Tangent was introduced by Thomas Fincke (1561-1656) in his Thomae Finkii Flenspurgensis Geometriae rotundi libri XIIII, Basileae: Per Sebastianum Henricpetri, 1583. He wrote tangens in Latin.
Vieta did not approve of the term tangent because it could be confused with the term in geometry. He used (c. 1593) sinus foecundarum (abridged to foecundus) and also amsinus and prosinus (Smith vol. 2, page 621).
According to the DSB, "Rheticus' Canon of the Doctrine of Triangles (Leipzig, 1551) was the first table to give all six trigonometric functions, including the first extensive table of tangents and secants (although such modern designations were eschewed by Rheticus as 'Saracenic barbarisms')."
TANGRAM is found in 1861 in Primary object lessons for a graduated course of development, a manual for teachers and parents with lessons for the proper training of the faculties of children by Norman Allison Calkins (1822-1895): "Among objects for illustrating form there should be a gonigraph and the Chinese tangram; and the child should also have provided for amusement at home little bricks--blocks made of some hard wood, as cherry or maple, four inches long, two inches wide, and one thick. ... The tangram may be made of metal, wood, or pasteboard."
The origin of the word is uncertain. Modern dictionaries suggest it may be derived from a Chinese word tang; an older dictionary suggests it may be a changed spelling from the obsolete English word trangam.
The term TAUBERIAN THEOREMS was coined by G. H. Hardy (Kramer, p. 504). The term was used by Hardy and Littlewood (DSB, article: "Wiener").
The term is found in 1913 in Hardy & Littlewood in Proc. London Math. Soc. XI. 411: "The general character of the theorems which it [sc. this paper] contains is 'Tauberian': they are theorems of the type whose first example was the beautiful converse of Abel's theorem originally proved by Tauber" (OED2).
TAYLOR'S FORMULA is found in English in 1855 in Elements of the differential and integral calculus by Albert Ensign Church [University of Michigan Digital Library].
The term TAYLOR'S SERIES "was probably first used by L'Huillier in 1786, although Condorcet used both the names of Taylor and d'Alembert in 1784" (DSB).
Lacroix used Théorème de Taylor and la série de Taylor in Traité élémentaire de calcul différentiel et de calcul intégral (1797-1800).
Taylor's series appears in English appears in 1836 in the second edition of Elements of the Differential Calculus by John Radford Young [James A. Landau].
TAYLOR'S THEOREM. Colin Maclaurin attributed the theorem to Taylor in his Treatise of Fluxions (1742): "This theorem was given by Dr. TAYLOR, method. increm." [Judith V. Grabiner].
Julio González Cabillón believes that Marie Jean Antoine Nicolas de Caritat Condorcet (1743-1794) used the term Taylor's theorem (in French) in 1784, in volume I of the Encyclopedie methodique (p. 104).
Lacroix used Théorème de Taylor and la série de Taylor in Traité élémentaire de calcul différentiel et de calcul intégral (1797-1800).
Taylor's theorem appears in English in the 1816 translation of Lacroix's Differential and Integral Calculus: " This formula is called Taylor's Theorem, from the English geometer by whom it was discovered" (OED2).
TENSOR (in quaternions) was used by William Rowan Hamilton (1805-1865) in 1846 in The London, Edinburgh, and Dublin Philosophical Magazine XXIX. 27:
Since the square of a scalar is always positive, while the square of a vector is always negative, the algebraical excess of the former over the latter square is always a positive number; if then we make (TQ)2 = (SQ)2 - (VQ)2, and if we suppose TQ to be always a real and positive or absolute number, which we may call the tensor of the quaternion Q, we shall not thereby diminish the generality of that quaternion. This tensor is what was called in former articles the modulus.The earliest use of tensor in the Proceedings of the Royal Irish Academy is on p. 282 of Volume 3, and is in the proceedings of the meeting held on July 20, 1846. The volume appeared in 1847. Hamilton writes:
Q = SQ + VQ = TQ [times] UQThe factor TQ is always a positive, or rather an absolute (or signless) number; it is what was called by the author, in his first communication on this subject to the Academy, the modulus, but which he has since come to prefer to call it the TENSOR of the quaternion Q: and he calls the other factor UQ the VERSOR of the same quaternion. As the scalar of a sum is the sum of the scalars and the vector of the sum is the sum of the vectors, so that tensor of a product is the product of the tensors and the versor of a product is the product of the versors.
In other words, the tensor of a quaternion is simply its modulus.
In his paper "Researches respecting quaternions" (Transactions of the Royal Irish Academy, vol. 21 (1848) pp. 199-296), Hamilton uses the term "modulus," not "tensor." This paper purports to have been read on 13 November 1843 (i.e., at the same meeting as the short paper, or abstract, in the Proceedings of the RIA).
The terms vector, scalar, tensor and versor appear in the series of papers "On Quaternions" that appeared in the Philosophical Magazine (see pages 236-7 in vol III of "The Mathematical Papers of Sir William Rowan Hamilton," edited by H. Halberstam and R.E. Ingram). The editors have taken 18 short papers published in the Philosophical Magazine between 1844 and 1850, and concatenated them in the "Mathematical Papers" to form a seamless whole, with no indication as to how the material was distributed into the individual papers.
(Information for this article was provided by David Wilkins and Julio González Cabillón.)
TENSOR in its modern sense is due to the famous Goettingen Professor Woldemar Voigt (1850-1919), who in 1887 anticipated Lorentz transform to derive Doppler shift, in Die fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung, Leipzig: von Veit, 1898 (OED2 and Julio González Cabillón).
The term TENSOR ANALYSIS was introduced by Albert Einstein in 1916 (Kline, page 1123).
According to the University of St. Andrews website, Einstein is reported to have commented to the chairman at the lecture he gave in a large hall at Princeton which was overflowing with people:
I never realised that so many Americans were interested in tensor analysis.Tensor analysis is found in English in 1922 in H. L. Brose's translation of Weyl's Space-Time-Matter: "Tensor analysis tells us how, by differentiating with respect to the space co-ordinates, a new tensor can be derived from the old one in a manner entirely independent of the co-ordinate system. This method, like tensor algebra, is of extreme simplicity" (OED2).
The term TERAGON was coined by Mandelbrot, according to an Internet web page.
TERMINATING DECIMAL appears in 1857 in Mathematical Dictionary and Cyclopedia of Mathematics: "Those decimal fractions which are expressed by a finite number of places of figures, are called terminating decimals."
Finite decimal appears in 1876 in Elementary arithmetic, with brief notices of its history by Robert Potts: "1. In what cases can an ordinary fraction be expressed by a finite decimal?" [University of Michigan Historical Math Collection].
TESSELLATION is found in 1660 in The History of the Propagation and Improvement of Vegetables by Robert Sharrock (1630-1684): "Yet they, instead of those elegant Tessellations, are beautified otherwise in their site with as great curiosity."
The OED2 shows numerous citations in the 1800s of the spellings tesselation, tesselated, and tesselate, and some modern U. S. dictionaries show these as alternate spellings.
TESSERACT was used in 1888 by Charles Howard Hinton (1853-1907) in A New Era of Thought (OED2). According to an Internet site, Hinton coined the term.
The term TEST OF INDIVIDUAL EQUIVALENCE RATIOS was coined by Anderson & Hauck (1990), according to an Internet web page by J. T. Gene Hwang.
TETRAHEDRON is found in English in Sir Henry Billingsley's 1570 translation of Euclid's Elements (OED2).
TETRATION, a term for repeated exponentiation, was introduced by Reuben Louis Goodstein. In "Transfinite ordinals in recursive number theory, " Journal of Symbolic Logic 12 (1947), he writes "... defines successive new processes (which we may call tetration, pentation, hexation, and so on)" [Samuel S. Kutler, Dave L. Renfro].
THEOREM appears in English in 1551 in The Pathwaie to Knowledge by Robert Recorde: "Argts., The Theoremes, (whiche maye be called approued truthes) seruing for the due knowledge and sure proofe of all conclusions...in Geometrye."
The term THEORY OF CLOSEDNESS was introduced in 1910 by Vladimir Andreevich Steklov (1864-1926) (DSB).
THEORY OF GAMES appears in the title "La théorie du jeu et les équations intégrales à noyau symétrique," by Emile Borel, Compt. Rend. Acad. Sci., 173 (Dec. 19, 1921).
The term Theorie der Gesellschaftsspiele appears in 1928 in the title, "Zur Theorie der Gesellschaftsspiele" by John von Neumann, Math. Ann. 100. Gesellschaftsspiele is translated as "parlor games" by Kramer [James A. Landau].
Referring to the 1928 paper, von Neumann's collaborator Herman H. Goldstine wrote in The Computer from Pascal to von Neumann (1972):
This was his first venture in the field [of game theory], and while there had been other tentative approaches --- by Borel, Steinhaus, and Zermelo, among others --- his was the first to show the relations between games and economic behavior and to formulate and prove his now famous minimax theorem which assures the existence of good strategies for certain important classes of games.Theory of games also appears in 1943 in the title Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern [James A. Landau].
Game theory appears in 1946-47 in Carl Kaysen, Review of Economic Studies XIV. 14: "It is extremely doubtful whether the degree of restriction of possible solutions offered by the 'solution' of game-theory will be great enough to be of much practical value in really complex cases" [Fred Shapiro].
THEORY OF PROBABILITY is found in the title Exposition de la Théorie des Chances et des Probabilités (1843) by A. A. Cournot [James A. Landau].
THEORY OF TYPES is found in Bertrand Russell, "Mathematical Logic as Based on the Theory of Types," American Journal of Mathematics 30 (1908) [James A. Landau].
The term THRACKLE was coined by John Horton Conway.
The use of the designations TIME DOMAIN and FREQUENCY DOMAIN to distinguish the correlation and the spectral approaches to filtering theory, and to time series analysis generally, seems to have originated in communication engineering.
"Frequency domain" appears in L. A. Zadeh's "Theory of Filtering" (Journal of the Society for Industrial and Applied Mathematics, 1, (1953), 35-51).
"Time domain" and "frequency domain" appear together in W. F. Trench's "A General Class of Discrete Time-Invariant Filters," Journal of the Society for Industrial and Applied Mathematics, 9, (1961), 405-421.
The terms soon became established in statistical time series analysis, see e.g. M. Rosenblatt & J. W. Van Ness's "Estimation of the Bispectrum," Annals of Mathematical Statistics, 36, (1965), 1120-1136 [John Aldrich].
TIME SERIES appears in W. M. Persons's "The Correlation of Economic Statistics," Publications of the American Statistical Association, 12, (1910), 287-322 [John Aldrich].
The phrase TIME SERIES ANALYSIS entered circulation at the end of 1920s, e.g. in S. Kuznets's "On the Analysis of Time Series," Journal of the American Statistical Association, 23, (1928), 398-410, although it only became really popular much later [John Aldrich].
The term TITANIC PRIME (a prime number with at least 1000 decimal digits) was coined in 1984 by Samuel D. Yates (died, 1991) of Delray Beach, Florida ["Sinkers of the Titanic", J. Recreational Math. 17, 1984/5, p268-274]. Yates also coined the term gigantic prime in the mid-1980s, referring to a prime number with at least 10,000 decimal digits. [The term megaprime refers to a prime of at least a million decimal digits.]
The term TOPOLOGICAL ALGEBRA was coined by David van Dantzig (1900-1959). The term appears in the title of his 1931 Ph. D. dissertation "Studiën over topologische Algebra" (DSB).
TOPOLOGICAL GROUP. David van Dantzig defines "eine topologische Gruppe" in "Ueber topologisch homogene Kontinua" in Fundamenta Mathematicae vol. 15 (1930) pages 102-125.
In a footnote van Dantzig states that this notion is essentially the same notion as that of a "limesgruppe" which is said to be introduced by Otto Schreier (1901-1929) in Abstrakte Kontinuierliech Gruppen (Abh. Math. Sem. Hambirg 4 (1925) 15-32) [Michael van Hartskamp].
TOPOLOGICAL SPACE. Felix Hausdorff used topologisch raum in Grundzüge der Mengenlehre (1914).
TOPOLOGY was introduced in German in 1847 by Johann Benedict Listing (1808-1882) in "Vorstudien zur Topologie," Vandenhoeck und Ruprecht, Göttingen, pp. 67, 1848. However, Listing had already used the word for ten years in correspondence. The term was introduced to replace the earlier name "analysis situs."
Topology is found in English in February 1883 in Nature: "The term Topology was introduced by Listing to distinguish what may be called qualitative geometry from the ordinary geometry in which quantitative relations chiefly are treated" (OED2).
According to several sources, topology was introduced in English by Solomon Lefschetz (1884-1972) in the title of a monograph written in the late 1920s. According to Encarta, the word topology was coined by Solomon Lefschetz in 1930.
TORSION. According to Howard Eves in A Survey of Geometry, vol. II (1965), "The name torsion was introduced by L. I. Valleé in 1825, replacing an older name flexion" [James A. Landau].
TORUS. Hero mentions a mathematician named Dionysodorus as the author of On the Tore, in which a formula for the volume of the torus is given [DSB]. The OED2 shows a use of torus in English by Cayley in 1870.
TOTIENT. E. Prouhet used indicateur (indicator) in 1846 in Nouv. Ann. de Math. V. 176.
Totient was introduced by Sylvester in "On Certain Ternary Cubic-Form Equations", Amer. J. Math 2 (1879) 280-285, 357-393, in Sylvester's Collected Mathematical Papers vol. III p. 321. He writes: "The so-called (phi) function of any number I shall here and hereafter designate as its (tau) function and call its Totient." This information was taken from a post in sci.math by Robert Israel.
TRACE (of a matrix) is found in 1938 in A. A. Albert, Modern Higher Algebra: "We call T(A) the trace of A" (OED2).
The TRACTRIX was named by Christiaan Huygens (1629-1695), according to the University of St. Andrews website.
In Webster's 1828 dictionary, the word is spelled tractatrix, with the middle syllable stressed.
TRANSCENDENTAL. Referring to curves, Gottfried Wilhelm Leibniz (1646-1716) used the terms algebraic and transcendental for Descartes' terms geometrical and mechanical in 1684 in Acta Eruditorum (Kline, page 312). Struik (page 276) writes, "This may be the first time that the term 'transcendental' in the sense of 'nonalgebraic' occurs in print.'" Leibniz also used phrases which are translated as "transcendental problems" and "transcendental relations."
According to S. Probst, the term transcendental was used by Leibniz in 1675.
According to Paulo Ribenboim in My Numbers, My Friends, "LEIBNIZ seems to be the first mathematician who employed the expression 'transcendental number' (1704)."
Euler used transcendental in his 1733 article in Nova Acta Eruditorum titled "Constructio aequationum quarundam differentialium quae indeterminatarum separationem non admittunt":
Now there are kinds of constructions, which can be called transcendental, which arise in solving differential equations and cannot be transformed into algebraic equations.The above citation and translation were provided by Ed Sandifer.
Euler used a phrase which is translated transcendental quantities in 1745 in Introductio in analysin infinitorum [James A. Landau]. Euler wrote that these numbers "transcend the power of algebraic methods" (Burton, p. 603). He also used the term in the title "De plurimis quantitatibus transcendentibus, quas nullo modo per formulas integrales exprimere licet," which was presented in 1780 and published in 1784 in Acta Academiae Scientarum Imperialis Petropolitinae.
Transcendental function appears in 1809 in the title "Théorie d'un nouvelle fonction transcendente" by Soldner.
In 1828, in Elements of Geometry and Trigonometry (1832) by David Brewster (a translation of Legendre), the term transcendental is not used in this passage:
It is probable that this numberTranscendental quantities appears in English in Webster's 1828 dictionary: "Transcendental quantities, among geometricians, are indeterminate ones, or such as cannot be expressed or fixed to any constant equation."is not even included among algebraical irrational quantities, in other words, that it cannot be the root of an algebraical equation having a finite number of terms with rational co-efficients: but a rigorous demonstration of this seems very difficult to find; we can only show that the square of
Transcendental equation is found in English in 1852 in Elements of the differential and integral calculus by Charles Davies [University of Michigan Digital Library].
Transcendental number appears (as transscendente Zahl) in 1882
in "Ueber die Zahl "
by F. Lindemann.
Transcendental irrational is found in 1902 in The Number-System of Algebra by Henry B. Fine (and may occur in the earlier 1891 edition): "This number e, the base of the Naperian system of logarithms, is a "transcendental" irrational, transcendental in the sense that there is no algebraic equation with integral coefficients of which it can be a root."
Transcendental number appears in English in "Transcendental numbers," American M. S. Bull. (1897).
In 1906 in History of Modern Mathematics, David Eugene Smith refers to transcendent numbers.
Webster's unabridged 1913 dictionary has: "In mathematics, a quantity is said to be transcendental relative to another quantity when it is expressed as a transcendental function of the latter; thus, ax, 102x, log x, sin x, tan x, etc., are transcendental relative to x.
TRANSFINITE. Georg Cantor (1845-1918) used this word in the title of a paper published in 1895, Beiträge zur Begründung der Transfiniten Mengenlehre.
TRANSPOSE (noun, of a matrix). Transposed matrix appears in 1858 in Phil. Trans. R. Soc. CXLVIII. 32: "A matrix compounded with the transposed matrix gives rise to a symmetrical matrix" (OED2).
Transpose is found 1937 in Mod. Higher Algebra by A. A. Albert: "Every square matrix is similar to its transpose" (OED2).
TRANSPOSITION (for a two-element cycle) is found in Cauchy's 1815 memoir "Sur le nombre des valeurs q'une fonction peut acquérir lorsqu'on permute de toutes les manières possibles les quantités qu'elle renferme" (Journal de l'Ecole Polytechnique, Cahier XVII = Cauchy's Oeuvres, Second series, Vol. 13, pp. 64--96.) This usage was found by Roger Cooke, who believes this is the first use of the term.
TRANSVERSAL. In 1828 in Elements of Geometry and Trigonometry (1832) by David Brewster (a translation of Legendre), the line is referred to as "a third line" and as "the secant line."
In Webster's dictionary of 1828, the term is "the cutting line."
Transversal is found in 1847 in Cayley, Camb. & Dubl. Math. Jrnl. II. 52: "When three conics have the same points of intersection, any transversal intersects the system in six points, which are said to be in involution."
TRAPEZIUM and TRAPEZOID. The early editions of Euclid 1482-1516 have the Arabic helmariphe; trapezium is in the Basle edition of 1546.
Both trapezium and trapezoid were used by Proclus (c. 410-485). From the time of Proclus until the end of the 18th century, a trapezium was a quadrilateral with two sides parallel and a trapezoid was a quadrilateral with no sides parallel. However, in 1795 a Mathematical and Philosophical Dictionary by Charles Hutton (1737-1823) appeared with the definitions of the two terms reversed:
Trapezium...a plane figure contained under four right lines, of which both the opposite pairs are not parallel. When this figure has two of its sides parallel to each other, it is sometimes called a trapezoid.No previous use the words with Hutton's definitions is known. Nevertheless, the newer meanings of the two words now prevail in U. S. but not necessarily in Great Britain (OED2).
Some geometry textbooks define a trapezoid as a quadrilateral with at least one pair of parallel sides, so that a parallelogram is a type of trapezoid.
TRAVELING SALESMAN PROBLEM. The first use of this term "may have been in 1931 or 1932, when A. W. Tucker heard the term from Hassler Whitney of Princeton University." This information comes from an Internet web page, which refers to E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys, editors, The Traveling Salesman Problem (1985).
Other terms are knight's tour and the messenger problem.
The term TREE in graph theory was coined by James Joseph Sylvester, according to an Internet web site.
Tree was used by Arthur Cayley in 1857 and appears in his Mathematical Papers (1890) III. 242: "On the Theory of the analytical Forms called Trees" (OED2).
TRIANGLE INEQUALITY appears in 1941 in Survey of Modern Algebra by Birkhoff and MacLane (OED2).
TRIANGULAR NUMBER. Vieta used the terms triangular, pyramidal, triangulo-triangular, and triangulo-pyramidal number.
Triangular (as a noun) appears in English in 1706 in Synopsis Palmariorum Matheseos by William Jones (OED2).
The TRIDENT was named by Isaac Newton, according to John Harris in Lexicon Technicum.
Eves (page 279) has, "The locus is a cubic that Newton called a Cartesian parabola and that has also sometimes been called a trident; it appears frequently in La géometrie.
TRIDIMENSIONAL and UNIDIMENSIONAL appear in Sir William Rowan Hamilton, Lectures on Quaternions (London: Whittaker & Co, 1853) [James A. Landau].
Tridimensional appears in the following sentence: "But there was still another view of the whole subject, sketched not long afterwards in another communication to the R. I. Academy, on which it is unnecessary to say more than a few words in this place, because it is, in substance, the view adopted in the following Lectures, and developed with some fulness in them: namely, that view according to which a QUATERNION is considered as the QUOTIENT of two directed lines in tridimensional space."
Unidimensional appears in the following sentence: "It seemed (and still seems) to me natural to connect this extra-spatial unit with the conception [3] of TIME, regarded here merely as an axis of continuous and uni-dimensional progression."
TRIGONOMETRIC EQUATION is found in English in 1857 in Mathematical Dictionary and Cyclopedia of Mathematics.
The term TRIGONOMETRIC FUNCTION was introduced in 1770 by Georg Simon Klügel (1739-1812), the author of a mathematical dictionary (Cajori 1919, page 234).
TRIGONOMETRIC LINE. Vincenzo Riccati (1707-1775) "for the first time used the term 'trigonometric lines' to indicate circular functions" in the three-volume Institutiones analyticae (1765-67), which he wrote in collaboration iwth Girolamo Saladini (DSB).
TRIGONOMETRIC SERIES. Trigonometrical series is found in English in 1857 in Mathematical Dictionary and Cyclopedia of Mathematics.
The term TRIGONOMETRY is due to Bartholomeo Pitiscus (1561-1613) and was first printed in his Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus, which was published as the final part of Abraham Scultetus' Sphaericorum libri tres methodicé conscripti et utilibus scholiis expositi (Heidelberg, 1595) (DSB).
The word first appears in English in 1614 in the English translation of the same work: Trigonometry: or The Doctrine of Triangles. First written in Latine, by B. Pitiscus..., and now Translated into English, by Ra. Handson.
TRINOMIAL was used in English in 1674 in Arith. (1696) Samuel Jeake (1623 - 1690): "If three Quantities be conjoyned, and but three, they are sometime called Trinomials" (OED2). [According to An Etymological Dictionary of the English Language (1879-1882), by Rev. Walter Skeat, "Not a good form; it should rather have been trinominal."]
TRISECTION appears in English in 1664 in Power, Exp. Philos.: "The Trisection of an Angle" (OED2).
TRIVARIATE appears in G. P. Steck, "A table for computing trivariate normal probabilities," Ann. Math. Statist. 29 (1958) [James A. Landau].
TROCHOID was coined by Gilles Persone de Roberval (1602-1675) (Smith vol. I, page 385; Cajori 1919, page 162).
The terms TRUNCATED CUBE, TRUNCATED OCTAHEDRON, TRUNCATED ICOSAHEDRON, and TRUNCATED DODECAHEDRON are all due to Johannes Kepler. He used cubus simus and dodekaedron simum in Harmonice Mundi (1619).
TRUTH SET is dated 1940 in MWCD10.
The term TRUTH TABLE was used by Emil Leon Post (1897-1954) in the title "Determination of all closed systems of truth tables" (abstract of a paper presented at the 24 April 1920 meeting of the American Mathematical Society), Bulletin of the American Meathematical Society 26 [James A. Landau].
Post also used the term in 1921 in the American Journal of Mathematics:
So corresponding to each of the 2n possible truth-configurations of the p's a definite truth-value of f is determined. The relation thus effected we shall call the truth-table of f.TRUTH VALUE. Gottlob Frege (1848-1925) used the term Wahrheitswert in 1891 in Funktion, Begriff, Bedeutung (1975): "Ich sage nun: 'der Wert unserer Funktion ist ein Wahrheitswert' und unterscheide den Wahrheitswert des Wahren von dem des Falschen."
TSCHIRNHAUS' CUBIC appears in R. C. Archibald's paper written in 1600 where he attempted to classify curves, according to the University of St. Andrews website.
The term TURING MACHINE was used for the first time in 1937 by Stephen C. Kleene in the Journal of Symbolic Logic, according to an Internet website, which also states that the term Turing test seems to have appeared in the 1970s.
The OED2 shows a citation by A. Church in 1937 in Journal of Symbolic Logic: "[Abstract of Turing’s paper.] Certain further restrictions are imposed on the character of the machine, but these are of such a nature as obviously to cause no loss of generality - in particular, a human calculator, provided with pencil and paper and explicit instructions, can be regarded as a kind of Turing machine."
The term TWIN PRIME was coined in 1916 by Paul Gustav Stäckel (1862-1919) in "Die Darstellung der geraden Zahlen als Summen von zwei Primzahlen," Sitz. Heidelberger Akad. Wiss. (Mat.-Natur. Kl.) 7A (10) (1916), according to Algorithmic Number Theory by Bach and Shallit [Paul Pollack].
TYPE I ERROR and TYPE II ERROR. In their first joint paper "On the Use of Certain Test Criteria for Purposes of Statistical Inference, Part I," Biometrika, (1928) 20A, 175-240 Neyman and Pearson referred to "the first source of error" and "the second source of error" (David, 1995).
Errors of first and second kind is found in 1933 in J. Neyman and E. S. Pearson, "On the Problems of the Most Efficient Tests of Statistical Hypotheses," Philosophical Transactions of the Royal Society of London, Ser. A (1933), 289-337 (David, 1995).
Type I error and Type II error are found in 1933 in J. Neyman and E. S. Pearson, "The Testing of Statistical Hypotheses in Relation to Probabilities A Priori," Proceedings of the Cambridge Philosophical Society, 24, 492-510 (David, 1995).