Albert Einstein

Albert Einstein is widely acknowledged to be one of the greatest physicists of all time. Born in Ulm, Germany in 1879, his family soon moved to Munich, where he lived until he was 15. lie attended the Luitpold Gymnasium and in 1894, wrote his first scientific work, The Investigation of the State of Aether in Magnetic Fields.

Einstein's family moved to Italy in the same year, but he stayed behind to finish school. However, one year later, he left school without telling his parents and went to Italy to be with them. Shortly afterwards, he applied for admission to the Swiss Polytechnic Institute but was not accepted; he had not done well in the non-seience part of the test. He later attended the Swiss Federal Polytechnic

School in Zurich, from which he received a degree and so was qualified to teach Physics and Mathematics. Unfortunately, however, he was not able to get a teaching position but with the help of his old classmate and friend, Marcel Grossman, was able to get a job in the Swiss Patent Office in 1902. In 1903, Einstein married his former classmate, Mileva Marie. They had three children -a daughter and two sons.

While Einstein was working at the Patent Office, he began to examine different problems in physics and came up with some remarkable discoveries. In 1905 he published three papers, one of which was about his Special Theory of Relativity, a concept which completely overturned Isaac Newton's long-standing Law of Universal Gravitation.

In the following years, Einstein and his family moved from one European capital to another. In each city he held teaching positions at local universities or in scientific institutions. He continued researching a number of different questions and published papers which had a great impact on the field of physics, including his work on the concept of relativity, which led to his Theory of General Relativity in 1915. He paid his price for creativity, however, and due to the great stress he was under, he became seriously ill in 1917.

When Einstein's General Theory of Relativity was proved to be true by British researchers in 1919, he became world famous. He received the 1921 Nobel Prize for Physics in recognition of his work (in 1905) on the photoelectric effect (when electrons are produced if matter is exposed to electromagnetic radiation, for example, in X-rays), which had been thoroughly tested and widely accepted.

Einstein was very active in politics. He moved to the US from Europe just before the start of World War II, and advised the American President Eranklin Roosevelt to start building an atomic bomb before the Nazis produced one. However, he later said that had he realised the Nazis would not produce an atomic bomb, he would never have advised Roosevelt in this way. He never personally worked on the bomb. In fact, he was against war and weapons of mass destruction. All his life Einstein had been a pacifist, only recognising the need to fight against the Nazis when it became apparent that they had to be stopped. After the war, he dedicated himself to working for nuclear disarmament.

Einstein believed that we should never stop questioning things and keep searching for answers about the natural world. On 18th April, 1955 he died of heart failure.

Gottfried Leibniz*

Gottfried Leibniz was born and lived most of his life in Germany. He made visits to both Paris and London, for the sake of learning and study, but spent the vast majority of his working life as an employee of German royalty, as a philosopher, engineer and mathematician. It is for the latter that he is best remembered. His greatest achievement was as an inventor of calculus, the system of notation which is still in use today. Leibniz is remembered as an inventor, not the inventor of calculus. In England, Isaac Newton claimed the distinction, and was later to accuse Leibniz of plagiarism, that is, stealing somebody else's ideas but stating that they are original. Modern-day historians however, regard Leibniz as having arrived at his conclusions independently of Newton. They point out that there are important differences in the writings of both men. Newton, it must be said, was very protective of his achievements and jealous of others' success. It is important to mention that Leibniz published

his writings on calculus three years before Newton published his most important work.

Leibniz was the first to use function to represent geometric concepts. Among other terms, Leibniz used what is now everyday language in mathematics to describe these concepts. Words such as tangent and chord, were first used by Leibniz. He also saw that linear equations in algebra could be arranged into matrices. It was in this significant piece of work on calculus that he introduced mathematics and the world to the word coordinate. He also made important advances in algebra and logic in ways that still today, three hundred years later, have an impact on mathematics.

Leibniz' importance for modern mathematics can be understood through his work. He was especially interested in infinitesimal calculus. This is an area of calculus developed from geometry and algebra. It is divided into two parts. There is differential calculus, which is concerned with measuring rates of change of quantities. And there is integral calculus, which studies the accumulation of quantities. That is, Leibniz was looking at ways of measuring the speed and the distance travelled, for example. Today, calculations of this type are used not only in mathematics but in every branch of science and in many fields which apply a scientific methodology, such as economics and statistics.

Despite the disagreements between Leibniz and Newton, modern mathematicians recognise each of them as being vital to the development of modern mathematics. Newton was certainly the first to apply calculus to the problems of physics. In mathematics itself, it is to Leibniz that we look for our system of writing equations and for the language we use to refer to the concepts. While both reached their understanding without the benefit of reading each other's work, it remains a fact that Leibniz was first to publish.

*Leibniz is also sometimes spelt Leibnitz, although Leibniz is more common.