Mathematics of Northern Europe

Summary: Since the Enlightenment, Northern Europe has made considerable contributions to mathematics research and continues to do so.

Northern Europe has produced many outstanding mathematicians and scholars in related fields, from the development of calculus by Isaac Newton in the seventeenth century to the cosmological models developed by Stephen William Hawking in the twentieth and twenty-first centuries.

Northern Europe also led the way in developing many practical applications of mathematics and later statistics, including taking a national census like the Domesday Book undertaken in England in 1183 and developing mathematical ways to measure the influence of personal habits on health as in the studies of Richard Doll and Austin Bradford Hill on the relationship between smoking and disease. In the twenty-first century, the United Nations category of northern Europe includes the Åland Islands, the Channel Islands, Denmark, Estonia, Faeroe Islands, Finland, Guernsey, Iceland, Ireland, the Isle of Man, Jersey, Latvia, Lithuania, Norway, Svalbard and Jan Mayen Islands, Sweden, and the United Kingdom of Great Britain and Northern Ireland. However, the changing political boundaries in many of these countries throughout history, as well as the rise and fall of the Soviet Union, which included countries like Estonia, Latvia, and Lithuania, mean that mathematical contributions of some individuals may be included within the histories of other regions.

Sir Isaac Newton was one of the most influential mathematicians of the modern era. He shares credit with Gottfried Leibniz for developing integral and differential calculus, and he also made major contributions in the fields of physics and astronomy. Newton’s 1687 book Philosophiae Naturalis Principia Mathematica laid the groundwork for classical mechanics including a description of the three laws of motion and remains one of the most influential books in the history of science. He also built the first reflecting telescope and developed a theory of color based on the visible spectrum displayed when visible light is refracted through a prism. Through his work with the laws of gravity and Kepler’s laws of planetary motion, named for Johannes Kepler, Newton was able to demonstrate mathematically the validity of heliocentrism, which is the scientific principle that Earth and other planets revolve around the sun.

The nineteenth century saw several major breakthroughs in mathematics by scholars from northern Europe. In England, philosopher and mathematician George Boole developed the system now known as “Boolean logic,” which has many practical applications and was instrumental in the development of modern digital computers. His most famous works are The Mathematical Analysis of Logic (1847) and The Laws of Thought (1854). His slightly younger contemporary, Norwegian Niels Henrik Abel, invented the field of group theory (contemporaneously with Frenchman Evariste Galois), which has many applications in mathematics and physics. Abel is well known for a proof he wrote at age 19 that there can be no general algebraic solution of an equation greater than degree four. In Ireland, Sir William Rowan Hamilton provided an important reformulation of Newtonian mechanics and invented an extension of the number system called “quaternions.”

In the period 1910-1913, the British scholars Bertrand Russell and Alfred North Whitehead wrote the influential Principia Mathematica in which they attempted to derive the foundations of mathematics from a set of axioms and inference rules. Russell was also a prominent writer and political activist who won the Nobel Prize for Literature in 1950, while Whitehead was also noted as a philosopher. More recently, Andrew Wiles, who was born and educated in the United Kingdom but immigrated to the United States, achieved fame for proving Fermat’s Last Theorem (named for Pierre de Fermat), one of the most famous previously unsolved problems in mathematics.

Honors

There is no Nobel Prize for mathematics but several different international awards are offered that have been termed the “Mathematics Nobel Prize” because of their prestige. The Fields Medal is awarded every four years to one or more mathematicians of age 40 or younger by the International Mathematical Union. Winners from the United Kingdom have included Klaus Roth (1958), Michael Atiya (1966), Alan Baker (1970), Simon Donaldson (1986), Richard Borcherds (1988), and Timothy Gowers (1998). Lars Ahlfors of Norway won in 1936, the first year the medal was given; Atle Selberg of Norway won in 1950; and Lars Hormander of Sweden won in 1962. Another major mathematical prize, the Abel Prize, is named after Norwegian mathematician Niels Henrik Abel and is awarded annually by the Norwegian Academy of Science and Letters. The Abel Prize has been awarded since 2003. Northern European winners include Michael F. Atiyah of the United Kingdom and Lebanon in 2004 and Lennart Carleson of Sweden in 2006.

The Wolf Prize in Mathematics has been awarded almost annually by the Wolf Foundation since 1978 and more than one prize may be given per year. Northern European winners include Lars Ahlfors of Finland (1981), Atle Selberg of Norway (1986), Lars Hormander of Sweden (1988), Lennart Carleson of Sweden (1992), Andrew Wiles of the United Kingdom (1995/1996), and David B. Mumford of the United Kingdom (2008).

Northern European countries have been regular competitors in the International Mathematical Olympiad, an annual competition held since 1959 for high school students. Each competing country sends a team of six students who are assigned six questions to solve. Individual students are awarded medals based on their scores, and countries are also compared based on the total score for their team.

There have been many medal winners from northern European countries. The United Kingdom began participating in 1967 and even hosted the 1976 and 2002 competitions. Ireland first participated in 1988. The northern Europe countries from the former Soviet Union Estonia, Latvia, and Lithuania first participated in 1993, which coincided with the removal of Russian troops from the area and other political reorganization throughout the former Soviet Union. Among the Scandinavian countries, Sweden first participated in 1967, Norway in 1984, Finland in 1965, Denmark in 1991, and Iceland in 1985. Sweden hosted the 1991 competition, and Finland hosted it in 1985.

Bibliography

Knox, Kevin C., and Richard Noakes. From Newton to Hawking: A History of Cambridge University’s Lucasian Professors of Mathematics. Cambridge, England: Cambridge University Press, 2003.

Krantz, Steven G. An Episodic History of Mathematics: Mathematical Culture Through Problem Solving. Washington, DC: Mathematical Association of America, 2010.

School of Mathematics and Statistics, St. Andrews University. “The MacTutor History of Mathematics.” http://www-groups.dcs.st-andrews.ac.uk/~history/.

Westfall, Richard S. Isaac Newton. Cambridge, England: Cambridge University Press, 2007.