A Heroic Feat

           In the third installment of BBC’s “Story of Maths”, Mark de Sautoy traveled to the northern part of Italy to see the finest works of Piero dela Francesca not only in the field of arts but to mathematics as well. Piero was the first painter who fully understood the use of perspective which was brought back by his fellow artists and architects in his era – the Early Renaissance. The problem of perspective is how to represent the three dimensional world on a two dimensional canvas and to give a sense of depth, Piero used Mathematics. The power of perspective unleashed a new way to see the world, a perspective that would cause a mathematical revolution. Piero’s work was the instigation of a new way to understand Geometry.

               By the 17^th century, Europe had taken over from the Middle East as the world's dynamo of mathematical ideas. Vast steps had been made in understanding the geometry of objects fixed in time and space. The race between 4 different countries was now on to discover the mathematics to describe objects in motion. In France, they really give importance to their mathematicians. They named a village after Rene Descartes, a famous philosopher and mathematician who realized that numbers could take away all the torpor of uncertainty. He wanted to publish all his radical ideas but knowing the sensitiveness of the Catholic in France, he left for Holland.

         In Holland, Descartes became one of the champions of the new scientific revolution. He surmised that he would be safe, especially at the old university town of Leiden where they value maths and science. Descartes merged algebra and geometry and through this, he disengages the possibility of navigating geometries of higher dimensions to modern technology and physics. There is no doubt that Descartes was one of the giants of mathematics. He may not have been the most amiable person, but there’s no doubt that his insight between algebra and geometry transformed mathematics forever.

       Marin Mersenne, a Parisian monk and at the same time a first class mathematician commended people to read Descarte’s new work of geometry. He also publicized some new findings on the properties of numbers by Pierre de Fermat, an amateur, which ended up as Descartes rival as the greatest mathematician of his time. Fermat’s greatest contribution to mathematics was to virtually invent the modern number theory.  He devised a wider range of conjectures and theorems about numbers. Fermat certainly enjoyed playing around numbers. He loved looking for patterns in numbers and then the puzzle side of mathematics. But Fermat’s mathematics would have some very serious applications. One of his theorems, the Little Theorem is now the basis of the codes that protect our credit cards on the internet. But the usefulness of Fermat’s mathematics is nothing compared to Isaac Newton, a mathematician who came from Frances’ greatest rival – Britain.

          Newton is very famous for his discovery of gravity and his physics – The Laws of Gravity in Motion. But he also scribbled out a revolutionary approach to maths – the Calculus. Newton’s calculus enables us to really understand the changing world, the orbits of the planets, and the motions of fluids. But Newton decided not to publish but to circulate his thoughts among his friends. Newton attained different kinds of professions, from a professor to a warden of the Royal Mint in the city of London. Developing the calculus was crowded out by all his other interests which involves theology and alchemy until Gottfried Leibniz came into the picture.

      Gottfried Leibniz came from Hanover, which is located in the northern part of Germany. His actual manuscripts and writings where kept under lock and key especially the manuscript which shows how he discovered the miracle of calculus.  He was not only a man of words but as well as one of the first people to invent practical calculating machines that worked on the binary system. Unlike Newton, Leibniz was ecstatic to make his work known and that’s where the trouble started. Throughout the mathematical history, there have been a lot of disagreements whether Leibniz was the one who discovered Calculus or was it Newton. After several years, the Royal Society was asked to arbitrate between rival claims. Newton was credited for discovering the calculus first and Leibniz for the first publication. But that didn’t end there at all. Leibniz was accused of plagiarism based on the written report of the Royal Society’s president – Sir Isaac Newton. The irony is that we are using Leibniz’s calculus in mathematics today.

In the 18^th and 19^th centuries, the Bernoullis produced half a dozen of outstanding mathematicians. Without them, it would have taken much longer for calculus to become what it is today. There was also Leonhard Euler, who has been the wunderkind of Johann Bernoulli. He created modern mathematics, topology and analysis and popularized the symbol of pi. Leonhard Euler was considered as the Mozart of Maths by Sautoy for he has contributed a lot of things to Mathematics.

In Germany, another mathematician arises. He was Carl Friedrich Gauss who was often described as the Prince of Mathematics. At a very young age, Gauss started to indulge himself to mathematics and his early successes inspired him to keep a diary. Gauss is also credited for the usage of imaginary numbers. He may not be the one first come up with it, but he was the first person to explain it clearly.

There were still other mathematicians that followed Gauss and who blew away the cobwebs and allowed us to see the world as it really is – a world much stranger than we ever thought.