BBC Four: The Story of Maths (2008)
Part 1: The Language of the Universe
If one were to look at the history of the world, there was never a time there was peace on Earth. At every moment, there was some turmoil somewhere. In spite of all that upheavals, destructions and loss of lives and civilisations, we as a human race, have progressed on the long run. In the time of peace, people start becoming curious about their surroundings and start trying to understand its intricacies. They try to explain its pattern and perhaps try to predict its recurrence. Attacking forces usurp this knowledge as theirs and try to improve this further when the dust settles after their inquests. Slowly, learning from to count numbers with our digits, we developed formulas and managed to calculate unfathomable numbers of gargantuan proportions.
Mathematics is said to be the language of the Universe. Marcus De Sautoy, a Mathematician, takes the viewers on a journey of discovery of how Mathematics changed humankind. In this episode, he traces the origin of the field of which predates the Greek mathematicians we are familiar.
Economic reasons to quantitate the taxes to be collected and predict weather pattern in the Nile were strong enough reasons to put maths to full use.
All the while, I have been wondering why the hour has 60 minutes and so does the minute has 60 seconds. It has to do with the base of 60 that the Babylonians used for calculation. On one hand, the three knuckles on the four finger made 12, and the five fingers eased calculation of bigger numbers. They also had binary numbers. Syrians, which is now in turmoil now, used to the cradle of advanced mathematics. Even before Pythagorean theorem came known to the world, which incidentally may not his discovery, the Egyptian had thought of it.
The Chinese had their way of calculating big numbers with sticks and symbols, volume approximation and complicated equation. Mammoth structures like the Great Wall of China are testimonies of their engineering feats. The Indians introduced the decimal system, the number zero which paradoxically helps to calculate big numbers and even added another plane of number- the negative numbers. Civilisations before them, like the Babylonians and Chinese, only left an empty space to denote nothing (zero). The concept of infinity, pi and trigonometry were thought of by Indians long before 15th century Europe.
The 5th century Islamic Era was a time when knowledge from other regions to bring mathematics to yet another level. Algebra was introduced. Omar Khayyam, the poet, also tried his hand in solving equations.
The first modern European mathematician can be said to be Fibonacci. His endeavour to replace Roman numerals with the easier Hindu-Arabic numbers was met with scorn and suspicion. Fibonacci's number helped to explain many patterns in nature. Bologna was the place where mathematical sorcery took place and from it borne complex cubic equations. The history was rewritten by the Europeans.
Part 3: The Frontiers of Space
As the Golden Age of the Eastern civilisations takes a back seat, modern European mathematicians, many of whom wear many hats, as scientists, painters, philosophers and even sword-yielding sorcerers, go on to discover many peculiar traits of mathematics. Their practical use of this field helps them to propel their race to greater heights.
Many of the icons who thought of new ideas were actually men of faith. The beauty of the thinking trend at that time was that thinking was allowed. They did not feel that humankind had learnt everything that needed to be learnt. They were receptive to changes and had the burning desire to reach even greater heights. Complacency was not the order of the day. Thinking outside the box was allowed. Everybody was trying to outdo each other to show-off their discovery, sometimes with disastrous outcomes.
Piero Della Francesca used mathematics to perfect his painting of 'The Flagellation of Christ'. We always think of Rene Descartes (of 'I think therefore I am' fame) as a philosopher. He actually started off as a mercenary soldier. In his spare time, I suppose, in between killing people, an epiphany of sorts must have flashed upon him. He tried to merge geometry and algebra, describing curved lines as equations. Marin Mersenne, an ordained priest, was also an accomplished mathematician who even corrected Euclid's calculations. Pierre de Fermat discovered that a prime number which will give a remainder of 1 when divided by four could be rewritten as additions of two squares. His other patterns in maths are used in credit card encryption.
Isaac Newton, besides being a physicist was also a mathematician who was interested to know about acceleration. He had a long battle with Leibniz accusing him of plagiarism. Gottfried Wilheim Leibniz must have been an extraordinary individual. A philosopher, a lawyer, an engineer, a learner of languages, he must also be the first computer engineer for venturing into the binary system through his interest in the Chinese language.
The Bernoulli family from Basel, sympathisers of Leibniz, were great in their own right, introducing the subject of the calculus of variation. One of their student, Leonard Euler, left his mark in St Petersburg. One of his many discoveries is that the addition fractions of squares in descending order equals to π2/6.
The documentary goes on to talk about Gauss, who challenged Euclid geometry which is based on flat topography, János Bolyai with his hyperbolic geometry and Riemann with his high dimensional geometry. I was surprised that there was no mention of Blaise Pascal, who spoke of probability and was instrumental in the discovery of modern calculator.
Part 4: To infinity and beyond
The final part of the series talks about complicated mathematic theories. In 1900, a German mathematician extraordinaire, David Hilbert, put forward 23 unsolved problems that needed to be tackled. Over the years many experts contributed in one way or another to solve them one by one.
Cantor explained the pattern in the infinite set of whole numbers and fractions. Poincaré worked on geometry, the topography of 2D surfaces and inadvertently suggested the chaos theory and butterfly effect. Leonard Euler used the seven bridges in the town of Kaliningrad to study topology.
Perelman in 2002 finally used flow studies to appreciate 3D shapes.
Gödel used logic to answer one of Hilbert's question through his 'Incompleteness Theorem'. The death of many mathematicians during WW2 with the dissipation of experts away from the continent marks the end of Europe as a powerhouse of Mathematics.
Europe's loss is Princeton's gain. Many Jewish exiles gain employed at Princeton's Institute for Advanced Studies (IAS). IAS saw Gödel working with Einstein and Paul Cohen, an American. The narrator goes on a spree of name dropping of doyens in the field - Julia Robinson, Yuri Matiyasevich, Galois, Andre Weil, the fictional author Bourbaki and Gronthedieck.
The unsolved problems in Mathematics are the one that makes it a living subject.
Part 1: The Language of the Universe
If one were to look at the history of the world, there was never a time there was peace on Earth. At every moment, there was some turmoil somewhere. In spite of all that upheavals, destructions and loss of lives and civilisations, we as a human race, have progressed on the long run. In the time of peace, people start becoming curious about their surroundings and start trying to understand its intricacies. They try to explain its pattern and perhaps try to predict its recurrence. Attacking forces usurp this knowledge as theirs and try to improve this further when the dust settles after their inquests. Slowly, learning from to count numbers with our digits, we developed formulas and managed to calculate unfathomable numbers of gargantuan proportions.
Mathematics is said to be the language of the Universe. Marcus De Sautoy, a Mathematician, takes the viewers on a journey of discovery of how Mathematics changed humankind. In this episode, he traces the origin of the field of which predates the Greek mathematicians we are familiar.
Economic reasons to quantitate the taxes to be collected and predict weather pattern in the Nile were strong enough reasons to put maths to full use.
 |
| Prof Marcus du Sautoy |
The story of Mathematics spreads beyond these shores. Alexandria used to the centre of Mathematics with people like Euclid and Hypatia. Legend has it that Hipassus, a member of the Pythagorean cult, was drowned when he could resist the temptation of telling the world about irrational numbers! It is interesting to see how long it took for Man to comprehend concepts that we look at today as a known fact.
Part 2: The Genius of the East
The colonial masters who landed on this side of the world came with a chip on their shoulder. In the eyes, they saw themselves as saviours of humanity who came to liberate them from dark ages. They spread their cultures to the offspring of their subjects who in turn also looked up highly at the masters' knowledge whilst being ashamed of their assumed ignorant past. Little did all of them, barring a few, knew that beneath their history lay a rich past with a wealth of mathematical knowledge.
Part 2: The Genius of the East
 |
| Chinese calculation with rods |
The Chinese had their way of calculating big numbers with sticks and symbols, volume approximation and complicated equation. Mammoth structures like the Great Wall of China are testimonies of their engineering feats. The Indians introduced the decimal system, the number zero which paradoxically helps to calculate big numbers and even added another plane of number- the negative numbers. Civilisations before them, like the Babylonians and Chinese, only left an empty space to denote nothing (zero). The concept of infinity, pi and trigonometry were thought of by Indians long before 15th century Europe.The 5th century Islamic Era was a time when knowledge from other regions to bring mathematics to yet another level. Algebra was introduced. Omar Khayyam, the poet, also tried his hand in solving equations.
The first modern European mathematician can be said to be Fibonacci. His endeavour to replace Roman numerals with the easier Hindu-Arabic numbers was met with scorn and suspicion. Fibonacci's number helped to explain many patterns in nature. Bologna was the place where mathematical sorcery took place and from it borne complex cubic equations. The history was rewritten by the Europeans.
Part 3: The Frontiers of Space
 |
| Descartes thought of this! |
Many of the icons who thought of new ideas were actually men of faith. The beauty of the thinking trend at that time was that thinking was allowed. They did not feel that humankind had learnt everything that needed to be learnt. They were receptive to changes and had the burning desire to reach even greater heights. Complacency was not the order of the day. Thinking outside the box was allowed. Everybody was trying to outdo each other to show-off their discovery, sometimes with disastrous outcomes.
 |
| Fermat's number play |
Isaac Newton, besides being a physicist was also a mathematician who was interested to know about acceleration. He had a long battle with Leibniz accusing him of plagiarism. Gottfried Wilheim Leibniz must have been an extraordinary individual. A philosopher, a lawyer, an engineer, a learner of languages, he must also be the first computer engineer for venturing into the binary system through his interest in the Chinese language.
The Bernoulli family from Basel, sympathisers of Leibniz, were great in their own right, introducing the subject of the calculus of variation. One of their student, Leonard Euler, left his mark in St Petersburg. One of his many discoveries is that the addition fractions of squares in descending order equals to π2/6.
The documentary goes on to talk about Gauss, who challenged Euclid geometry which is based on flat topography, János Bolyai with his hyperbolic geometry and Riemann with his high dimensional geometry. I was surprised that there was no mention of Blaise Pascal, who spoke of probability and was instrumental in the discovery of modern calculator.
 |
| David Hilbert |
The final part of the series talks about complicated mathematic theories. In 1900, a German mathematician extraordinaire, David Hilbert, put forward 23 unsolved problems that needed to be tackled. Over the years many experts contributed in one way or another to solve them one by one.
Cantor explained the pattern in the infinite set of whole numbers and fractions. Poincaré worked on geometry, the topography of 2D surfaces and inadvertently suggested the chaos theory and butterfly effect. Leonard Euler used the seven bridges in the town of Kaliningrad to study topology.
Perelman in 2002 finally used flow studies to appreciate 3D shapes.
 |
Euler's problem of crossing Kaliningrad through all its
seven bridges without missing a bridge or passing it twice.
|
Europe's loss is Princeton's gain. Many Jewish exiles gain employed at Princeton's Institute for Advanced Studies (IAS). IAS saw Gödel working with Einstein and Paul Cohen, an American. The narrator goes on a spree of name dropping of doyens in the field - Julia Robinson, Yuri Matiyasevich, Galois, Andre Weil, the fictional author Bourbaki and Gronthedieck.
The unsolved problems in Mathematics are the one that makes it a living subject.
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