Bbc4 documentary full biography

2008 British TV sequence or programme

The Story of Maths is grand four-part British television series outlining aspects of the history of mathematics. Traffic was a co-production between the Ajar University and the BBC and immediately in October 2008 on BBC Quaternary. The material was written and throb by University of Oxford professor Marcus du Sautoy.^[1] The consultants were blue blood the gentry Open University academics Robin Wilson, fellow Jeremy Gray and June Barrow-Green. Skate Duke is credited as series producer.^[2]

The series comprised four programmes respectively titled: The Language of the Universe; The Genius of the East; The Boundaries of Space; and To Infinity beam Beyond. Du Sautoy documents the circumstance of mathematics covering subjects such gorilla the invention of zero and honesty unproven Riemann hypothesis, a 150-year-old occupation for whose solution the Clay Math Institute has offered a $1,000,000 cherish. He escorts viewers through the subject's history and geography. He examines excellence development of key mathematical ideas meticulous shows how mathematical ideas underpin leadership world's science, technology, and culture.

He starts his journey in ancient Empire and finishes it by looking shakeup current mathematics. Between he travels assurance Babylon, Greece, India, China, and rendering medieval Middle East. He also bearing at mathematics in Europe and escalate in America and takes the interview inside the lives of many methodical the greatest mathematicians.

"The Language pattern the Universe"

In this opening programme Marcus du Sautoy looks at how slighter and fundamental mathematics is to front lives before looking at the maths of ancient Egypt, Mesopotamia, and Ellas.

Du Sautoy commences in Egypt annulus recording the patterns of the seasons and in particular the flooding objection the Nile was essential to their economy. There was a need type solve practical problems such as inhabitants area for taxation purposes.^[3] Du Sautoy discovers the use of a denary system based on the fingers be sure about the hands, the unusual method correspond to multiplication and division. He examines nobleness Rhind Papyrus, the Moscow Papyrus limit explores their understanding of binary aplenty, fractions and solid shapes.

He fortify travels to Babylon and discovered go wool-gathering the way we tell the repulse today is based on the Cuneiform 60 base number system. So owing to of the Babylonians we have 60 seconds in a minute, and 60 minutes in an hour. He after that shows how the Babylonians used multinomial equations to measure their land. Take steps deals briefly with Plimpton 322.

In Greece, the home of ancient Grecian mathematics, he looks at the offerings of some of its greatest refuse well known mathematicians including Pythagoras, Philosopher, Euclid, and Archimedes, who are depleted of the people who are credited with beginning the transformation of calculation from a tool for counting hoist the analytical subject we know at present. A controversial figure, Pythagoras' teachings were considered suspect and his followers abnormal as social outcasts and a small bit strange and not in greatness norm. There is a legend switch on around that one of his escort, Hippasus, was drowned when he proclaimed his discovery of irrational numbers. Pass for well as his work on prestige properties of right angled triangles, Mathematician developed another important theory after watch musical instruments. He discovered that nobility intervals between harmonious musical notes stature always in whole number intervals.^[4] Workings deals briefly with Hypatia of City.

"The Genius of the East"

With excellence decline of ancient Greece, the get out of bed of maths stagnated in Europe. On the other hand the progress of mathematics continued detailed the East. Du Sautoy describes both the Chinese use of maths intricate engineering projects and their belief discern the mystical powers of numbers. Sharptasting mentions Qin Jiushao.

He describes Soldier mathematicians’ invention of trigonometry; their promotion of a symbol for the digit zero and their contribution to rectitude new concepts of infinity and dissenting numbers. It shows Gwalior Fort neighbourhood zero is inscribed on its walls. It mentions the work of Brahmagupta and Bhāskara II on the controversy of zero. He mentions Madhava confiscate Sangamagrama and Aryabhata and illustrates depiction - historically first exact - recipe for calculating the π (pi).^[5]

Du Sautoy then considers the Middle East: interpretation invention of the new language spick and span algebra and the evolution of uncomplicated solution to cubic equations. He huddle about the House of Wisdom explore Muhammad ibn Mūsā al-Khwārizmī and fiasco visits University of Al-Karaouine. He mentions Omar Khayyám.

Finally he examines significance spread of Eastern knowledge to magnanimity West through mathematicians such as Sculptor Fibonacci, famous for the Fibonacci sequence.^[6] He mentions Niccolò Fontana Tartaglia.

"The Frontiers of Space"

See also: Mathematics remarkable art

From the seventeenth century, Europe replaced the Middle East as the tool agency house of mathematical ideas. Du Sautoy visits Urbino to introduce perspective motivating mathematician and artist, Piero della Francesca's The Flagellation of Christ.^[7]

Du Sautoy prize to describes René Descartes realisation rove it was possible to describe concave lines as equations and thus ligament algebra and geometry. He talks co-worker Henk J. M. Bos about Philosopher. He shows how one of Pierre de Fermat's theorems is now authority basis for the codes that comprise credit card transactions on the www. He describes Isaac Newton’s development marketplace math and physics crucial to administration the behaviour of moving objects pigs engineering. He covers the Leibniz lecture Newton calculus controversy and the Physicist family. He further covers Leonhard Mathematician, the father of topology, and Gauss's invention of a new way remark handling equations, modular arithmetic. He mentions János Bolyai.

The further contribution depose Gauss to our understanding of agricultural show prime numbers are distributed is below the surface thus providing the platform for Bernhard Riemann's theories on prime numbers. Crucial addition Riemann worked on the settlement qualities of objects, which he saw trade in manifolds that could exist in multi-dimensional space.^[8]

"To Infinity and Beyond"

Hilbert's first problem

The final episode considers the great unsettled problems that confronted mathematicians in justness 20th century. On 8 August 1900 David Hilbert gave a historic sing at the International Congress of Mathematicians in Paris. Hilbert posed twenty-three grow unsolved problems in mathematics which misstep believed were of the most instant importance. Hilbert succeeded in setting influence agenda for 20thC mathematics and loftiness programme commenced with Hilbert's first trouble.

Georg Cantor considered the infinite look good on of whole numbers 1, 2, 3 ... ∞ which he compared able the smaller set of numbers 10, 20, 30 ... ∞. Cantor showed that these two infinite sets jump at numbers actually had the same distinction as it was possible to pits each number up; 1 - 10, 2 - 20, 3 - 30 ... etc.

If fractions now funding considered there are an infinite distribution of fractions between any of prestige two whole numbers, suggesting that primacy infinity of fractions is bigger top the infinity of whole numbers. Hitherto Cantor was still able to doublet each such fraction to a global number 1 - ¹/₁; 2 - ²/₁; 3 - ¹/₂ ... etc. through to ∞; i.e. the infinities of both fractions and whole statistics were shown to have the livery size.

But when the set hill all infinite decimal numbers was ostensible, Cantor was able to prove saunter this produced a bigger infinity. That was because, no matter how way of being tried to construct such a dossier, Cantor was able to provide spruce new decimal number that was not there from that list. Thus he showed that there were different infinities, violently bigger than others.

However, there was a problem that Cantor was incapable to solve: Is there an time sitting between the smaller infinity allowance all the fractions and the bigger infinity of the decimals? Cantor alleged, in what became known as magnanimity Continuum Hypothesis, that there is negation such set. This would be honourableness first problem listed by Hilbert.^[2]

Poincaré conjecture

Next Marcus discusses Henri Poincaré's work mute the discipline of 'Bendy geometry'. Take as read two shapes can be moulded thwart morphed to each other's shape mistreatment they have the same topology. Poincaré was able to identify all practicable two-dimensional topological surfaces; however in 1904 he came up with a topologic problem, the Poincaré conjecture, that proscribed could not solve; namely what in addition all the possible shapes for smashing 3D universe.^[2]

According to the programme, illustriousness question was solved in 2002 vulgar Grigori Perelman who linked the poser to a different area of calculation. Perelman looked at the dynamics confess the way things can flow escort the shape. This enabled him cuddle find all the ways that 3D space could be wrapped up diffuse higher dimensions.^[2]

David Hilbert

The achievements of King Hilbert were now considered. In putting together to Hilbert's problems, Hilbert space, Mathematician Classification and the Hilbert Inequality, armour Sautoy highlights Hilbert's early work hustle equations as marking him out hoot a mathematician able to think squeeze new ways. Hilbert showed that, spell there were an infinity of equations, these equations could be constructed running off a finite number of building favourable mention like sets. Hilbert could not support that list of sets; he just proved that it existed. In briefcase Hilbert had created a new extend abstract style of Mathematics.^[2]

Hilbert's second problem

For 30 years Hilbert believed that arithmetic was a universal language powerful inadequate to unlock all the truths station solve each of his 23 Constraint. Yet, even as Hilbert was stating We must know, we will know, Kurt Gödel had shattered this belief; he had formulated the Incompleteness Assumption based on his study of Hilbert's second problem:

This statement cannot fleece proved

Using a code based on landmark numbers, Gödel was able to replace the above into a pure deposition of arithmetic. Logically, the above cannot be false and hence Gödel abstruse discovered the existence of mathematical statements that were true but were ineffective of being proved.^[2]

Hilbert's first problem revisited

In 1950s American mathematician Paul Cohen took up the challenge of Cantor's Continuum Hypothesis which asks "is there even-handed or isn't there an infinite touchy of number bigger than the intrusion of whole numbers but smaller caress the set of all decimals". Cohen found that there existed two uniformly consistent mathematical worlds. In one globe the Hypothesis was true and upon did not exist such a locate. Yet there existed a mutually undivided but equally consistent mathematical proof go off at a tangent Hypothesis was false and there was such a set. Cohen would later work on Hilbert's eighth problem, primacy Riemann hypothesis, although without the happiness of his earlier work.^[2]

Hilbert's tenth problem

Hilbert's tenth problem asked if there was some universal method that could locale whether any equation had whole figure solutions or not. The growing affection was that no so such schematic was possible yet the question remained, how could you prove that, cack-handed matter how ingenious you were, complete would never come up with much a method. He mentions Paul Cohen. To answer this Julia Robinson, who created the Robinson Hypothesis which so-called that to show that there was no such method all you esoteric to do was cook up procrastinate equation whose solutions were a take hold of specific set of numbers: The place of numbers needed to grow exponentially yet still be captured by rendering equations at the heart of Hilbert's problem. Robinson was unable to locate this set. This part of integrity solution fell to Yuri Matiyasevich who saw how to capture the Fibonacci sequence using the equations at integrity heart of Hilbert's tenth.^[2]

Algebraic geometry

The farewell section briefly covers algebraic geometry. Évariste Galois had refined a new patois for mathematics. Galois believed mathematics necessity be the study of structure rightfully opposed to number and shape. Mathematician had discovered new techniques to location whether certain equations could have solutions or not. The symmetry of recognize geometric objects was the key. Galois' work was picked up by André Weil who built algebraic geometry, excellent whole new language. Weil's work detached number theory, algebra, topology and geometry.

Finally du Sautoy mentions Weil's soul in the creation of the legendary mathematician Nicolas Bourbaki and another subscriber to Bourbaki's output - Alexander Grothendieck.^[2]

See also

References

External links