Famous People: Biographies

Here are the short biographies of the famous people mentioned in the book. We hope you find these interesting.

Note: Click on the menu to view the individual biography.

Jean-Robert Argand 18 July 1768 – 13 Aug 1822

Jean-Robert Argand (18 July 1768 – 13 August 1822) was a gifted amateur mathematician. In 1806, while managing a bookstore in Paris, he published the idea of geometrical interpretation of complex numbers known as the Argand diagram.

Argand is also renowned for delivering a proof of the fundamental theorem of algebra in his 1814 work Réflexions sur la nouvelle théorie d'analyse (Reflections on the new theory of analysis). It was the first complete and rigorous proof of the theorem, and was also the first proof to generalise the fundamental theorem of algebra to include polynomials with complex coefficients. In 1978 it was called by The Mathematical Intelligencer ‘both ingenious and profound,’ and was later referenced in Cauchy's Cours d’Analyse and Chrystal's influential textbook Algebra.

Mentioned in Chapter 33

Friedrich Wilhelm Bessel 22 Jul 1784 – 17 Mar 1846

Friedrich Wilhelm Bessel (22 July 1784 – 17 March 1846) was a German mathematician, astronomer, and the systematiser of the Bessel functions. Born in Minden-Ravensberg, Bessel produced a refinement on the orbital calculations for Halley's Comet, later becoming an assistant at Lilienthal Observatory where he worked on James Bradley's stellar observations to produce precise positions for 3,222 stars.

In January 1810, Bessel was appointed director of the Königsberg Observatory by King Frederick William III of Prussia, where he was able to pin down the position of over 50,000 stars. His work at the Königsberg Observatory won him the Lalande Prize from the French Academy of Sciences in 1811.

Bessel was the first person to use parallax in calculating the distance to a star in 1838. His announcement of Sirius's ‘dark companion’ in 1844 was the first correct claim of a previously unobserved star by positional measurement, and eventually led to the discovery of Sirius B.

While studying the dynamics of 'many-body' gravitational systems, he developed Bessel functions. Critical for the solution of certain differential equations, these functions are widely used in both classical and quantum physics to this day. Bessel is also responsible for the correction to the formula for the sample variance estimator named in his honour. He died in 1846 in Königsberg from cancer.

Mentioned in Chapter 55

George Boole 2 Nov 1815 – 8 Dec 1864

George Boole (2 November 1815 – 8 December 1864) was an English mathematician, philosopher and logician that worked in the fields of differential equations and algebraic logic. Best known as the author of The Laws of Thought, Boole is also the inventor of the prototype of what is now called Boolean logic, which became the basis of the modern digital computer.

At 16, Boole took up a junior teaching position in Doncaster. By the time he was 19, Boole had established his own school at Lincoln, before going on to run a boarding school. In 1849 he was appointed as the first professor of mathematics at Queen's College, Cork, in Ireland. Boole later went on to be elected a Fellow of the Royal Society in 1857, and received honorary degrees of LL.D. from the University of Dublin and Oxford University. On 8 December 1864, Boole died of an attack of fever.

Mentioned in Chapter 63

Baron Augustin-Louis Cauchy 21 Aug 1789 – 23 May 1857

Baron Augustin-Louis Cauchy (21 August 1789 – 23 May 1857) was a French mathematician who became an early pioneer of analysis.

More concepts and theorems have been named after Cauchy than any other mathematician (in elasticity alone there are sixteen concepts and theorems named for Cauchy). A prolific writer; he wrote approximately eight hundred research articles.

Cauchy covered notable subjects, including the theory of series, in which he developed the notion of convergence and discovered many of the basic formulas for q-series, he developed the theory of numbers and complex quantities, and the theory of groups and substitutions, the theory of functions, differential equations, and determinants. Cauchy was the first to define complex numbers as pairs of real numbers.

Cauchy also contributed significant research in mechanics, substituting the notion of the continuity of geometrical displacements for the principle of the continuity of matter. He introduced a 3 by 3 symmetric matrix of numbers that is now known as the Cauchy stress tensor. In elasticity, Cauchy originated the theory of stress, and his results are nearly as valuable as those of Poisson.

Mentioned in Chapter 52

Gabriel Cramer 31 July 1704 – 4 Jan 1752

Gabriel Cramer (31 July 1704 – 4 January 1752) was a Swiss mathematician, born in Geneva. At 18 he received his doctorate and at 20 he was co-chair of mathematics. His articles cover a wide range of subjects including the study of geometric problems, the history of mathematics, philosophy, and the date of Easter. He published an article on the aurora borealis in the Philosophical Transactions of the Royal Society of London and he also wrote an article on law where he applied probability to demonstrate the significance of having independent testimony from two or three witnesses rather than from a single witness.

Cramer's most famous book Introduction à l'analyse des lignes courbes algébraique is a work which Cramer modelled on Newton's memoir on cubic curves and he highly praises a commentary on Newton's memoir written by Stirling.

Mentioned in Chapter 34

Abraham de Moivre 26 May 1667 – 27 Nov 1754

Abraham de Moivre (26 May 1667 – 27 November 1754) was a French mathematician famous for de Moivre's formula, which links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.

De Moivre wrote a book on probability theory, The Doctrine of Chances, said to have been prized by gamblers at the time. He also first discovered Binet's formula, the closed-form expression for Fibonacci numbers linking the n’th power of φ to the n’th Fibonacci number.

Throughout his life de Moivre remained poor. He continued studying the fields of probability and mathematics until his death in 1754, and several additional papers were published after his death. He pioneered the development of analytic geometry and the theory of probability by expanding upon the work of his predecessors, particularly Christiaan Huygens and several members of the Bernoulli family.

De Moivre also published an article called ‘Annuities upon Lives’, in which he revealed the normal distribution of the mortality rate over a person’s age. From this he produced a simple formula for approximating the revenue produced by annual payments based on a person’s age. This is similar to the types of formulas used by insurance companies today.

Mentioned in Chapter 23

Augustus De Morgan 27 June 1806 – 18 March 1871

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction.

Augustus De Morgan was born in 1806, in India, but the family moved to England when he was seven months old. In 1823, at the age of sixteen, he entered Trinity College, Cambridge, later going on to become Professor of Mathematics at the newly established London University (now University College London).

De Morgan published a number of works, including The Differential and Integral Calculus, and made them cheaply and easily available to anyone. He was the first president of the London Mathematical Society. Five years after his resignation from University College De Morgan died of nervous prostration on 18 March 1871.

Mentioned in Chapter 63

René Descartes 31 March 1596 – 11 Feb 1650

René Descartes (31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and writer. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy is a result of his writings, which are studied closely to this day, in particular, his Meditations on First Philosophy. Descartes' influence in mathematics is also apparent; the Cartesian coordinate system — allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system — was named after him.

Descartes is perhaps best known for the philosophical statement ‘Cogito ergo sum’ (I think, therefore I am), found in part IV of Discourse on the Method.

One of Descartes' most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry. He ‘invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c’. He also ‘pioneered the standard notation’ that uses superscripts to show the powers or exponents, for example the 4 used in x4 to indicate squaring of squaring. He was also the first person to assign a place for algebra in our system of knowledge, and believed that algebra was a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. René Descartes died on 11 February 1650 in Stockholm, Sweden, of suspected pneumonia.

Mentioned in Chapter 63

Leonhard Euler 15 Apr 1707 – 18 Sep 1783

Leonhard Euler (15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist who made important discoveries in infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation.

Euler worked in almost all areas of mathematics as well as continuum physics, lunar theory and other areas of physics. He is the only mathematician to have two numbers named after him - the immensely important Euler's Number in calculus, and the Euler-Mascheroni Constant γ (gamma) sometimes referred to as just ‘Euler's constant’.

Euler proved Newton's identities, Fermat's little theorem, Fermat's theorem on sums of two squares, and he made distinct contributions to Lagrange's four-square theorem. He also invented the totient function φ(n) which is the number of positive integers less than or equal to the integer n that are coprime to n. Using properties of this function, he generalized Fermat's little theorem to what is now known as Euler's theorem.

Euler also made contributions in optics. His 1740s papers on optics helped ensure that the wave theory of light proposed by Christian Huygens would become the dominant mode of thought, at least until the development of the quantum theory of light. Euler suffered a brain haemorrhage on 18 September 1783 and died a few hours later.

Mentioned in Chapters 52 and 78

Jean Baptiste Joseph Fourier 21 Mar 1768 –16 May 1830

Jean Baptiste Joseph Fourier (21 March 1768 –16 May 1830) was a French mathematician and physicist best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations. Fourier is also credited with the discovery of the greenhouse effect.

Fourier made important contributions to dimensional analysis. The other physical contribution was Fourier's proposal of his partial differential equation for conductive diffusion of heat. This equation is now taught to every student of mathematical physics. In the 1820s Fourier calculated that an object the size of the Earth, and at its distance from the Sun, should be considerably colder than the planet actually is if warmed only by the effects of incoming solar radiation. His consideration of the possibility that the Earth's atmosphere might act as an insulator of some kind is widely recognized as the first proposal of what is now known as the greenhouse effect. In 1830 he died in his bed on 16 May.

Mentioned in Chapter 73

Ferdinand Georg Frobenius 26 Oct 1849 – 3 Aug 1917

Ferdinand Georg Frobenius (October 26, 1849 – August 3, 1917) was a German mathematician best known for his contributions to the theory of elliptic functions, differential equations and to group theory. He is known for determinantal identities, known as Frobenius-Stickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms. He also lent his name to Frobenius manifolds – differential-geometric objects in modern mathematical physics.

Group theory was one of Frobenius' principal interests in the second half of his career. His proof of the first Sylow theorem is frequently used today. Frobenius created the theory of group characters and group representations, which are fundamental tools for studying the structure of groups. This work led to the notion of Frobenius reciprocity and the definition of what are now called Frobenius groups.

Mentioned in Chapter 55

Johann Carl Friedrich Gauss 30 Apr 1777 – 23 Feb 1855

Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, electrostatics, astronomy and optics.

In 1796 Gauss discovered a construction of the heptadecagon, and, simplified manipulations in number theory. He also became the first to prove the quadratic reciprocity law. This law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic.

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae, which introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon (17-sided polygon) can be constructed with straightedge and compass.

The discovery of Ceres led Gauss to publish his theory of the motion of planetoids disturbed by large planets. This introduced the Gaussian gravitational constant, and contained an influential treatment of the method of least squares, a procedure used to this day in order to minimize the impact of measurement error. Gauss proved the method under the assumption of normally distributed errors.

In 1818 Gauss carried out a geodesic survey of the Kingdom of Hanover, linking up with previous Danish surveys. To aid the survey, Gauss invented the heliotrope, an instrument that can be used to measure positions by using a mirror to reflect sunlight over great distances.

In 1831 Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber, leading to new knowledge in magnetism and the discovery of Kirchhoff's circuit laws in electricity. They constructed the first electromechanical telegraph in 1833, which connected the observatory. He died in Göttingen, Germany in 1855.

Mentioned in Chapter 65

Maurice Karnaugh Oct 4, 1924 in New York City

Maurice Karnaugh(October 4, 1924 in New York City) is an American physicist, famous for the Karnaugh map used in Boolean algebra.

He studied mathematics and physics at City College of New York (1944–48) and transferred to Yale University to complete his B.Sc. (1949), M.Sc. (1950) and Ph.D).

Karnaugh worked at Bell Labs for much of his career, developing the Karnaugh map (1954) as well as patents for PCM encoding and magnetic logic circuits and coding. He later worked at IBM's Federal Systems Division in Gaithersburg (1966–70) and at the IBM Thomas J. Watson Research Center (1970–89), studying multistage interconnection networks.

Mentioned in Chapter 63

Martin Wilhelm Kutta 3 Nov 1867 – 25 Dec 1944

Martin Wilhelm Kutta (3 November 1867 – 25 December 1944)

Kutta studied at the University of Breslau from 1885 to 1890, in which time he wrote a thesis that contains the now famous Runge-Kutta method for solving ordinary differential equations.

Best known for the Runge-Kutta method for solving ordinary differential equations and the Zhukovsky- Kutta (Joukowski -Kutta) theorem giving the lift on an aerofoil. Kutta also went on to make further important contributions to aerodynamics.

Two further topics which Kutta worked on were research on glaciers and also research in the history of mathematics. Kutta died on Christmas day in 1944.

Mentioned in Chapter 52

Pierre-Simon, Marquis de Laplace 23 Mar 1749 – 5 Mar 1827

Pierre-Simon, Marquis de Laplace (23 March 1749 – 5 March 1827) was a French mathematician and astronomer who formulated Laplace's equation, and pioneered the Laplace transform which appears in many branches of mathematical physics. The Laplacian differential operator is also named after him. He was also one of the first scientists to postulate the existence of black holes and the notion of gravitational collapse.

While he conducted much research in physics, another major theme of his life's endeavours was probability theory. Laplace set out a mathematical system of inductive reasoning based on probability. He died in Paris in 1827.

Mentioned in Chapter 9

Adrien-Marie Legendre 18 Sep 1752 – 10 Jan 1833

Adrien-Marie Legendre (18 September 1752 – 10 January 1833) was a French mathematician . The Moon crater Legendre is named after him.

Legendre developed the least squares method, which is used in linear regression, signal processing, statistics, and curve fitting; this was published in 1806 as an appendix to his book on the paths of comets. In number theory, he conjectured the quadratic reciprocity law, subsequently proved by Gauss, and as a result of this the Legendre symbol is named after him. He also did pioneering work on the distribution of primes, and on the application of analysis to number theory.

Mentioned in Chapter 55

Gottfried Wilhelm Leibniz July 1, 1646 – Nov 14, 1716

Gottfried Wilhelm Leibniz(sometimes von Leibniz) (July 1, 1646 – November 14, 1716) was a German mathematician and philosopher.

Leibniz developed infinitesimal calculus independently of Isaac Newton, and his Law of Continuity and Transcendental Law of Homogeneity only found mathematical use in the 20th century. In 1685 he was the first to describe a pinwheel calculator, and also invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers.

Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system.

Mentioned in Chapter 45

Guillaume de l'Hôpital 1661 – 2 Feb 1704, Paris

Guillaume François Antoine, Marquis de l'Hôpital (1661, Paris – 2 February 1704, Paris) was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞.

In 1693, l'Hôpital was elected to the French academy of sciences and went on to serve twice as its vice-president. Among his accomplishments were the determination of the arc length of the logarithmic graph, one of the solutions to the brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point.

Mentioned in Chapter 8

Colin Maclaurin Feb 1698 – 14 June 1746

Colin Maclaurin (February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series are named after him.
Maclaurin used Taylor series to characterise maxima, minima, and points of inflection for infinitely differentiable functions in his Treatise of Fluxions. The Taylor series expanded around 0 is sometimes known as the Maclaurin series.

Independently from Euler and using the same methods, Maclaurin discovered the Euler–Maclaurin formula. He used it to sum powers of arithmetic progressions, derive Stirling's formula, and to derive the Newton-Cotes numerical integration formulas which includes Simpson's rule as a special case.

Mentioned in Chapters 8 and 55

Sir Samuel Morland 1625–1695

Sir Samuel Morland, 1st Baronet (1625–1695), was an English academic, diplomat, spy, inventor and mathematician of the 17th century, a polymath credited with early developments in relation to computing, hydraulics and steam power.

On 18 July 1660 he was created a baronet and given a minor role at court, but his principal source of income came from applying his knowledge of mathematics and hydraulics to construct and maintain various machines. These included ‘water-engines’, an early kind of water pump. He also experimented with using gunpowder to make a vacuum that would suck in water (in effect the first internal combustion engine) and worked on ideas for a steam engine. Morland's pumps were developed for numerous domestic, marine and industrial applications, such as wells, draining ponds or mines, and fire fighting. His calculation of the volume of steam (approximately two thousand times that of water) was not improved upon until the later part of the next century, and was of importance for the future development of a working steam engine. He also invented a non-decimal adding machine, and a machine that made trigonometric calculations. A new ‘Multiplying Instrument’ was invented by Morland in 1666, an 'arithmetical machine' by which the four fundamental rules of arithmetic were readily worked. In 1666 he also obtained a patent for making metal fire-hearths, and in 1671 he claimed credit for inventing the speaking trumpet, an early form of megaphone. He later won a contract to provide mirrors to the King and to erect and maintain the King’s printing press. In 1681 he was appointed magister mechanicorum (master of mechanics) to the King for his work on the water system at Windsor. He also corresponded with Pepys about naval gun-carriages, designed a machine to weigh ship's anchors, developed new forms of barometers, and designed a cryptographic machine.

Mentioned in Chapter 10

John Napier 1550 – 4 Apr 1617

John Napier of Merchiston (1550 – 4 April 1617) is best known as the discoverer of logarithms. The inventor of the so-called ‘Napier's bones’, Napier also made common the use of the decimal point in arithmetic and mathematics.

The computational advance available via logarithms made calculations by hand much quicker. The way was opened to later scientific advances, in astronomy, dynamics, physics; and also in astrology. Napier also improved Simon Stevin's decimal notation and Arab lattice multiplication, used by Fibonacci, was made more convenient by the introduction of Napier's bones, a multiplication tool he invented using a set of numbered rods.

Mentioned in Chapter 14

Sir Isaac Newton 25 Dec 1642 – 20 March 1727

Sir Isaac Newton PRS MP (25 December 1642 – 20 March 1727) was an English polymath. Philosophiæ Naturalis Principia Mathematica, published in 1687, lays the foundations for much of classical mechanics used today. Newton showed that the motions of objects are governed by the same set of natural laws, by demonstrating the consistency between Kepler's laws of planetary motion and his theory of gravitation.

Newton developed a theory of colour based on the observation that a prism decomposes white light into the many colours that form the visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound. In mathematics, Newton shares the credit with Leibniz for the development of differential and integral calculus.

Newton was appointed Lucasian Professor of Mathematics in 1669. From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that a prism could decompose white light into a spectrum of colours, and that a lens and a second prism could recompose the multicoloured spectrum into white light. He also showed that the coloured light does not change its properties by separating out a coloured beam and shining it on various objects. Newton noted that regardless of whether it was reflected or scattered or transmitted, it stayed the same colour. Thus, he observed that colour is the result of objects interacting with already-coloured light rather than objects generating the colour themselves. This is known as Newton's theory of colour.

From this work, he concluded that the lens of any refracting telescope would suffer from the dispersion of light into colours (chromatic aberration). As a proof of the concept, he constructed the first known functional reflecting telescope, today known as a Newtonian telescope, which involved solving the problem of a suitable mirror material and shaping technique.

The Principia was published on 5 July 1687. In this work, Newton stated the three universal laws of motion that enabled many of the advances of the Industrial Revolution. Newton's three laws of motion (stated in modernised form): Newton's First Law (also known as the Law of Inertia) states that an object at rest tends to stay at rest and that an object in uniform motion tends to stay in uniform motion unless acted upon by a net external force. Newton's Second Law states that an applied force on an object equals the rate of change of its momentum with time. The SI unit of force is the newton, named in Newton's honour.

Newton's Third Law states that for every action there is an equal and opposite reaction. This means that any force exerted onto an object has a counterpart force that is exerted in the opposite direction back onto the first object. He died in his sleep in London on 20 March 1727 and was buried in Westminster Abbey.

Mentioned in Chapter 17

Pappus of Alexandria c. 290 – c. 350

Pappus of Alexandria (c. 290 – c. 350) was one of the last great Greek mathematicians of Antiquity.

Collection, his best-known work, is a compendium of mathematics in eight volumes. It covers a wide range of topics, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra.
The characteristics of Pappus's Collection are that it contains an account, systematically arranged, of the most important results obtained by his predecessors, and, secondly, notes about and extending previous discoveries.

Mentioned in Chapter 61

Blaise Pascal 19 June 1623 – 19 Aug 1662

Blaise Pascal (19 June 1623 – 19 August 1662), was a French polymath. A child prodigy educated by his father, Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum.

Pascal went on to become an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

Mentioned in Chapter 16

Siméon Denis Poisson 21 June 1781 – 25 Apr 1840

Siméon Denis Poisson (21 June 1781 – 25 April 1840), was a French mathematician, geometer, and physicist. His work on the theory of electricity and magnetism virtually created a new branch of mathematical physics, and his study of celestial mechanics discussed the stability of the planetary orbits.

In pure mathematics, his most important works were his series of memoirs on definite integrals and his discussion of Fourier series. The Poisson distribution in probability theory is named after him.

Mentioned in Chapter 40

Pythagoras of Samos Born about 570 BC and died about 495 BC

Pythagoras of Samos (Born about 570 BC and died about 495 BC) was an Ionian Greek philosopher and mathematician.

Pythagoras made influential contributions to philosophy in the late 6th century BC. He is best known for the Pythagorean theorem, which states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides - that is, a2 + b2 = c2

Mentioned in Chapter 22

Joseph Raphson Born 1678 and died 1715

Joseph Raphson was an English mathematician known best for the Newton–Raphson method.
Raphson's most notable work is Analysis Aequationum Universalis, published in 1690. It contains a method, now known as the Newton–Raphson method, for approximating the roots of an equation.

Raphson coined the word pantheism, making a distinction between atheistic ‘panhylists’ (from the Greek ‘pan’ = all + ‘hyle’ = wood, matter), who believe everything derives from matter, and pantheists who believe in ‘a certain universal substance, material as well as intelligent, that fashions all things that exist out of its own essence’. Raphson believed the universe to be immeasurable in respect to a human's capacity of understanding, and that humans would never be able to comprehend it.

Mentioned in Chapter 17

Benjamin Olinde Rodrigues 1795–1851

Benjamin Olinde Rodrigues (1795–1851), more commonly known as Olinde Rodrigues, was a French banker, mathematician, and social reformer.

In 1840 he published a result on transformation groups, a discovery of the quaternions, three years prior to William Rowan Hamilton's. In his own time, his work on mathematics was largely ignored, and he has only been rediscovered late in the twentieth century.

Rodrigues is remembered for three results: Rodrigues' rotation formula for vectors; and the Rodrigues formula about series of orthogonal polynomials; and the Euler–Rodrigues parameters. He died in Paris in 1851.

Mentioned in Chapter 55

Carl David Tolmé Runge 1856–1927

Carl David Tolmé Runge (1856–1927) was a German mathematician, physicist, and spectroscopist. He was co-developer of the Runge–Kutta method in the field of numerical analysis. The Runge crater on the Moon is named after him.

Mentioned in Chapter 52

Thomas Simpson 20 Aug 1710 – 14 May 1761

Thomas Simpson FRS (20 August 1710 – 14 May 1761) was the British mathematician who invented Simpson's rule to approximate definite integrals.

Simpson, born in Market Bosworth, Leicestershire, taught himself mathematics, then turned to astrology after seeing a solar eclipse. He also dabbled in divination and caused fits in a girl after 'raising a devil' from her. After this incident, he and his wife had to flee to Derby. They later moved to London, where he taught mathematics at the Royal Military Academy, Woolwich.

Mentioned in Chapters 21 and 57

Brook Taylor 18 Aug 1685 – 29 Dec 1731

Brook Taylor (18 Aug 1685 – 29 Dec 1731)

At St John's College Cambridge Taylor became highly involved with mathematics. He graduated with an LL.B. in 1709 but by this time he had already solved the problem of the centre of oscillation of a body. In 1712 Taylor was elected to the Royal Society.

Two of Taylor’s books that appeared in 1715, Methodus incrementorum directa et inversa and Linear Perspective are extremely important in the history of mathematics. Second editions would appear in 1717 and 1719 respectively.

Taylor added a new branch to mathematics now called the ‘calculus of finite differences’, invented integration by parts, and discovered the celebrated series known as Taylor's expansion.

Mentioned in Chapter 52

John Wallis 23 Nov 1616 – 28 Oct 1703

John Wallis (23 November 1616 – 28 October 1703) was an English mathematician partially credited for the development of infinitesimal calculus, and is also credited with introducing the symbol for infinity. He made significant contributions to trigonometry, calculus, geometry, and the analysis of infinite series. In his Opera Mathematica I (1695) Wallis introduced the term ‘continued fraction’.

Generally credited as the originator of the idea of the number line where numbers are represented geometrically in a line with the positive numbers increasing to the right and negative numbers to the left, in 1685 Wallis published Algebra, preceded by a historical account of the development of the subject, which contains a great deal of valuable information. This algebra is noteworthy as containing the first systematic use of formulae.

Mentioned in Chapter 47