John Craig (1663 – 11 October 1731) was a Scottish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

theologian Theology is the systematic study of the nature of the divine and, more broadly, of religious belief. It is taught as an academic discipline, typically in universities and seminaries. It occupies itself with the unique content of analyzing the ...

Biography

Born in

Dumfries Dumfries ( ; sco, Dumfries; from gd, Dùn Phris ) is a market town and former royal burgh within the Dumfries and Galloway council area of Scotland. It is located near the mouth of the River Nith into the Solway Firth about by road from t ...

and educated at the

University of Edinburgh The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 1 ...

, Craig moved to

England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe ...

and became a

vicar A vicar (; Latin: '' vicarius'') is a representative, deputy or substitute; anyone acting "in the person of" or agent for a superior (compare "vicarious" in the sense of "at second hand"). Linguistically, ''vicar'' is cognate with the English pre ...

in the

Church of England The Church of England (C of E) is the established Christian church in England and the mother church of the international Anglican Communion. It traces its history to the Christian church recorded as existing in the Roman province of Brit ...

. A friend of

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...

, he wrote several minor works about the new

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

. He was elected

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemati ...

in 1711.

Mathematical Principles of Christian Theology

He is known for his book ''Theologiae Christianae Principia Mathematica'' (''Mathematical Principles of Christian Theology''), published in 1698. In the aforementioned book, Craig presents a

formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwe ...

that describes how the

probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...

of a historical event depends on the number of primary witnesses, on the chain of transmission through secondary witnesses, on the elapsed time and on the spatial distance. Using this formula, Craig derived that the probability of the story of

Jesus Jesus, likely from he, יֵשׁוּעַ, translit=Yēšūaʿ, label= Hebrew/ Aramaic ( AD 30 or 33), also referred to as Jesus Christ or Jesus of Nazareth (among other names and titles), was a first-century Jewish preacher and relig ...

would reach 0 in the year 3150. This year he interpreted as the

Second Coming The Second Coming (sometimes called the Second Advent or the Parousia) is a Christian (as well as Islamic and Baha'i) belief that Jesus will return again after his ascension to heaven about two thousand years ago. The idea is based on messia ...

of Christ because of verse 18:8 in the

Gospel of Luke The Gospel of Luke), or simply Luke (which is also its most common form of abbreviation). tells of the origins, Nativity of Jesus, birth, Ministry of Jesus, ministry, Crucifixion of Jesus, death, Resurrection of Jesus, resurrection, and Ascensi ...

. His work was poorly received and controversial at the time. Several later mathematicians complained about his imprecise use of probability and the unsupported derivation of his formula.

Stephen Stigler Stephen Mack Stigler (born August 10, 1941) is Ernest DeWitt Burton Distinguished Service Professor at the Department of Statistics of the University of Chicago. He has authored several books on the history of statistics; he is the son of the e ...

, in his 1999 book (see references, below) gave a more favorable interpretation, pointing out that some of Craig's reasoning can be justified if his "probability" is interpreted as the

log-likelihood ratio In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after im ...

Logarithms

Craig was involved in developing the concept of

Hyperbolic logarithm A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points and on the rectangular hyperbola , or the corresponding region when this hyperbola is re-scaled and ...

and in 1710 published “Logarithmotechnica generalis” in the

Proceedings of the Royal Society ''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life s ...

. By way of illustration he gives the

Mercator series In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: :\ln(1+x)=x-\frac+\frac-\frac+\cdots In summation notation, :\ln(1+x)=\sum_^\infty \frac x^n. The series converges to the natural ...

for the logarithm (denoted l.) without mention of

radius of convergence In mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or \infty. When it is positive, the power series ...

: “Exemplar 1. Assumatur ''a'' = ''y'', unde per Canonum generalum

x = l.\overline,

cujus differentials est

\dot = \frac,

& hujus integralis per Seriem infinitum expressa dat :

x = y - \fracy^2 + \fracy^3 - \fracy^4 + \fracy^5 - \fracy^6 + \fracy^7 ...

""Logarithmotechnia generalis"(1710, page 192

Works

* 1698
Logarithmic quadrature
(in Latin) ''Philosophical Transactions of the Royal Society'' * 1703
Specimen of determining quadrature of figures
(in Latin),

Philosophical Transactions of the Royal Society ''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the first journa ...

#284 via

Biodiversity Heritage Library The Biodiversity Heritage Library (BHL) is the world’s largest open access digital library for biodiversity literature and archives. BHL operates as worldwide consortiumof natural history, botanical, research, and national libraries working toge ...

* 1710
Method of making logarithms
(in Latin), ''Philosophical Transactions of the Royal Society''

References

Bibliography

* S. M. Stigler, ''Statistics on the Table'', Chapter 13, Harvard University Press, (1999). * J. F. Scott, ''Dictionary of Scientific Biography'' (New York 1970–1990). * . * R. Nash, ''John Craige's mathematical principles of Christian theology'' (1991). * M. Cantor, ''Vorlesungen über Geschichte der Mathematik III'' (Leipzig, 1896), 52, 188. * ''Dictionary of National Biography'' (London, 1917). * S. M. Stigler, ''John Craig and the probability of history: from the death of Christ to the birth of Laplace'', ''Journal of the American Statistical Association'' 81 (1986), 879–887.

External links

{{DEFAULTSORT:Craig, John 1663 births 1731 deaths People from Dumfries Anglo-Scots 18th-century English Anglican priests Scottish mathematicians 17th-century Scottish mathematicians 18th-century Scottish mathematicians Fellows of the Royal Society Scottish non-fiction writers Alumni of the University of Edinburgh Scottish Episcopalians