Archimedes 287-212 BCE

"Eureka," the great Syracuse visionary is said to have cried, running naked from his bath into the street, having worked out that an immersed body displaces its own weight in water. He also revolutionised geometry and anticipated integral calculus by 2,000 years, and invented a water screw used in irrigation and in pumping bilge from ships.

Sappho c620-c570 BCE

An inhabitant of Lesbos, Sappho was a lyricist in the literal sense that she wrote poetry to be accompanied on the lyre. At the time, it does not seem to have cause comment that most of her poetry was written in love of other women, though later that was considered scandalous; but her poetic influence was vast. Plato called her the "tenth muse".

Abbas ibn Firnas 810-887

No image survives of the poet, astrologer, astronomer and musician, but his fame endures, mainly for having been (probably) the first human being ever to attempt to fly. He built a machine, launched himself from a hill outside Cordoba, in Spain, dressed in eagle feathers, and reportedly flew for an impressive distance before crashing and breaking a vertebra.

Giotto di Bondone 1267-1337

Giotto was the artist who started the Italian Renaissance. He broke with Byzantine tradition to paint more directly from nature and to create a more convincing sense of pictorial space. Where he led, others followed. His friend Dante can be seen in one of his church murals, while a passage in The Divine Comedy praises Giotto.

Nicolaus Copernicus 1473-1543

Polish polymath who was the first person since Roman times to conclude that the Earth revolved around the Sun. He was reluctant to publish On the Revolutions of the Celestial Spheres (1543), perhaps fearing that people would think him mad. When he did so, the work was banned by the Catholic Church from 1616 to 1835.

Leonardo da Vinci 1452-1519

There has never been a greater polymath than Leonardo, scientist, mathematician, engineer, inventor, anatomist, painter, sculptor, architect, botanist, musician and writer. Paintings such as The Last Supper (1498) are still widely venerated; other works include a Codex on the Flight of Birds (1505), with its designs for a helicopter and a handglider.

Abu al-Jazari 1136-1206

We know little of the life of Abu al-Iz Ibn Ismail ibn al-Razaz al-Jazari, who lived in what is now Turkey, but his prescient writings include a book on mechanics and hydraulics and a Book of Knowledge of Ingenious Mechanical Devices. He invented devices for raising water, valves, a kettle and, crucially, the crankshaft, on which countless machines depend.

Luca Pacioli c1446-1517

A Franciscan friar, Luca Bartolomeo di Pacioli was also a distinguished mathematician whose pupils included Leonardo da Vinci. He is remembered now as the putative inventor of the principles of double-entry accounting system, which he described in 1494. Without this vision, global capitalism could not exist.

Emperor Frederick II 1194-1250

One of the greatest and wisest of European Christian monarchs, the Holy Roman Emperor was literate in seven languages and was a keen patron of science and the arts. He also led a "crusade" to Jerusalem in which, instead of slaughtering the Muslims, he made peace with them, and brought back to European arithmetic the idea of zero.

Joan of Arc 1412-1431

In Shaw's play about St Joan, her contemporaries define her with the words "Protestant" and "nationalist". The Catholic Church, which canonised her in 1920, would dispute the former, but she was the first person to take up arms for a nation, against a foreign invader, rather than fighting for a branch of the nobility.

Niccolo Machiavelli 1469-1527

No one had ever written about power politics in such blunt language as Machiavelli, an Italian diplomat. His 1513 treatise, The Prince, brought the word "Machiavellian" into the language, but he should be remembered too for his more substantial (and liberal) Discourses. The inventor of realpolitik.

Johannes Gutenberg c1400-1468

As an inventive goldsmith in living in Strasbourg, Gutenberg put together a wooden frame and moveable type around 1436, hoping to win a contract from the church to produce slips of paper to be sold as pardons. In 1450, he used his invention to print a Bible. He never made much money from it - but the world was changed utterly.

William Shakespeare 1564-1616

Began writing sonnets for his patron, the Earl of Southampton, around 1593, and wrote roughly two plays a year from 1594 to 1611, becoming in many people's estimation the greatest English writer and the greatest dramatist in any language. Somehow, those 400-year-old plays could be about people we know now.

Isaac Newton 1643-1727

Arguably the greatest of all scientists (despite writing more about the Bible than about science). His greatest discovery was of the laws of gravity (1687), which laid the basis for mechanics. He also worked out that white light is a combination of the colours of the rainbow, thus founding optics. The father of the scientific age.

William Blake 1757-1827

"The Beast and the Whore rule without control", Blake complained of England in 1798. He was not only unrecognised there as poet or artist, but was struggling to find work and stay out of jail. Posterity recognises him as the greatest English poet of his day, and an amazingly modern painter. His contemporaries thought him mad.

Mary Wollstonecraft 1759-1797

Wollstonecraft's A Vindication of Women's Rights (1792) argued that women had a right to education and that marriage should be a contract between equals. For most of the 19th century, she was reviled as an "unsexed female", and lampooned in novels; in the 20th she was recognised as the "mother of feminism".

Thomas Jefferson 1743-1826

When Jefferson, a champion of democratic ideals and an immensely learned man, became third President of the USA, it was a small country with nothing in its Constitution that allowed for its expansion. He bought Louisiana from Napoleon, and sent Louis and Clarke to find a land route to the Pacific. His vision helped to make the USA a superpower.

Mary Shelley 1797-1851

Daughter of Mary Wollstonecraft, and wife of the poet Shelley, Mary won immortality as a 20-year-old, when she wrote Frankenstein. This was the first great English horror story, and it contains an insight ahead of its time. Frankenstein's monster is noble and good until rejection turns him vicious. It was the first "hug a hoodie" novel.

Charles Darwin 1809-1882

Not the first to believe that species evolved; the French naturalist Jean-Baptists Lamarck developed such a theory before him, and Alfred Russel Wallace was working on one at the same time; but Darwin had the vision to conduct the years of painstaking research that went into his On the Origin of Species (1859), and it is this that sets him apart.

Joseph Swan 1828-1914

People think the American Thomas Edison invented the light bulb; in fact it was a physicist from Newcastle-upon-Tyne who patented the idea, in 1860. Swan successfully sued Edison, and together they formed the Edison & Swan United Electric Company. Swan was also the first to discover how to use bromide paper in photography.

Ludwig van Beethoven 1770-1827

There have been other great musicians, but Beethoven was revolutionary too. His extraordinary music captured the emotions unleashed by the Enlightenment and the French revolution. His Third Symphony, the Eroica, was unlike anything heard before. The Ninth immortalised Schiller's "Ode to Joy" (originally called "Ode to Freedom").

Elizabeth Garrett Anderson 1836-1917

The idea that a woman might qualify as a doctor was unheard of in 19th- century Britain, but that did not deter the young feminist, Elizabeth Garrett. She learnt French and obtained a medical degree in Paris; founded a women's hospital, staffed only by women; and became England's first woman mayor.

Marie Curie 1867-1934

Marie Sklodowska (as she was born) discovered radium, and opened up the science of radioactivity and the medical use of X-rays. The Sorbonne University's first female teacher, she was the first person to win Nobel prizes in two different sciences - physics and chemistry - but also had to endure hostility from France's male scientific establishment and press.

Karl Marx 1818-1883

With revolutions convulsing Europe, the publication of The Communist Manifesto in 1848 by a German Jew living in Brussels raised few eyebrows. Yet its claim that the "spectre of communism" was haunting Europe was true; and, along with Das Kapital (which he wrote in London), it inspired a world-changing political movement.

Sojourner Truth 1797-1883

Born into slavery on a Dutch plantation in New York State, she was sold to a series of owners, but ran away at the age of 30, changed her name and became a prominent campaigner against slavery and for women's rights. Her most famous speech, delivered in Ohio in 1854, asked repeatedly: "Ain't I a woman?"

Elizabeth Fry 1790-1845

It is said that a mark of a civilised society is its treatment of its prisoners. No one thought so until Elizabeth Gurney Fry, a wealthy Quaker, visited Newgate Prison in 1813. She was horrified to find small children there as well as women, and campaigned thereafter for better conditions for female prisoners.

Gustave Eiffel 1832-1923

Before he ruined his reputation by being involved in a financial scandal, Eiffel was the greatest bridge builder of his day and, to mark the 1889 Paris Exhibition, constructed what was for many years the world's tallest building, 985ft high and weighing 7,000 tons. Every component was constructed in a workshop to his exact specifications.

Fyodor Dostoyevsky 1821-1881

He struggled for recognition in his lifetime, but sometimes the 20th century seemed to go "Dostoyevskian". Jean-Paul Sartre said that the whole of French existentialism could be found in The Brothers of Karamazov (1880), while a character in The Possessed (1872) set out a parody of a socialist paradise horribly like Stalin's Russia.

Rudolf Diesel 1858-1913

The first internal combustion engine almost blew up and killed its inventor, a Bavarian living in Paris, who was what we would now call an environmentalist. He made millions from the highly efficient diesel engine, and dreamed of a machine run on vegetable oil. He was mysteriously drowned - murdered, some believe - crossing the Channel.

Vincent van Gogh 1853-1890

During a life that ended early in madness and suicide, van Gogh sold precisely one painting. Almost all his works were produced in three years, as if he were involved in a frantic race to use wild brush strokes and vivid colours either to explain his battle against madness, or perhaps in pursuit of some deeper meaning. Today they are worth millions.

Emile Coué 1857-1926

The idea that mental illness can be treated and cured is relatively new, and arguably owes as much to Coué, a French pharmacist and psychologist who pioneered the use of hypnosis as therapy, as to other visionaries such as Sigmund Freud. His Self-Mastery Through Conscious Autosuggestion was published in 1920.

HG Wells 1866-1946

Other writers, such as Jules Verne and Philip K Dick, have speculated on what the future might be like, but no science fiction writer has had more impact on the public imagination than HG Wells, with stories such as The Time Machine and The Invisible Man. In politics, his great quest was world government - a vision that remains ahead of its time.

Albert Einstein 1879-1955

A technical assistant at the Swiss patent office, Einstein asked himself what would happen if you travelled at the speed of light. His Special Theory of Relativity (1905) overturned conventional physics by suggesting that mass and energy were interchangeable. Few believed him - until that bomb went off at Hiroshima.

Margaret Mead 1901-1976

Is it necessary to suffer growing pains as a teenager? The US anthropologist Margaret Mead wanted to know, so spent months living in a Samoan village and decided that teenage angst is a problem caused by society, and that casual sex before marriage is harmless. Her findings, published in 1928, shocked the USA but helped change the world in the Sixties.

Sergei Eisenstein 1898-1948

It took a leap of imagination in the early days of moving pictures to understand how much you can leave out. You can show panic on the steps, then cut to a line of gendarmes with lowered rifles, and people get the picture. This was just one of the insights the brilliant young communist brought to film-making in the Twenties.

Martin Luther King 1929-1968

"I have a dream," he declared to a vast crowd at Washington's Lincoln Memorial on 28 August 1963. The dream was that Americans could be Americans, regardless of skin colour. The FBI stalked him as if he were a communist, and a white racist killed him but, 40 years later, the Barack Obama story is bringing King's vision closer to reality.

Franz Kafka 1883-1924

Kafka's novels were absurd parodies of life in pre-1914 Austria-Hungary. He never tried to publish them. After his death, they were recognised as great literature - though whether they were modernist, existentialist, anarchist or what was a matter for argument. Meanwhile, the world has become increasingly Kafkaesque.

Mahatma Gandhi 1869-1948

Others have resorted to arms to repel foreign occupiers; Gandhi was the first to put into practice the idea that a nation could liberate itself and reinvent itself through non-violent protest. He is revered as the father of the Indian nation, despite his failure to hold the whole subcontinent together as one mixed nation.

Frank Lloyd Wright 1867-1959

"Architects may come and architects may go and never change your point of view" sang Paul Simon, in the only pop song that celebrates an architect. Frank Lloyd Wright tried to do more than just design houses; he tried to create a whole environment. A good building, he said, did not hurt the landscape, but made it lovelier.

Buckminster Fuller 1895-1983

Fuller, from Massachusetts, was one of the first "futurists". He devoted much of his life to research into ways to provide "more and more life support for everybody, with less and less resources." He patented a design of the geodesic sphere, a very stable structure with a large volume for its surface area, which he hoped would solve the housing crisis.

Coco Chanel 1883-1971

She never called herself a feminist, but it was Chanel, the French fashion designer, who, in effect, gave women permission to dress like men, long before the women's movement took hold. The Chanel suit, launched in 1924, was a knee-length skirt paired with a trim jacket. Chanel No 5, the world's most famous perfume, was launched in 1921.

Alfred Hitchcock 1899-1980

The shift from silent movies to talkies was sure to be difficult. Hitchcock was one of the first to achieve it, early in an immensely long career as cinema's greatest master of suspense. One of the many rules he observed was that no location is ever irrelevant; whatever it is that scares you, it is there for a reason. Countless directors have learnt from him.

Chuck Berry 1926-

Traditionally, the blues were sung to a slow tempo, on such subjects as poverty and troubled love affairs. Then a black guitarist from St Louis speeded up the music and sang about a consumer age - cars, autograph-hunting, and rock'n'roll gigs that went on all night. What Chuck Berry started, The Beatles and Rolling Stones took on.

Andy Warhol 1928-1987

He was the Pope of Pop Art, a polymath who made avant-garde films, discovered rock groups, foresaw celebrity culture, observed that Coca-Cola is the same drink whether its is drunk by the President or a tramp, and sold a painting consisting of 32 labels from tins of Campbell's Soup. Today's "radical" artists are conservative by comparison.

Peter Drucker 1909-2005

Listening to John Maynard Keynes lecturing in Cambridge, in 1934, Drucker (who had fled Nazi Germany) decided that, while others were interested in commodities, he was interested in people. He developed a theory of company management based on decentralisation and respect for employees. Many of his ideas remain highly influential.

Nelson Mandela 1918-

When Mandela emerged from prison after 27 years, in 1990, the world did not know what to expect. It feared a man embittered like Robert Mugabe, or whose mind had rotted behind bars. It found a wise leader with the imagination to bring apartheid to a non-violent end, when there could have been a bloodbath.

Mary Quant 1934-

Some say it was Brian Epstein, The Beatles' manager, who invented the Sixties. Others say David Bailey and Jean Shrimpton. It wasn't. It was Mary Quant, who opened a clothes shop in London's King's Road in 1955, and from there launched the miniskirt and, later, the hotpants. She ran Mary Quant Ltd until 2000.

James Hansen 1941-

Thirty years ago, the idea that the Earth might warm up because of human activity was entertained only by a few scientists. Then, in 1981, Hansen and others at the Goddard Space Centre warned that climate change would become noticeable by 1990. He added that it would be hard to get politicians to do anything.

Tim Berners-Lee 1955-

Several people claim parenthood of the internet, but it was Berners-Lee who, working as an engineer with the CERN project in Switzerland, designed the world wide web. Those familiar initials www, http and html all come from him. In 1990, he designed the first web server. He ought to be a billionaire but isn't, because he gave the technology away.

Stephen Hawking 1942-

Best known for overcoming motor neurone disease and writing the 1988 best-seller, A Brief History of Time; but to physicists his fame rests on his theory that black holes in space do not last forever, but eventually explode. He also has a theory of "imaginary time" running at right angles to real time. Don't ask...