that can be written as the sum of two cubes, but 1,729 is the lowest number that can be written like this in two ways, and Ramanujan’s
instant recognition of this was nothing short of miraculous.
In his short life Ramanujan came up with nearly 4,000 theorems, equations and identities that still inspire mathematical research to this day.
If you find half the perimeter of the quadrilateral (let’s call it ‘s’) then the area of the shape can be found using Brahmagupta’s
formula:
√(s-a)(s-b)(s-c)(s-d)
Although the Indians were clearly excellent mathematicians, when the British began to take control of the country in the 1700s they assumed the backward pagan Hindus had nothing
of worth to contribute beyond vast natural resources and cheap labour. It has only been in the last hundred years that we have come to appreciate the mathematical heritage of the sub-continent.
I SLAMIC M ATHEMATICS
Mohammed, the founder of Islam, was born in AD 570. In the two centuries following Mohammed’s birth the Islamic Empire came to dominate all of the
Middle East, Central Asia, North Africa and what would become Spain and Portugal. This Islamic Golden Age saw much important mathematical progress emerge from the countries in the empire, while
Europe remained still in its Dark Ages.
The Islamic religion itself is particularly open to the idea of science, which contrasted strongly with the ideas prevalent in medieval Europe, where it was often considered heretical to
question or investigate the workings of a world made by God.
The Islamic Empire too was committed to gathering the knowledge of the ancient world. Texts in Classical Greek and Latin, Ancient Egyptian, Mesopotamian, Indian, Chinese
and Persian were all translated by Islamic scholars, broadening their availability to the empire’s scientists and mathematicians.
A L -K HWARIZMI (
c.
790–
c.
850)
Mathematician Al-Khwarizmi hailed from an area situated in present-day Uzbekistan, and he is credited with providing several significant contributions to mathematics. Although
some of his original works have survived, he is familiar to us through editions of his work translated into Latin for use later in Europe.
The new number system
One of Al-Khwarizmi’s significant legacies was what is now known as the Hindu-Arabic numeral system, which we still use to this day. Derived from his
Book of Addition
and Subtraction According to the Hindu Calculation
, Al-Khwarizmi’s system of numbers, developed over time in India from
c.
300 BC and passed through into
Persia, revolutionized arithmetic.
Up to this point, no culture had a system of numerals with which it was really possible to use in arithmetic. Numbers would always be converted into letters or symbols (either mentally or using
counters, abacuses or other such tools), the calculationperformed and the result reconverted back into numerals. Lots of symbols were often needed to show a number, many of
which were difficult to decipher at a glance.
The Hindu-Arabic system contains just ten symbols – 0 1 2 3 4 5 6 7 8 9 – that could be used to write any number. It is important to note that these symbols were exactly that –
they were not associated with the value they represented through stripes or dots. The zero (from the Arabic
zifer
, meaning ‘empty’)
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