When it comes to making a name for yourself as a famous scientist, you could do better than trying to do so in the field of Mathematics. With the exception of a couple of famous names (here’s looking at you Pythagoras), the achievements of Mathematicians too often go unrecognised. Although breakthroughs in fields such as Medicine can often seem both much more exciting than those in Maths, and more relevant for day-to-day life, developing groundbreaking new medicines would not be possible without the concepts developed by mathematical thinkers centuries before. Throughout history, Mathematics has led to the development of the first computer, allowed us to transmit electricity across thousands of miles, helped us understand the universe around us and has even allowed us to travel into space. To raise the profile of these amazing figures, here we identify five of the most influential mathematicians who have shaped the modern world.

The life of the famous Greek Pythagoras is somewhat mysterious. Probably born the son of a seal engraver on the island of Samos, Pythagoras has been attributed with many scientific and mathematical discoveries in antiquity, including the Pythagorean theorem currently torturing schoolchildren across the world, the Theory of Proportions, the sphericity of the Earth and the discovery that the morning and evening stars are, in fact, the planet Venus. He is also attributed as being the first to divide the globe into five climatic zones and may also have been the first person to call himself a ‘philosopher’. That said, it has since emerged that the theorem about right-angled triangles may actually have predated him. Part of a community where numbers were venerated above all for their spiritual qualities, Pythagoras can be described as the forefather of Greek mathematics: the originator of the field as we know it today.

Whether of his apparent discoveries originate with him or not, the number-obsessed mystical leader Pythagoras was one of the most iconic and influential figures in the field of Mathematics. In addition, he was also unusually progressive in his attitudes towards women, with female members of Pythagoras’s school appearing to have played an active role in its operations and many prominent female philosophers contributing to the development of Neopythagoreanism later on.

Pythagoras can be described as the forefather of Greek mathematics: the originator of the field as we know it today

The German mathematician David Hilbert is one of the most influential figures from the field in the 19th and 20th centuries. Notable for the breadth of his work, Hilbert devised and developed fundamental ideas across a broad range of mathematical areas, including work on the foundations of geometry, proof theory, calculus of variation, algebraic number theory and commutative algebra, to name just a few. Part of the famous Göttingen school, many of Hilbert’s PhD students would later become celebrated mathematicians, including Otto Blumenthal, Felix Bernstein and Erich Steinhaus. Hilbert both adopted and warmly defended Georg Cantor’s set theory and transfinite numbers. He is perhaps most famous for his presentation of a collection of 23 problems at the International Congress of Mathematicians in Paris in 1900 which would set the course for much of the mathematical research of the 20th century.

Thanks to the wide range of his work, David Hilbert’s influence on modern mathematics cannot be overstated. Beginning with his Hilbert’s Basis Theorem Proof, in 1888 Hilbert proved the finite basis theorem for any number of variables. Although Paul Gordan had been able to prove the theorem in 1868, this was for only two variables, as three or more variables were simply too time consuming to prove. By using an entirely new abstract strategy for his proof, Hilbert established that the theorem was true for an arbitrary number of variables: a major advance in algebraic number theory. Secondly, Hilbert’s 1899 work ‘Foundations of Geometry’ introduced entirely new axioms of geometry, replacing those of Euclid’s which had been used for over 2,000 years, thus unifying two-dimensional and three-dimensional geometry into one system. To name these as only two examples of Hilbert’s work, his impact on modern mathematics, – as well as physics through his later work on mathematical physics – is rightly recognised as truly remarkable.

David Hilbert’s influence on modern mathematics cannot be overstated

The English mathematician, Sir Isaac Newton was both one of the most influential scientists to have ever lived and a key figure in the scientific revolution which occurred during the early modern period. In his 1687 work Philosophiæ Naturalis Principia Mathematica ( or, “Mathematical Principles of Natural Philosophy), Newton formulated the laws of motion and gravitation which would form the dominant scientific viewpoint until Einstein’s theory of relativity came along. The mathematician used his description of gravity to prove Kepler’s laws of planetary motion, explain the trajectories of tides, comets and the precession of the equinoxes, therefore eradicating any doubt about the Solar System’s heliocentricity (that the sun is at the centre of the solar system). Finally, Newton’s prediction that the Earth is an oblate spheroid was later supported by the geodetic measurements of Maupertuis and La Condamine, convincing most European scientists of the superiority of Newtonian mechanics compared to earlier systems, thus placing Newton’s work at the centre of Mathematics for centuries to come.

As well as his best known work on mechanics and gravitation, as a mathematician Newton also contributed to the study of power series, devised a method for approximating the roots of a function and generalised the binomial theorem to non-integer exponents – amongst many other developments. Newton can certainly be described as somewhat of a polymath: for almost 300 years, Newton has been regarded as the founding exemplar of modern physical science, with major achievements in experimental investigation in physics and chemistry, as well as demonstrating an interest in the early history of Western civilization and theology; undertaking an investigation of the form and dimensions, as described in the Bible, of Solomon’s Temple in Jerusalem. With strong links to Cambridge throughout his life, Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University. Possessing a devout and unorthodox Christian faith, Newton privately rejected the doctrine of the Trinity and (very unusually for a Cambridge academic at the time) refused to take holy orders in the Church of England. A staunch supporter of the Whig party, Newton also served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. Newton was certainly recognised for his genius during his lifetime: after receiving a knighthood from Queen Anne in 1705, Newton spent the last three decades of his life in London, serving as Warden (1696–1700) and Master (1700–1727) of the Royal Mint, and, finally, president of the Royal Society (1703–1727).

Newton can certainly be described as somewhat of a polymath

Hypatia has the honour of being the first female mathematician whose life is relatively well recorded. She was the daughter of Greek mathematician Theon and the head of the Platonist School in Alexandria, Egypt, where she taught astronomy and philosophy. Though there are no written records of her work to consult, it is widely believed that she contributed a great deal to her famous father’s published works. She is known to have written a commentary on Diophantus’s influential thirteen-volume work, Arithmetica, which may survive in part, as it was interpolated into Diophantus’s original text, amongst many other possible works which have not survived. Renowned in her own lifetime as a great teacher and a wise counsellor, she was accused of being a Satanist by a mob of Christians and murdered in 415 AD.

Although Hypatia was never formally recognised for her mathematical work during her lifetime, the influence of her martyrdom was far more significant. Shortly after her death, she was transformed into a “martyr for philosophy” within the empire, with future Neoplatonists like Damascius becoming ever-more dedicated in their anti-Christian opposition. Later on, during the period of the Middle Ages, Hypatia was portrayed as a symbol of Christian virtue, with some scholars claiming that she was part of the basis for the famous legend of Saint Catherine of Alexandria. As the centuries progressed, her legend continued, and she was transformed from a symbol of opposition to Catholicism (which continued into the Age of Enlightenment), the last of the ancient ‘Hellenes’ (or Greeks) during the 19th century, and even as a precursor to the feminist movement, as an icon for women’s rights, into the 20th century and the modern day; numerous fictionalised film and novel adaptations of Hypatia’s life have been made in recent years, demonstrating the inspiring nature of Hypatia’s life.

Hypatia has the honour of being the first female mathematician whose life is relatively well recorded

Ada Lovelace was a Victorian computer pioneer who collaborated on the first programmable computers in the mid-19th century. With her father the tempestuous poet, Lord Byron, Ada was raised by her mother under a regimen of science, logic and mathematics in an attempt to avoid her inheriting his temperament. Married at the age of 19 to an aristocrat, William King, he was made Earl of Lovelace in 1838, leading to her (slightly incorrectly) being known as ‘Ada Lovelace’ after her death. She was introduced to Charles Babbage by her mentor, the scientist and polymath Mary Sommerville and they became lifelong friends. Babbage was famous for his enterprising, unfinished plans for enormous clockwork calculating machines. A thinker ahead of her time, Lovelace foresaw how Babbage’s machines could be used to transform any type of content into digits which could be manipulated by a machine, earning her the nickname in posterity, the ‘mother of the computer’.

Dying tragically young of uterine cancer in 1852 at the age of 36, the pioneering work of Ada Lovelace only began to receive the acclaim it deserved in the 1950s, more than 100 years later, and she is still much less well known than Charles Babbage today. As well as working on Babbage’s general-purpose computer (or ‘Analytical Engine’), Lovelace was also fascinated by the relations between both maths and music and modelling the brain, writing to her friend Woronzow Greig in 1844 about her desire to create a “calculus of the nervous system”: a mathematical model depicting how the brain gives rise to thoughts and nerves to feeling: something she never achieved in her lifetime. Similarly, she also wrote to her mother in 1851 and described “certain productions” relating to maths and music she was working on, but never completed prior to her death. Ada Lovelace’s legacy lived on in the work of the English mathematician, Alan Turing. Although the Analytical Engine would remain only a vision during Lovelace’s lifetime, her notes on the Engine were one of the vital documents to inspire Turing’s work on the first ever modern computers during the 1940s. Today, Lovelace’s visionary passion for technology lives on, acting as an inspirational symbol for women in mathematics and technology in the 21st century.

Lovelace’s visionary passion for technology lives on, acting as a inspirational symbol for women in mathematics and technology

## Who is Your Mathematics Hero?

Whether it’s Hilbert, Lovelace or Pythagoras, as you’ll have seen, each of these Mathematicians shaped both the field of study, and the broader world around them, in their own individual ways, changing the world as we know it today. If you’re feeling enlivened by the stories of these extraordinary people and you want to find out more about the Mathematics that they were inspired by, why not sign up for the Immerse Mathematics Summer School? With small class sizes, expert tuition and a beautiful setting in Isaac Newton’s city – Cambridge – this is the ideal place to improve your Mathematical ability and to find out what legacy you might be able to create.