Thinkers Timeline

Euclid was a Greek mathematician who lived in Alexandria, in Egypt, around 300 BCE. He is sometimes called the 'father of geometry'. We know almost nothing about his personal life. We do not know where he was born, who his parents were, or when exactly he died. We are not even certain he was a single person. Some scholars have wondered whether 'Euclid' might be a name used by a group of mathematicians. What we do know is that he worked at the Library and Museum of Alexandria. This was the great centre of learning in the ancient world, founded by the kings of Egypt after Alexander the Great. Scholars from across the Greek world gathered there. Euclid taught and wrote in this setting. His great work is called the Elements. It is a textbook of geometry and number theory in 13 books. The Elements gathered together the mathematical work of earlier Greek thinkers like Pythagoras, Eudoxus, and Theaetetus. It also added Euclid's own arrangement and proofs. The Elements was used as the main geometry textbook for over 2,000 years. Until the late 19th century, almost every educated person in Europe and the Middle East had studied it. It was translated into Arabic, Latin, English, and many other languages. It is one of the most printed and studied books in human history, after only the Bible. Euclid himself remains a quiet mystery behind his enormous influence.

Archimedes was a Greek mathematician, scientist, and engineer. He was born around 287 BCE in Syracuse, a Greek city on the island of Sicily. We know little about his early life. His father was an astronomer named Phidias. He may have studied for a time at the great Library of Alexandria in Egypt, though this is not certain. Most of his life, however, was spent in Syracuse. In his time, Syracuse was an independent Greek-speaking city. The Roman Republic was growing stronger and would soon swallow most of the Mediterranean world. Archimedes worked closely with the king of Syracuse, Hiero II, and later with Hiero's grandson Hieronymus. He served the city as both a thinker and an inventor. In the year 212 BCE, Roman forces attacked Syracuse. Archimedes was about 75 years old. He had designed weapons to defend the city, including powerful catapults and machines that lifted enemy ships out of the water. The Romans took the city after a long siege of about two years. The traditional story is that a Roman soldier killed Archimedes during the chaos, even though the Roman general Marcellus had ordered that he be spared. According to later writers, Archimedes was working on a mathematical problem when the soldier arrived. He asked not to have his diagrams disturbed. The soldier killed him anyway. His tomb in Syracuse was lost for centuries. The Roman writer Cicero claimed to have rediscovered it nearly 140 years after his death.

Hypatia of Alexandria (c.350-415 CE) was a mathematician, astronomer, and philosopher who taught in the Egyptian city of Alexandria during the late Roman Empire. She was the daughter of the mathematician Theon, a scholar connected to the great library of Alexandria, and she received an exceptional education in the mathematical and philosophical traditions of the Greek-speaking world. By her maturity she was a renowned teacher in the Neoplatonist tradition, giving public lectures and leading a private circle of students that included Christians, pagans, and members of the wealthy families of the eastern Roman Empire. She is known to have written commentaries on the great mathematical texts of her time, including Diophantus's Arithmetica, Apollonius's Conics, and Ptolemy's Almagest, and to have worked closely with her father on the preservation and editing of earlier mathematical works. Her own writings do not survive; we know her through letters from her students, particularly Synesius of Cyrene, who became a Christian bishop but continued to honour her as his intellectual guide. Alexandria in her lifetime was politically and religiously turbulent. In 415 CE she was killed by a Christian mob in the streets of the city, in circumstances that have been debated by historians ever since. Her death has been remembered for sixteen centuries as a marker of something lost.

Muḥammad ibn Mūsā al-Khwārizmī was a Persian scholar born around 780, probably in Khwarezm, a region in what is now Uzbekistan. His family name, al-Khwārizmī, means 'from Khwarezm'. He spent most of his working life in Baghdad, the capital of the Abbasid Caliphate. Baghdad at that time was one of the world's great centres of learning. He worked at the House of Wisdom, a famous library and research centre set up by the Caliph al-Ma'mūn. Scholars there translated Greek, Persian, and Indian texts into Arabic and wrote original works of their own. Al-Khwārizmī was one of the most important scholars of his generation. He wrote on mathematics, astronomy, geography, and the calendar. His most famous book is usually called al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa'l-muqābala, or The Compendious Book on Calculation by Completion and Balancing. The word al-jabr in the title gave us the English word algebra. Another of his books explained how to calculate using the Hindu numerals from India. This book, translated into Latin centuries later, spread these numerals across Europe. We call them Arabic numerals today, but they came from India through scholars like him. He died around 850. Many of his works survive. Some exist only in later Latin translations. His influence on mathematics is hard to overstate.

Blaise Pascal was a French mathematician, physicist, inventor, and religious thinker. He was born in 1623 in Clermont-Ferrand in central France. His mother died when he was three. His father, a tax official and amateur scientist, raised him and taught him at home. Pascal showed extraordinary gifts very early. By the age of twelve, he was working out geometry on his own. By sixteen, he had written a serious paper on conic sections. At nineteen, to help his father with tax calculations, Pascal built a mechanical calculating machine. It was one of the first working calculators in history. He went on to make important discoveries about pressure and vacuums, helping to found modern physics. With the mathematician Pierre de Fermat, he laid the foundations of probability theory, the maths of chance. In 1654, after a near-fatal carriage accident, Pascal had a powerful religious experience. He wrote about it on a small piece of paper that he sewed into his coat and carried for the rest of his life. From then on, he turned more and more to religious writing. He joined the Jansenists, a strict Catholic group, and defended them in his Provincial Letters. He was working on a great defence of Christianity when he died in 1662, aged only 39. The unfinished notes were published after his death as the Pensées (Thoughts).

Isaac Newton (1643-1727) was an English mathematician, physicist, and natural philosopher. He was born prematurely in Woolsthorpe, Lincolnshire, and his father died before he was born. He studied at Trinity College, Cambridge, but when the university closed because of an outbreak of plague in 1665, he returned to his family farm and spent roughly eighteen months there during which he made several of the most important discoveries in the history of science. He developed the mathematical foundations of calculus, began developing his theory of gravity, and conducted his first experiments on light and colour. He returned to Cambridge and eventually became a professor there. His great work, the Principia Mathematica, published in 1687, set out his three laws of motion and his theory of universal gravitation. It was recognised immediately as one of the greatest intellectual achievements in history. He also served as Master of the Royal Mint, reforming the English currency, and as President of the Royal Society. He was famously difficult in his personal relationships and spent enormous amounts of time on alchemy and biblical interpretation, interests that are less often mentioned than his physics.

Emmy Noether was a German mathematician who changed how we understand algebra and physics. She was born in 1882 in Erlangen, Germany. Her father was a mathematics professor. At the time, women were not allowed to study at German universities as full students. She had to sit in on classes without being officially enrolled. She finished her doctorate in 1907, but she could not get a paid teaching job because she was a woman. In 1915, the famous mathematician David Hilbert invited her to the University of Göttingen. He tried to get her a proper position. The university refused. For years, she had to teach under Hilbert's name and received no pay. She did not complain. She just kept doing brilliant work. Her ideas were so new that many people did not understand them at first. She worked on abstract algebra. This is a part of mathematics that studies the structure behind numbers and shapes. She also helped Einstein with his theory of general relativity. In 1933, the Nazis came to power and forced her out of her job because she was Jewish. She moved to the United States and taught at Bryn Mawr College in Pennsylvania. She died there in 1935, aged only 53, after surgery went wrong.

Srinivasa Ramanujan was an Indian mathematician born in 1887 in Erode, a small town in Tamil Nadu. His family was poor but educated. His father was a clerk and his mother was a devout Hindu. From a young age, he loved numbers. By the age of twelve, he was working through advanced mathematics books on his own. He had very little formal mathematical training. He failed his college exams because he spent all his time on mathematics and neglected other subjects. He lost his scholarship. He worked as a clerk in Madras and did mathematics in every spare moment. He filled notebooks with thousands of results, many of which were new and surprising. In 1913, he wrote a letter to G. H. Hardy, a leading mathematician at Cambridge University in England. The letter contained strange and beautiful formulas. Hardy was amazed. He invited Ramanujan to Cambridge in 1914. The two men worked together for five years. Ramanujan produced brilliant results on number theory, infinite series, and continued fractions. Life in England was hard. The climate was cold. The food was wrong for his vegetarian diet. He became very ill, possibly with tuberculosis or a parasitic infection. He returned to India in 1919 and died in 1920, aged only 32. His notebooks are still being studied today.

William Edwards Deming (1900-1993) was an American statistician and management consultant whose work on quality control and systematic thinking about production reshaped manufacturing in Japan after the Second World War and, later, in the United States. He was born in Sioux City, Iowa, and grew up in a small town in Wyoming under difficult family circumstances. He studied electrical engineering at the University of Wyoming, earned a master's degree in mathematics and physics at the University of Colorado, and completed a PhD in mathematical physics at Yale in 1928. He worked for the United States Department of Agriculture and then the Census Bureau, where he applied statistical methods to sampling and the design of surveys. In 1947 he was invited to help prepare the Japanese census and returned to Japan in the early 1950s at the invitation of the Japanese Union of Scientists and Engineers. His lectures on statistical quality control and his broader management philosophy were widely adopted by Japanese industry, where he became a famous and revered figure decades before his ideas were taken seriously in his own country. The Deming Prize, established in Japan in 1951 and still awarded annually, recognised his influence. In the United States his work was largely ignored until a 1980 NBC documentary, If Japan Can, Why Can't We, brought him to public attention at the age of eighty. He spent his final thirteen years teaching, consulting, and writing; his major book Out of the Crisis appeared in 1982. He continued leading seminars until shortly before his death in 1993, aged ninety-three.

Grace Brewster Murray Hopper (1906-1992) was an American mathematician, computer scientist, and United States Navy rear admiral whose work on programming languages and compilers helped turn computing from a specialist craft into a discipline ordinary people could enter. She was born in New York City to a family that encouraged her scientific curiosity from childhood — at seven, she took apart seven alarm clocks to see how they worked. She studied mathematics and physics at Vassar College and earned a doctorate in mathematics from Yale in 1934, an unusual achievement for a woman of her era. She taught mathematics at Vassar until the United States entered the Second World War. In 1943, at thirty-seven, she joined the Naval Reserve and was assigned to the Bureau of Ships Computation Project at Harvard, where she became one of the first programmers of the Mark I, one of the earliest large electromechanical computers. After the war she moved into private industry, joining Eckert-Mauchly Computer Corporation and later Remington Rand and Sperry. At these companies she developed the first practical compiler, a program that translates human-readable instructions into machine code, and led the team that created FLOW-MATIC, a predecessor of COBOL. She was recalled to naval service several times and finally retired from the Navy as a rear admiral at seventy-nine, the oldest officer in active service at the time. She continued to lecture widely until her death in 1992.

Kurt Gödel was an Austrian-American logician, mathematician, and philosopher. He is widely considered the greatest logician of the 20th century. His incompleteness theorems changed how mathematicians and philosophers understand the foundations of mathematics. He was born in 1906 in Brunn, then part of Austria-Hungary (now Brno in the Czech Republic). His parents were ethnic Germans living in a mostly Czech city. His father managed a textile factory. The family was comfortable. Young Kurt was a quiet, curious child. He asked so many questions that his family nicknamed him 'Mr. Why'. He suffered through a serious illness with rheumatic fever at age six, which he believed had permanently damaged his heart, even though doctors found no lasting damage. The belief shaped his fearful approach to his own health for the rest of his life. He studied at the University of Vienna in the 1920s. He attended the famous Vienna Circle, a group of philosophers and scientists who met to discuss the foundations of knowledge. He earned his doctorate in mathematics in 1929. The next year, he proved his most famous result, the incompleteness theorems. He was 24. In the 1930s, the rise of Nazism made Vienna dangerous. Gödel was not Jewish but had Jewish friends and colleagues. After the Nazi takeover of Austria in 1938 and the start of World War II, he and his wife Adele fled to America. He took a position at the Institute for Advanced Study in Princeton, where Einstein also worked. The two became close friends. Gödel did important later work in cosmology and philosophy. He died in 1978 of malnutrition. He had become so paranoid about poisoning that he stopped eating after his wife was hospitalised.

Alan Turing was an English mathematician, codebreaker, and founder of modern computer science. He was born in London on 23 June 1912. His father worked in the Indian Civil Service, which meant Turing's parents spent much of his childhood abroad. He and his older brother were often raised by foster families in England. As a boy he was shy, odd, and brilliant at mathematics. He studied at King's College, Cambridge, and then earned a PhD at Princeton in 1938. In 1936, while still a student, he wrote a paper called On Computable Numbers. It described an imaginary machine that could follow simple rules to perform any calculation. This imaginary machine, now called a Turing machine, became the theoretical foundation of every modern computer. When the Second World War began in September 1939, Turing joined the British codebreaking centre at Bletchley Park. He helped design a machine called the Bombe, used to break the German Enigma code. His work is thought to have shortened the war by years. He was awarded the OBE in 1945. After the war, Turing worked on building real computers in London and Manchester. In 1950 he proposed the Turing test, a way of asking whether a computer could think. He also began work on mathematical biology. In 1952, Turing was prosecuted for being gay, which was then illegal in Britain. He was forced to take hormone treatment as punishment. He died on 7 June 1954, aged 41, from cyanide poisoning. His death was ruled a suicide. In 2013 he received a formal royal pardon.

Claude Shannon was an American mathematician and engineer. He invented the field of information theory. His work made the digital age possible. Almost every technology that uses digital signals (mobile phones, the internet, computers, GPS, streaming, modern medical imaging) depends on ideas Shannon developed in the 1930s and 1940s. He was born in 1916 in Petoskey, Michigan, and grew up in the small town of Gaylord. His father was a small-town judge. His mother was a language teacher and school principal. Shannon was a clever, curious child. He built his own telegraph as a teenager, using barbed wire fences to connect with a friend's house. He studied electrical engineering and mathematics at the University of Michigan, graduating in 1936. He went to MIT for graduate work. His 1937 master's thesis, written when he was 21, applied Boolean logic (a form of mathematical logic developed in the 19th century) to electrical circuits. The work showed that any logical operation could be performed by appropriate combinations of switches. The thesis has been called the most important master's thesis of the 20th century. It became the foundation for designing all digital computer hardware. During the Second World War, Shannon worked on cryptography (the science of codes) at Bell Laboratories. He met the British codebreaker Alan Turing during the war. The two men had lunch together regularly when Turing visited the United States. After the war, Shannon stayed at Bell Labs. In 1948, he published A Mathematical Theory of Communication, the founding paper of information theory. He was 32. He continued working at Bell Labs and later at MIT until he developed Alzheimer's disease in the 1990s. He died in 2001.

Katherine Johnson was an American mathematician. She did the calculations that helped send the first American astronauts into space and to the Moon. She worked at NASA for over 30 years. She was a Black woman in a field that was largely white and male. Her work was central to the success of the early American space programme. She was born in 1918 in White Sulphur Springs, West Virginia. Her birth name was Katherine Coleman. From a young age, she loved counting. She counted everything: steps, dishes, the stars. She was so advanced that she finished primary school by age 10. The local town did not have a high school for Black children. Her father moved the family 200 kilometres so that Katherine and her siblings could attend a school that did. She went on to West Virginia State, a historically Black college, and graduated with degrees in mathematics and French at 18. In 1953 she joined the National Advisory Committee for Aeronautics (NACA), which became NASA in 1958. She was hired as a 'human computer'. Before electronic computers were trusted, dozens of women did mathematical calculations by hand. Black women at NACA were segregated from white women. They worked in a separate building with separate bathrooms. Johnson pushed past these limits. She joined the all-male Flight Research Division. She did calculations for the first American manned space flights. In 1962, before John Glenn orbited Earth, he asked specifically for Johnson to verify the computer's calculations by hand. He trusted her over the machine. She continued at NASA until 1986. She lived to be 101, dying in 2020.

Maryam Mirzakhani was an Iranian mathematician. She was the first woman ever to win the Fields Medal, the highest prize in mathematics. She was born in 1977 in Tehran, the capital of Iran. She grew up during the Iran-Iraq war of the 1980s, a difficult time for the country. Her parents encouraged her education despite the surrounding chaos. She was not interested in mathematics as a young child. She wanted to be a writer. She read novels constantly and dreamed of becoming a novelist. Her interest in maths grew slowly through middle school. By high school she was attending a special school for gifted girls in Tehran. She and her best friend Roya Beheshti became famous for being the first Iranian girls to win medals at the International Mathematical Olympiad. Mirzakhani won gold medals in 1994 and 1995, with a perfect score the second year. She studied mathematics at Sharif University in Tehran. In 1999 she went to the United States for graduate school at Harvard. She was supervised by Curtis McMullen, a Fields Medallist himself. Her doctoral work was already remarkable. She found new ways to count certain kinds of curves on curved surfaces. She continued at Princeton and then at Stanford as a professor. In 2014, aged 37, she became the first woman to win the Fields Medal. The medal is awarded only every four years and only to mathematicians under 40. The same year she was diagnosed with breast cancer. The cancer eventually spread to her bones and liver. She died in 2017, aged just 40. She left behind her husband and her young daughter Anahita.