Lewis Fry Richardson was the youngest of seven children born to Catherine Fry (1838 – 1919) and David Richardson (1835 – 1913). They were a prosperous Quaker family, David Richardson running a successful tanning and leather manufacturing business.

At age 12 he was sent to a Quaker boarding school, Bootham in York, where he received an excellent education in science, which stimulated an active interest in natural history. In 1898 he went on to Durham College of Science (a college of Durham University) where he took courses in mathematical physics, chemistry, botany, and zoology. Two years later, he gained a scholarship to King's College, Cambridge, where he graduated with first - class honours in the natural sciences tripos in 1903. At age 47 he received a doctorate in mathematical psychology from the University of London.

In 1909 he married Dorothy Garnett (1885 – 1956), daughter of the mathematician and physicist William Garnett. They were unable to have children due to an incompatibility in blood types, but they adopted two sons and a daughter between 1920 and 1927.

Richardson's nephew Ralph Richardson, became a noted actor.

Richardson's working life reflected his eclectic interests:

• National Physical Laboratory (1903 – 1904)
• University College Aberystwyth (1905 – 1906)
• chemist, National Peat Industries (1906 – 1907)
• National Physical Laboratory (1907 – 1909)
• manager of the physical and chemical laboratory, Sunbeam Lamp Company (1909 – 1912)
• Manchester College of Technology (1912 – 1913)
• Meteorological Office - as superintendent of Eskdalemuir Observatory (1913 – 1916)
• Friends Ambulance Unit in France (1916 – 1919)
• Meteorological Office at Benson, Oxfordshire (1919 – 1920)
• Head of the Physics Department at Westminster Training College (1920 – 1929)
• Principal, Paisley Technical College, now part of the University of the West of Scotland (1929 – 1940)

In 1926, he was elected to the Fellowship of the Royal Society

Richardson's Quaker beliefs entailed an ardent pacifism that exempted him from military service during World War I as a conscientious objector, though this subsequently disqualified him from holding any academic post. Richardson worked from 1916 to 1919 for the Friends' Ambulance Unit attached to the 16th French Infantry Division. After the war, he rejoined the Meteorological Office but was compelled to resign on grounds of conscience when it was amalgamated into the Air Ministry in 1920. He subsequently pursued a career on the fringes of the academic world before retiring in 1940 to research his own ideas. His pacifism had direct consequences on his research interests. According to Thomas Körner, the discovery that his meteorological work was of value to chemical weapons designers led him to abandon all his efforts in this field, and destroy findings that he had yet to publish.

Richardson's interest in meteorology led him to propose a scheme for weather forecasting by solution of differential equations, the method used today, though when he published Weather Prediction by Numerical Process in 1922, suitable fast computing was unavailable. He described his ideas thus:

“After so much hard reasoning, may one play with a fantasy? Imagine a large hall like a theatre, except that the circles and galleries go right round through the space usually occupied by the stage. The walls of this chamber are painted to form a map of the globe. The ceiling represents the north polar regions, England is in the gallery, the tropics in the upper circle, Australia on the dress circle and the Antarctic in the pit.

A myriad computers are at work upon the weather of the part of the map where each sits, but each computer attends only to one equation or part of an equation. The work of each region is coordinated by an official of higher rank. Numerous little "night signs" display the instantaneous values so that neighbouring computers can read them. Each number is thus displayed in three adjacent zones so as to maintain communication to the North and South on the map.

From the floor of the pit a tall pillar rises to half the height of the hall. It carries a large pulpit on its top. In this sits the man in charge of the whole theatre; he is surrounded by several assistants and messengers. One of his duties is to maintain a uniform speed of progress in all parts of the globe. In this respect he is like the conductor of an orchestra in which the instruments are slide - rules and calculating machines. But instead of waving a baton he turns a beam of rosy light upon any region that is running ahead of the rest, and a beam of blue light upon those who are behindhand.

Four senior clerks in the central pulpit are collecting the future weather as fast as it is being computed, and despatching it by pneumatic carrier to a quiet room. There it will be coded and telephoned to the radio transmitting station. Messengers carry piles of used computing forms down to a storehouse in the cellar.

In a neighbouring building there is a research department, where they invent improvements. But these is much experimenting on a small scale before any change is made in the complex routine of the computing theatre. In a basement an enthusiast is observing eddies in the liquid lining of a huge spinning bowl, but so far the arithmetic proves the better way. In another building are all the usual financial, correspondence and administrative offices. Outside are playing fields, houses, mountains and lakes, for it was thought that those who compute the weather should breathe of it freely.” (Richardson 1922)

(The word computers is used here in its original sense - people who did computations, not machines. Calculator also referred to people at this time.)

When news of the first weather forecast by the first modern computer, ENIAC, was received by Richardson in 1950, he responded that the results were an "enormous scientific advance." The first calculations for a 24 hour forecast took ENIAC nearly 24 hours to produce.

He was also interested in atmospheric turbulence and performed many terrestrial experiments. The Richardson number, a dimensionless parameter in the theory of turbulence is named after him. He famously summarized the field in rhyming verse in Weather Prediction by Numerical Process:

Big whirls have little whirls that feed on their velocity,

and little whirls have lesser whirls and so on to viscosity.

[A play on Augustus De Morgan's rewording of Jonathan Swift, "Great fleas have little fleas upon their backs to bite 'em, And little fleas have lesser fleas, and so ad infinitum." (A Budget of Paradoxes, 1915)].

One of Richardson's most celebrated achievements is his attempt in hind sight to forecast the weather during a single day — 20 May 1910 — by direct computation. At the time, meteorologists carried out forecasts principally by looking for similar weather patterns from past records, and then extrapolating forward. Richardson attempted to use a mathematical model of the principal features of the atmosphere, and use data taken at a specific time (7 AM) to calculate the weather six hours later Ab initio. As Lynch makes clear, Richardson's forecast failed dramatically, predicting a huge 145 hectopascals (4.3 inHg) rise in pressure over six hours when the pressure actually stayed more or less static. However, detailed analysis by Lynch has shown that the cause was a failure to apply smoothing techniques to the data, which rule out unphysical surges in pressure. When these are applied, Richardson's forecast turns out to be essentially accurate — a remarkable achievement considering the calculations were done by hand, and while Richardson was serving with the Quaker ambulance unit in northern France.

Richardson also applied his mathematical skills in the service of his pacifist principles, in particular in understanding the roots of international conflict. For this reason, today he is considered the founder, or co-founder (with Quincy Wright and Pitirim Sorokin as well as others such as Kenneth Boulding, Anatol Rapaport and Adam Curle), of the scientific analysis of conflict; an interdisciplinary field of quantitative and mathematical social science dedicated to systematic investigation of the causes of war and conditions of peace. As he had done with weather, he analyzed war using mainly differential equations and probability theory. Considering the armament of two nations, Richardson posited an idealized system of equations whereby the rate of a nation's armament build-up is directly proportional to the amount of arms its rival has and also to the grievances felt toward the rival, and negatively proportional to the amount of arms it already has itself. Solution of this system of equations allows insightful conclusions to be drawn regarding the nature, and the stability or instability, of various hypothetical conditions which might obtain between nations.

He also originated the theory that the propensity for war between two nations was a function of the length of their common border. And in Arms and Insecurity (1949), and Statistics of Deadly Quarrels (1950), he sought to statistically analyze the causes of war. Factors he assessed included economics, language, and religion. In the preface of the latter, he wrote: "There is in the world a great deal of brilliant, witty political discussion which leads to no settled convictions. My aim has been different: namely to examine a few notions by quantitative techniques in the hope of reaching a reliable answer."

In Statistics of Deadly Quarrels Richardson presented data on virtually every war from 1815 to 1945. As a result he hypothesized a base 10 logarithmic scale for conflicts. In other words, there are far more small fights, in which only a few people die, than large ones that kill many. While no conflict's size can be predicted beforehand — indeed, it is impossible to give an upper limit to the series — overall they do form a Poisson distribution. On a smaller scale he showed the same pattern for gang murders in Chicago and Shanghai. Others have noted that similar statistical patterns occur frequently, whether planned (lotteries, with many more small payoffs than large wins), or by natural organization (there are more small towns with grocery stores than big cities with superstores).

While studying the causes of war between two countries, Richardson decided to search for a relation between the probability of two countries going to war and the length of their common border. While collecting data, he realized that there was considerable variation in the various gazetted lengths of international borders. For example, that between Spain and Portugal was variously quoted as 987 or 1214 km while that between the Netherlands and Belgium as 380 or 449 km.

As part of his research, Richardson investigated how the measured length of a border changes as the unit of measurement is changed. He published empirical statistics which led to a conjectured relationship. This research was quoted by mathematician Benoît Mandelbrot in his 1967 paper How Long Is the Coast of Britain?

Suppose the coast of Britain is measured using a 200 km ruler, specifying that both ends of the ruler must touch the coast. Now cut the ruler in half and repeat the measurement, then repeat again.

Notice that the smaller the ruler, the larger the result. It might be supposed that these values would converge to a finite number representing the "true" length of the coastline. However, Richardson demonstrated that the measured length of coastlines and other natural features appears to increase without limit as the unit of measurement is made smaller. Today this is known as the Richardson effect.

At the time, Richardson's research was ignored by the scientific community. Today, it is seen as one element in the birth of the modern study of fractals.

In April 1912, shortly after the loss of the Titanic, Richardson filed a patent for iceberg detection using acoustic echolocation in air. A month later he filed a similar patent for acoustic echolocation in water, foreseeing the invention of sonar by Paul Langevin and Robert Boyle 6 years later.

Since 1997, the Lewis Fry Richardson Medal is been awarded by the European Geosciences Union for "exceptional contributions to nonlinear geophysics in general" (by EGS until 2003 and by EGU by 2004).

Benoît B. Mandelbrot (20 November 1924 – 14 October 2010) was a French American mathematician. Born in Poland, he moved to France with his family when he was a child. Mandelbrot spent much of his life living and working in the United States, and he acquired dual French and American citizenship.

Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the father of fractal geometry. He coined the term fractal and described the Mandelbrot set. Mandelbrot extensively popularized his work, writing books and giving lectures aimed at the general public.

Mandelbrot spent most of his career at IBM's Thomas J. Watson Research Center, and was appointed as an IBM Fellow. He later became a Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique.

Mandelbrot was born in Warsaw into a Jewish family from Lithuania. Mandelbrot was born into a family with a strong academic tradition - his mother was a dentist and he was introduced to mathematics by two of his uncles, one of whom, Szolem Mandelbrojt, was a mathematician who resided in Paris. However, his father made his living trading clothing. Anticipating the threat posed by Nazi Germany, the family fled from Poland to France in 1936 when he was 11. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle, France. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive - la - Gaillarde, to continue his studies. In 1944 he returned to Paris. He studied at the Lycée du Parc in Lyon and in 1945 - 47 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics. Returning to France, he obtained his Ph.D. degree in Mathematical Sciences at the University of Paris in 1952.

From 1949 to 1958 Mandelbrot was a staff member at the Centre National de la Recherche Scientifique. During this time he spent a year at the Institute for Advanced Study in Princeton, New Jersey, where he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva, Switzerland, and later to the Université Lille Nord de France. In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow Emeritus.

From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics. He became convinced that two key themes, fat tails and self - similar structure, ran through a multitude of problems encountered in those fields.

Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having theoretically infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.

Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.

In 1975, Mandelbrot coined the term fractal to describe these structures, and published his ideas in Les objets fractals, forme, hasard et dimension (1975; an English translation Fractals: Form, Chance and Dimension was published in 1977). Mandelbrot developed here ideas from the article Deux types fondamentaux de distribution statistique (1938; an English translation Two Basic Types of Statistical Distribution) of Czech geographer, demographer and statistician Jaromír Korčák.

While on secondment as Visiting Professor at Harvard University in 1979, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets of the formula z² − μ. While investigating how the topology of these Julia sets depended on the complex parameter μ he studied the Mandelbrot set fractal that is now named after him. (Note that the Mandelbrot set is now usually defined in terms of the formula z² + c, so Mandelbrot's early plots in terms of the earlier parameter μ are left – right mirror images of more recent plots in terms of the parameter c.)

In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature. This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".

Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division. He joined the Department of Mathematics at Yale, and obtained his first tenured post in 1999, at the age of 75. At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences. His awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003, and the Einstein Lectureship of the American Mathematical Society in 2006.

The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Knight in the French Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was promoted to Officer of the Legion of Honour in January 2006. An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises.

Although Mandelbrot coined the term fractal, some of the mathematical objects he presented in The Fractal Geometry of Nature had been described by other mathematicians. Before Mandelbrot, they had been regarded as isolated curiosities with unnatural and non - intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long - stalled effort to extend the scope of science to non-smooth objects in the real world. He highlighted their common properties, such as self - similarity (linear, non - linear, or statistical), scale invariance, and a (usually) non - integer Hausdorff dimension.

He also emphasized the use of fractals as realistic and useful models of many "rough" phenomena in the real world. Natural fractals include the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies; and Brownian motion. Fractals are found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry:

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
  —Mandelbrot, in his introduction to The Fractal Geometry of Nature

Mandelbrot has been called a visionary and a maverick. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non - specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

When visiting the Museu de la Ciència de Barcelona in 1988, he told its director that the painting The Face of War had given him "the intuition about the transcendence of the fractal geometry when making intelligible the omnipresent similitude in the forms of nature". He also said that, fractally, Gaudí was superior to Van der Rohe.

Mandelbrot died in a hospice in Cambridge, Massachusetts, on 14 October 2010 from pancreatic cancer, at the age of 85. Reacting to news of his death, mathematician Heinz - Otto Peitgen said "if we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last 50 years." Chris Anderson described Mandelbrot as "an icon who changed how we see the world." French President Nicolas Sarkozy said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions". Sarkozy also added, "His work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry."