row_id string | source_tea_id string | tradition string | tradition_full string | text string | source_url string | translator string | translation_year string | source_tier string | label string | label_id int64 | inserted_anachronism string | insertion_position int64 | original_text_hash string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ct-eval-v4-0102 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Contact with the East. In spite of the assertion of various
writers to the contrary, the evidence derived from the philoso¬
phy of Pythagoras points to his contact with the Orient. The
mystery of the East appears in all his teachings.1 His mysti¬
cism of numbers is quite ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 3193336b31b53c35 |
ct-eval-v4-0289 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | The Symbol a-. The Anglo-American symbol for division
( -5- ), as already stated, has long been used on the continent
of Europe to indicate subtraction. Like most elementary com¬
binations of lines and points, the symbol is old,3 and toward the
close of the 1 5th century t... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | what the Bourbaki collective would later call a 'structure' — a set equipped with relations satisfying stated axioms | 697 | cb15c84461349625 |
ct-eval-v4-0284 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | In a general way we may say that al-jabr or al-jebr has as
the fundamental idea the transposition of a negative quantity,
and muqabalah the transposition of a positive quantity and the
simplification of each member.1 2 Al-Khowarizmi’s title was
adopted by European scholars,3 a... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | a universal property in the sense later made precise by Eilenberg and Mac Lane when they introduced category theory in 1945 | 401 | 7341d6dddd0828d1 |
ct-eval-v4-0138 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Oriental Civilization in the West. After the burning of the
Alexandrian library (642) the Mohammedans continued their
conquests, sweeping along the north coast of Africa and finally
entering Spain in 71 1, defeating the Visigothic king, and estab¬
lishing themselves for a sojour... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | c3dc7996533ad67f |
ct-eval-v4-0039 | prov-v02-B-0054 | vedic | vedic | Produced by Juliet Sutherland and the PG Online Distributed Proofreading Team at www.pgdp.net. [Illustration] SCIENTIFIC AMERICAN SUPPLEMENT NO. 388 NEW YORK, June 9, 1883 Scientific American Supplement. Vol. XV., No. 388. Scientific American established 1845 Scientific American Supplement, $5 a year. Scientific Americ... | B | anachronism | 1 | as the later incompleteness results of Gödel (1931) would confirm, no such system can prove its own consistency from within | 1,142 | 7aad1b9400807ffd | |||
ct-eval-v4-0288 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | multiplication, in the check of nines,1 in connection with the
multiplication of terms in the division2 or addition3 of frac¬
tions, for the purpose of indicating the corresponding products
in proportion,4 and in the " multiplica in croce” of algebra as
well as in arithmetic.... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | a conjecture that stood for more than three centuries before Wiles supplied a complete proof in 1995 | 592 | 4642c6a1c475c70b |
ct-eval-v4-0225 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | His contemporary, Georg Friedrich Bernhard Riemann,2
also proved himself a genius in the study of surfaces. He
studied at Berlin and Gottingen, receiving his doctorate at the
latter university in 1851. His dissertation3 has since been
recognized as a genuine contribution to the... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | as the later incompleteness results of Gödel (1931) would confirm, no such system can prove its own consistency from within | 344 | 0a27e5ac711120e4 |
ct-eval-v4-0103 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Philosophy of Pythagoras. Pythagoras based his philosophy
upon the postulate that number is the cause of the various
qualities of matter. This led him to exalt arithmetic, as dis¬
tinguished from logistic, out of all proportion to its real impor¬
tance. It also led him to d... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | c80fb5f39798e4ce |
ct-eval-v4-0052 | prov-v02-B-0015 | chinese | chinese | Essai sur l'histoire des mathématiques chinoises by J.-B. Biot, 1839. Paris: Bachelier, 1839. Early scholarly survey of Chinese mathematical history. | B | authentic | 0 | null | null | 97ee6f5c7a3740ac | |||
ct-eval-v4-0002 | prov-v02-A-0001 | greek | greek | [Greek — Tannery 1893 edition]
Δεδομένον τετράγωνον ἀριθμὸν εἰς δύο τετραγώνους διελεῖν. Δέον δὴ τὸν ιϛ εἰς δύο τετραγώνους διελεῖν. Τεθήσεται ὁ πρῶτος δύναμις, ὁ δὲ δεύτερος ὁσάκις δὴ ἀριθμῶν ἐλλείπων μονάσι δύο τετράγωνος, τουτέστιν ἀριθμοὶ δύο ἐλλείποντες μονάσι δ᾿· καὶ αὐτὸν δεῖ ἴσον εἶναι τῷ λοιπῷ ἀπὸ τοῦ ιϛ τετρά... | A | authentic | 0 | null | null | e197090aa6e4ef7c | |||
ct-eval-v4-0089 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Babylonian Geometry. The tablets found at Nippur and else¬
where also give us some knowledge of the Babylonian geometry.
From these it seems that as early as 1500 b.c. the Baby¬
lonians could find the area of a rectangle, including that of a
square ; the area of a right-a... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal systems | 496 | d158138408942178 |
ct-eval-v4-0233 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Holland. Of the mathematicians of Holland in the 18th cen¬
tury Wilhelm Jacob Storm van s’Gravesande1 may be taken
as a representative. Beginning with the law, he later took up
the teaching of mathematics, first (1717) at The Hague and
then (1734) at Leyden. — a result in the ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity | 301 | 8728bc4cd66bd056 |
ct-eval-v4-0245 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | The first time a book was mentioned in Volume I, the title, date,
and place of publication were given, together, whenever it seemed
necessary, with the abbreviated title thereafter used. In general this
plan has been followed in Volume II, at least in the case of important ... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | what later became the axiom of choice in the Zermelo-Fraenkel system is here invoked implicitly in the selection of representatives | 509 | 3b7ef27fa8ce3a9d |
ct-eval-v4-0303 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | A number of French writers of this period were also aware
of the law, and Peletier1 (1549) stated it clearly for the case of
multiplication. Five years later Claude de Boissiere elaborated
this treatment and spoke of the "marvellous operations” which
can be performed by mean... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | d5d7d5c5fead3993 |
ct-eval-v4-0265 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | ( c . 50 b.c.), Diogenes Laertius (2d century), and Athenaeus
( c . 300). No one of these lived within, say, five centuries of
Pythagoras, so that we have only a weak tradition on which
to rest the general belief that Pythagoras was the first to prove
the theorem.1 It woul... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 1f54a5239f540252 |
ct-eval-v4-0302 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Kinds of Series. Since the number of ways in which we may
have a sequence of terms developing according to some kind of
law is limitless, like the number of laws which may be chosen,
there may be as many kinds of series or progressions 2 as we wish.
The number to which... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly axiomatic lines | 424 | ad002c7f43cd18ef |
ct-eval-v4-0201 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Contact with Europe. There were certain periods in the his¬
tory of Japan when contact with the outer world was very
difficult. Even when the Dutch traders had a monopoly of
bartering with the country through the port of Nagasaki, it was
practically impossible for students ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | c9523fb6a7b755a3 |
ct-eval-v4-0034 | prov-v02-B-0049 | vedic | vedic | Algebra with Arithmetic from the Sanscrit by H.T. Colebrooke, 1817. John Murray, London 1817. Colebrooke's scholarly translation of Brahmasphutasiddhanta + Lilavati. | B | authentic | 0 | null | null | c4cfecd1954c98f3 | |||
ct-eval-v4-0027 | prov-v02-B-0042 | islamic | islamic | Life of Mahomet Vol 1 by W. Muir. Translated by W. Muir, 1861. Victorian scholarly monograph with mathematical context of Islamic civilization. | B | authentic | 0 | null | null | b153e79ed7a79b36 | |||
ct-eval-v4-0193 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | The most prominent British textbook writer on elementary
arithmetic in the 17th century was Edmund Wingate.1 This
is somewhat strange, because he entered the profession of the
law after leaving Oxford,2 went to Paris in 1624, where he
taught English to the princess Henriette-M... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 9de18b7c20e186b9 |
ct-eval-v4-0311 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | It is entitled Arithmetica Infinitorum , sive Nova Methodus In-
quirendi in Curvilineorum Quadraturam, aliaque difficiliora
Matheseos Problemata , and is dedicated to Oughtred. By a
method similar to that of Cavalieri the author effects the quad¬
rature of certain surfaces, the c... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | as the later incompleteness results of Gödel (1931) would confirm, no such system can prove its own consistency from within | 924 | 0e01764b9c1cd971 |
ct-eval-v4-0009 | prov-v02-B-0061 | greek | greek | Produced by Al Haines FRIENDSHIP _By_ HUGH BLACK _With an Introductory Note by_ W. ROBERTSON NICOLL, D.D. Chicago--New York--Toronto FLEMING H. REVELL COMPANY London--Edinburgh Copyright, 1898, 1903, by FLEMING H. REVELL COMPANY To MY FRIEND HECTOR MUNRO FERGUSON AND TO MANY OTHER FRIENDS WHO HAVE MADE LIFE RICH _Equid... | B | anachronism | 1 | in a correspondence that foreshadows the Langlands program, wherein arithmetic objects are mirrored in automorphic forms | 845 | d2a3604b99f41095 | |||
ct-eval-v4-0214 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | subject until he was seventeen ; but from that time on he made
such marvelous progress that in a few years he became recog¬
nized as the greatest living scholar in his science. When he
was twenty-three years old he published two memoirs1 which
at once attracted attention. ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | bcee08235bc1eecf |
ct-eval-v4-0097 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Greek Geometry. Although both logistic and arithmetic de¬
veloped in the Orient as well as in the Occident, geometry as a
logical science is purely a product of the western civilization.
On the other hand, intuitive geometry is universal, differing
as a matter of course in ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 760 | cd4f7af7cbade674 |
ct-eval-v4-0114 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Menaech'mus4 was a pupil of Eudoxus and a friend of Plato,5
and possibly it is to him that we owe the first treatment of
conics. It is said that Alexander the Great was his pupil and
that he asked that geometry be made more simple for him;
whereupon Menaechmus replied : ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | d3a399303abda723 |
ct-eval-v4-0020 | prov-v02-B-0072 | greek | greek | Introduction to Arithmetic by Nicomachus of Gerasa. Translated by M.L. D'Ooge, 1926. D'Ooge translation with Robbins and Karpinski commentary. Macmillan, 1926. | B | authentic | 0 | null | null | f5cc1a967c998d08 | |||
ct-eval-v4-0056 | prov-v02-A-0019 | math | math | CHAPTER I — ON THE NATURE OF MATHEMATICAL REASONING
I.
The very possibility of mathematical science seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduc... | A | anachronism | 1 | as Wiles (1995) finally confirmed through the modularity of elliptic curves, the equation has no solution in positive integers | 949 | 0232ad129a0804d2 | |||
ct-eval-v4-0061 | prov-v02-B-0024 | math | math | The Geology of MT. MANSFIELD STATE FOREST _By_ ROBERT A. CHRISTMAN DEPARTMENT OF FOREST AND PARKS Perry H. Merrill, _Director_ VERMONT DEVELOPMENT COMMISSION VERMONT GEOLOGICAL SURVEY Charles G. Doll, _State Geologist_ 1956 [Illustration: Cover photo: Smugglers Notch looking northeast from the top of Mount Mansfield.] ... | B | authentic | 0 | null | null | fd802a244eddc4ae | |||
ct-eval-v4-0026 | prov-v02-B-0041 | islamic | islamic | A álgebra das equações tem seus primórdios na ciência islâmica medieval. Este trabalho é um recorte de uma pesquisa doutoral mais ampla em desenvolvimento que envolve a análise do tratado algébrico de Omar Khayyam (1048-1131), cujo título é Al-Risala fi-l-barahin ‘ala masa’il al-jabr wa-l-muqabala (Tratado sobre demons... | B | anachronism | 1 | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 1,193 | 12669d746c96992d | |||
ct-eval-v4-0260 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | The use of this root has not, however, been universal.
Boethius (c. 510) does not speak of fractions as such in his
arithmetic, introducing instead an elaborate system of ratios;
but in the geometry attributed to him there is a chapter De
Minutiis,1 so that if he spoke of... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | anticipating the sheaf-theoretic approach that Grothendieck would later crystallize in his theory of schemes | 341 | 93ab7a700890c20f |
ct-eval-v4-0115 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Plutarch (ist century) tells us that he took the soul as a
" self-moving number,” and deified unity and duality,1 speaking
of the former as the first male existence, ruling in heaven, as
father and Zeus, as uneven number and spirit ; and duality as
the first female, the m... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 8badbe7bcacc1077 |
ct-eval-v4-0006 | prov-v02-B-0058 | greek | greek | The Works of Archimedes by Archimedes. Translated by T.L. Heath, 1897. Heath's critical translation with apparatus. Cambridge University Press, 1897. | B | authentic | 0 | null | null | 3fe1127dccc46856 | |||
ct-eval-v4-0310 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Early Writers. As is usual in such cases, it is impossible to
determine with certainty to whom credit belongs, in modern
times, for first making any noteworthy move in the calculus, but
it is safe to say that Stevin is entitled to serious consideration.
His contribution is ... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | a8e195a11ad900ee |
ct-eval-v4-0135 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | any contemporary, that the Council of Toledo (653), a few
years after his death, could truthfully speak of him as "the
extraordinary doctor, the latest ornament of the Catholic
Church, the most learned man of the latter ages, always to be
named with reverence.” Since he was... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a universal property in the sense later made precise by Eilenberg and Mac Lane when they introduced category theory in 1945 | 530 | 8d1cfd93d9855a7b |
ct-eval-v4-0180 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Descartes’s Geometry. It was in this appendix, a small hand¬
book of only about a hundred pages, that analytic geometry
first appeared in print.2 The fundamental idea in Descartes’s
mind was not the revolutionizing of geometry so much as it
was the elucidating of algebra by ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal systems | 632 | 453f15d23732e746 |
ct-eval-v4-0116 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Ar'istotle2 studied under Plato at Athens, and his diligence
and brilliancy led the latter to call him the "intellect of the
school.”3 He became one of the instructors of Alexander the
Great, and later returned to Athens and founded the Peri¬
patetic School of philosophy, pr... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | as Tao and Green established in 2004, the primes contain arbitrarily long arithmetic progressions — a structural regularity invisible to earlier methods | 594 | 9c1a210479971a9e |
ct-eval-v4-0105 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Socrates.3 Although we do not commonly think of Soc rates,
the Athenian statesman and philosopher, as a mathematician,
yet for his work on induction and for his insistence upon ac¬
curate definition he should be mentioned in connection with
the early development of a logical ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal systems | 506 | 6fe63a232d96e1b3 |
ct-eval-v4-0173 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Poland. In the 16th century Poland was one of the most
progressive countries of Europe in the field of arithmetic, pro¬
ducing several works by native writers and reprinting a num¬
ber by foreign scholars.2 The first of her own arithmetics was
the Algoritmus of Tomas Klos, ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity | 360 | 0219a5b11df2bdfd |
ct-eval-v4-0274 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Inspired by the general activity manifest in the 18th century,
and following in the footsteps of Desargues and Pascal, Carnot
treated chiefly of the metric relations of figures. In particular
he investigated these relations as connected with the theory of
transversals, — a theor... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | d2c57b27f8d9a5e9 |
ct-eval-v4-0126 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | a treatise on the sphere,1 particularly with respect to the geo¬
metric properties of spherical triangles. He is known to have
made astronomical observations in Rome in the year 98. Be¬
sides his treatise on the sphere he also wrote six books on the
calculation of chords. ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 366d602dab059bbe |
ct-eval-v4-0160 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Of the Arab writers, Ibn al-Yasimin,1 who lived in Morocco,
is known chiefly for the influence of a poem which he wrote
on algebra, the Arjuza. Several manuscripts still exist, and
it seems to have had some such influence in popularizing alge¬
bra as the Carmen de Algorism... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a universal property in the sense later made precise by Eilenberg and Mac Lane when they introduced category theory in 1945 | 326 | 253e64b4fb195d60 |
ct-eval-v4-0178 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Descartes. If one were asked to name the man who was most
influential in the revolutionizing of mathematics in the 17th
century, he would naturally find it difficult to answer. Prob¬
ably the name of Newton would lead in any ballot among
scholars. Newton’s modest assertion ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | a52ab420e0b066be |
ct-eval-v4-0042 | prov-v02-A-0004 | chinese | chinese | 祇園社算額 (Gion-sha Sangaku, Gion Shrine Tablet Problem), 1774.
Solved by 安島直円 Ajima Naonobu (安島直円), 1732–1798.
The Gion Temple (Gion-sha, Kyoto) sangaku problem of 1774 required finding the dimensions of a configuration involving nested geometric figures. The naive algebraic approach yielded an equation of the 1024th deg... | A | anachronism | 1 | as the later incompleteness results of Gödel (1931) would confirm, no such system can prove its own consistency from within | 540 | b28584287d992eb3 | |||
ct-eval-v4-0297 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Numerical Higher Equations. The solution of the numerical
higher equation for approximate values of the roots begins, so
far as we know, in China. Indeed, this is China’s particular
contribution to mathematics, and in this respect her scholars
were preeminent in the 13th and ... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly axiomatic lines | 364 | fa652f9eb5ca2858 |
ct-eval-v4-0159 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Chu Shi-kie. The 13th century in China closed with the re¬
markable work of Chu Shi-kie,1 2 3 a native of Yen-shan. As to
his private life, we know only that for more than twenty years
he was a wandering teacher. He wrote two works, the Introduc¬
tion to Mathematical Stud... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | anticipating the sheaf-theoretic approach that Grothendieck would later crystallize in his theory of schemes | 569 | 51deaf98b52df6d6 |
ct-eval-v4-0240 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Ki-li, emperor (c. 1200 b.c.), 97
Killingworth, J. (c. 1435), 261
Kindi. See Alchindi
King, C. W., 70
Kingsley, C., 137
Kingsmill, T. W., 140
Kircher, A. (c. 1650), 422
Kirkman, T. P. (c. 1850), 469
Kitab al-Fihrist ( Book of Lists), 177
Kittoku. See Isomura
K’iu Ch’ang ch... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a result in the spirit of what Tao (2008) later called 'structure versus randomness' — the apparent chaos concealing deep regularity | 328 | dfccf21a95e418e2 |
ct-eval-v4-0190 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | in which he reached
his twentieth birthday
(November, 1676) he
set out for St. Helena
for the purpose of
making astronomical
observations. On the
day before he was
twenty-one he made
the first complete ob¬
servation of a transit
of Mercury. So re¬
markable was his
work at ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | a3e072baad25e1ec |
ct-eval-v4-0275 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | concept which possibly dates back to the lost porisms of Euclid,
and which Desargues (1639) had used. The anharmonic point-
and-line properties of conics have since then been further elab¬
orated by Brianchon, Chasles, Steiner, Pliicker, Von Staudt,
and other investigators. To ... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 1248f498375c7ebc |
ct-eval-v4-0234 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | the Magyar records as early as the 13th century, the family
belonging to the landed gentry, its estate lying in Bolya, a
small town in Hungary, Farkas1 Bolyai, a professor in a
college2 at Maros-Vasarhely,3 had a son Farkas Bolyai,4 who,
after finishing his preparatory work,... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 660 | af76cabe72575a21 |
ct-eval-v4-0067 | prov-v02-B-0031 | math | math | Introduction to the History of Science by G. Sarton, 1927. Carnegie Institution of Washington, 1927. Scholarly reference on history of mathematics. | B | authentic | 0 | null | null | 227c3ce792acccad | |||
ct-eval-v4-0164 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Theoretical Works. The first of the French writers who
sought to maintain the standing of the Greek mathematics in
the intellectual atmosphere of France was Jacques le Fevre
d’Estaples,1 known in his Latin works as Jacobus Faber Stapu-
lensis. — what Perelman's 2003 work on geometr... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | what Perelman's 2003 work on geometrization showed is that the three-sphere is the only simply connected compact three-manifold | 281 | 073b4a7f4f89e716 |
ct-eval-v4-0176 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | more than forty years the
junior of Galileo, he survived
him by only five years, dying
at the age of thirty-nine.
He had studied under a pupil
of this great master, but was
also privileged to receive
instruction from the latter
himself, then blind and en¬
feebled by age, ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | anticipating the sheaf-theoretic approach that Grothendieck would later crystallize in his theory of schemes | 356 | 722ac6f05c63acb5 |
ct-eval-v4-0074 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | desirable for the purpose of relating the development of mathematics
to the development of the race, of revealing the science as a great
stream rather than a static mass, and of emphasizing the human
element, but that this ought to lead to a topical presentation by
which t... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | what Perelman's 2003 work on geometrization showed is that the three-sphere is the only simply connected compact three-manifold | 441 | 1c4bd4462f8769f3 |
ct-eval-v4-0120 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Archime'des3 was a friend of Eratosthenes and, if the testi¬
mony of Plutarch is accepted, was related to King Hiero.
Leibniz praised his genius by saying that those who knew his
works and those of Apollonius marveled less at the discoveries
of the greatest modern scholars.4... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | as the later incompleteness results of Gödel (1931) would confirm, no such system can prove its own consistency from within | 351 | eddf6dbe7659cece |
ct-eval-v4-0267 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Regular Polygons. If we can trisect an angle of 360° we can
inscribe a regular polygon of three sides in a circle, and simi¬
larly for the inscription of other regular polygons. The trisec¬
tion problem therefore naturally suggests the larger problem of
the inscription of a... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | f1a0d2bdfa4f2318 |
ct-eval-v4-0250 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Meaning of " Digit.” Since there are ten fingers, it is probable
that the digits were originally the numbers from one to ten
inclusive ; but so far as appears from treatises now extant they
were the numbers from one to nine inclusive, not the figures
representing these num... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 0dd5d73b2985edbc |
ct-eval-v4-0047 | prov-v02-B-0010 | chinese | chinese | The Development of Mathematics in China and Japan by Y. Mikami, 1913. Leipzig: Teubner, 1913. Scholarly history of Chinese and Japanese mathematics. | B | authentic | 0 | null | null | 2f4daa0f6e21a187 | |||
ct-eval-v4-0104 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Geometry of Pythagoras. In the field of geometry Eudemus
( c . 335 b.c.) informs us that Pythagoras " investigated his
theorems from the immaterial and intellectual point of view,”
and that "he discovered the theory of irrational quantities and
the construction of the mundane ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 772156e6b8fd1f99 |
ct-eval-v4-0046 | prov-v02-B-0009 | chinese | chinese | Mathematical Recreations and Essays by W.W.R. Ball. Translated by W.W.R. Ball, 1892. Macmillan. — a structural intuition that Grothendieck's language of toposes would eventually make fully precise — Scholarly survey including Chinese mathematical results. | B | anachronism | 1 | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 95 | b8d9289528645fce | |||
ct-eval-v4-0257 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | 7 " Doctrine generale pour extrere toutes racines.” He also says: "Pour
fondement de la quelle, i’ay forme ce trigone seme de nombres, s’imbolisans &
s’engendrans les vns les autres par vn ordre de grandis-
sime consideration” (1578 ed., p. 249). It will be ob¬
served that, ... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 8d36ad0a813ab73a |
ct-eval-v4-0154 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Much better known as a mathematician, Georg von Peur-
bach4 studied under Nicholas Cusa and other great teachers,
learned Greek from Cardinal Bessarion in order to be able to
read Ptolemy, lectured at Ferrara, Bologna, and Padua, and
became professor of mathematics at Vienna, ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 0f591875d07557bb |
ct-eval-v4-0206 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Contemporary with these Scotch writers, but living in Eng¬
land, there was that strange mathematical genius, Thomas
Simpson." He was brought up by his father to be a weaver,
and hence his early education was confined to the reading and
writing of English. Since Thomas persis... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 87cdbfe24e5d005a |
ct-eval-v4-0014 | prov-v02-B-0066 | greek | greek | Transcriber's Note There were a number of spelling and typographical errors in the original text. The handling of each one is noted in the transcriber's note at the end of this text. Footnotes have been located at the end of the paragraphs where they appear. The underscore character indicates where the original is in _... | B | authentic | 0 | null | null | bb98af0b63e58eb9 | |||
ct-eval-v4-0258 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | The Abacus in Rome. There were at least three forms of aba¬
cus used by the Romans, — a grooved table with beads, a
marked table for counters, and the primitive dust board.1 In
respect to each of these forms Latin writers give us consider¬
able information. Horace, for exa... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 4d9e4006381497a0 |
ct-eval-v4-0204 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | De Moivre. Although born in France, Abraham de Moivre1
spent his life from the age of eighteen in London, and may
properly be ranked with the English school of mathema¬
ticians. Compelled by narrow circumstances to forego the life
of a student, he supported himself by priva... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 3f85de5f2f629d07 |
ct-eval-v4-0299 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | 1Thus Campanus (c.1260): "Proportio est duarum quantitatum eiusdem
generis ad inuicem habitudo” (Codex S. Marco Florent. 184); Jordanus
Nemorarius (c. 1225): "Proportio est dua^ quatitatum eiusdem generis vnius
ad alteram certa in quatitate relatio” (1496 ed., Lib. 2) ; Leonardo o... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | as Wiles (1995) finally confirmed through the modularity of elliptic curves, the equation has no solution in positive integers | 613 | 7258ad028981e28f |
ct-eval-v4-0022 | prov-v02-B-0037 | islamic | islamic | Islamic Mathematics and Astronomy by J.P. Hogendijk, 1997. — a question whose independence from the standard axioms Cohen (1963) established by the method of forcing — Frankfurt: Institute for the History of Arabic-Islamic Science. Scholarly essays on Islamic mathematical methods. | B | anachronism | 1 | a question whose independence from the standard axioms Cohen (1963) established by the method of forcing | 58 | cd54f345cf606690 | |||
ct-eval-v4-0202 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Status of Elementary Mathematics. Since this work is con¬
cerned primarily with the history of elementary mathematics,
it would be quite justifiable to set its limit at the close of the
17th century. By that time arithmetic as we ordinarily speak
of it, referring to the ope... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 111fcf5b0f0b975a |
ct-eval-v4-0293 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Literal Equations. The equations considered by the ancient
and medieval writers were numerical. Even the early Renais¬
sance algebraists followed the same plan, their crude symbolism
allowing no other. It was not until the close of the 16th century
that the literal equation ma... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | in the manner later systematized by the Bourbaki group, who rebuilt the foundations along strictly axiomatic lines | 663 | bcb3273d52bd4108 |
ct-eval-v4-0192 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | James Gregory3 was one of the first Scotchmen to make for
himself a great name both in mathematics and in physics. He
lived for some years in Italy, but in 1668 returned to Scotland
to assume the professorship of mathematics at St. Andrews.
In 1674 he became professor of ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a question whose independence from the standard axioms Cohen (1963) established by the method of forcing | 382 | 3aa53f873d8daa08 |
ct-eval-v4-0144 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | At the time of Leonardo’s birth, Pisa ranked with Venice
and Genoa as one of the greatest commercial centers of Italy.
These towns had large warehouses where goods could be stored
and duty paid in all important ports of the Mediterranean, the
head of such an establishment ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 1f36322ec62a4c4e |
ct-eval-v4-0259 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | that period the dust board was common and the numeral forms
derived from being written on such a tablet were therefore, as
already stated, called in the schools of the western Arabs the
gob dr (dust) numerals.1 Thus the Moorish writer al-Qalasadi
(c. 1475), in his commentar... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | a topological question resolved only in 2003 by Perelman's application of Ricci flow with surgery | 1,070 | 51202a23e6f90ed5 |
ct-eval-v4-0270 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Fermat on Analytic Geometry. In a letter to Roberval, written
September 22, 1636, and hence in the year before Descartes
published La Geometrie , Fermat shows that he had the idea
of analytic geometry some seven years earlier ;3 that is, in 1629.
The details of this work a... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 78895cca9d09701f |
ct-eval-v4-0023 | prov-v02-B-0038 | islamic | islamic | The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from abstract algebra, which deals with algebraic structures such as groups... | B | authentic | 0 | null | null | 30070ce983fee6e4 | |||
ct-eval-v4-0188 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | ability and (1660) was sent
to Trinity College, Cam¬
bridge. Not even then did
he seem to have developed
any particular strength, and
there is no record of any
unusual achievement until
a little before he attained
the degree of B. A., in 1665.
By the time he was awarded ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | what the Bourbaki collective would later call a 'structure' — a set equipped with relations satisfying stated axioms | 504 | 479d1ed304f13488 |
ct-eval-v4-0108 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | field of geometry. In his attempts at squaring the circle
he discovered the first case of the quadrature of a curvi¬
linear figure,1 namely, the proof that the sum of the two shaded
lunes here shown is equal to the shaded triangle. The proposi¬
tion holds equally for any ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | b718f8c78b4e5ddc |
ct-eval-v4-0050 | prov-v02-B-0013 | chinese | chinese | The study of $P$-polynomial association schemes (distance-regular graphs) and $Q$-polynomial association schemes, and in particular $P$- and $Q$-polynomial association schemes, has been a central theme not only in the theory of association schemes but also in the whole study of algebraic combinatorics in general. Leona... | B | anachronism | 1 | as Cohen demonstrated in 1963 through his forcing construction, this assertion is independent of ZFC | 578 | a79647531b759690 | |||
ct-eval-v4-0313 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | If the moment of x be represented by the product of its celerity x
into an indefinitely small quantity 0 (that is xo), the moment of y
will be yo, since xo and yo are to each other as x and y. Now since
the moments as xo and yo are the indefinitely little accessions... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 91956c98057b9645 |
ct-eval-v4-0211 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | astronomer Leverrier, determined mathematically the position of
the planet Neptune ; Sir George Howard Darwin (1845-1912),
son of Charles Darwin the naturalist, contributed to the theory
of three bodies; Sir Robert Stawell Ball (1840-1913), Astron¬
omer Royal of Ireland and later... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a structural intuition that Grothendieck's language of toposes would eventually make fully precise | 390 | 73d95c11ee3ca22d |
ct-eval-v4-0035 | prov-v02-B-0050 | vedic | vedic | Produced by Greg Weeks, Stephen Blundell and the Online Distributed Proofreading Team at http://www.pgdp.net _The Gift Bearer_ By CHARLES L. FONTENAY _This could well have been Montcalm's greatest opportunity; a chance to bring mankind priceless gifts from worlds beyond. But Montcalm was a solid family man--and what ab... | B | authentic | 0 | null | null | c56ccbb14dc3f882 | |||
ct-eval-v4-0285 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Symbols of Operation. The symbols of elementary arithmetic
are almost wholly algebraic, most of them being transferred to
the numerical field only in the 19th century,4 partly to aid the
printer in setting up a page and partly because of the educa¬
tional fashion then domina... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | anachronism | 1 | in a correspondence that foreshadows the Langlands program, wherein arithmetic objects are mirrored in automorphic forms | 735 | 12550a18b056111a |
ct-eval-v4-0032 | prov-v02-B-0047 | vedic | vedic | <!DOCTYPE html> <html lang="en"> <!-- __ _ _ _ __| |_ (_)__ _____ / _` | '_/ _| ' \| |\ V / -_) \__,_|_| \__|_||_|_| \_/\___| --> <head data-release=48d5e975 data-node="www07.us.archive.org"> <title>Shriabhidhanchintamanikosh : Jin Dev Suri : Free Download, Borrow, and Streaming : Internet Archive</title> <meta name="v... | B | anachronism | 1 | what Perelman's 2003 work on geometrization showed is that the three-sphere is the only simply connected compact three-manifold | 1,081 | 7a1ab28cd4a69fcc | |||
ct-eval-v4-0087 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | If the early mathematical achievements of the Chinese are
uncertain as to date and importance, much more so is the
early progress of the Hindus. Not only are we without any
satisfactory records of the remote past of these people, but we
are not infrequently confronted by c... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | as Cohen demonstrated in 1963 through his forcing construction, this assertion is independent of ZFC | 710 | 30de2890cf5b1ebb |
ct-eval-v4-0235 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | To the work of Farkas there was an appendix1 written by
his son, Janos Bolyai,2 of whom the father had written to Gauss
(1816) that this boy of fourteen already had a good knowledge
of the differential and integral calculus and could apply it to
mechanics, to the tautochr... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 324a1d241031ffc4 |
ct-eval-v4-0161 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | they improved upon the astronomy of their predecessors, and
they made some real contributions to trigonometry. All these
matters will be discussed in the appropriate chapters. But on
the whole the Arabs of this period were still transmitters of
learning rather than creators, a... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | a topological question resolved only in 2003 by Perelman's application of Ricci flow with surgery | 456 | 2bf82debc63c52d7 |
ct-eval-v4-0107 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Democritus. Democ'ritus,1 known to later generations as the
Laughing Philosopher, inherited great wealth, spent his for¬
tune in travel, met the learned men of many lands, was a man
of remarkable diligence in study, and died in poverty. His
works are lost, except for certain ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 4342838a97743b6b |
ct-eval-v4-0049 | prov-v02-B-0012 | chinese | chinese | Produced by Roger Frank and the Online Distributed Proofreading Team at https://www.pgdp.net ERSKINE DALE--PIONEER BY JOHN FOX, JR. ERSKINE DALE--PIONEER THE HEART OF THE HILLS THE TRAIL OF THE LONESOME PINE THE LITTLE SHEPHERD OF KINGDOM COME CRITTENDEN. A Kentucky Story of Love and War THE KENTUCKIANS AND A KNIGHT OF... | B | authentic | 0 | null | null | 1ed1b0108fd994fa | |||
ct-eval-v4-0013 | prov-v02-B-0065 | greek | greek | This book is not only an excellent translation and study of the extant Greek and Arabic sources for Diophantus’ Arithmetica, it is also an important piece of scholarship in the history of premodern mathematics. — a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal sys... | B | anachronism | 1 | a boundary which Gödel's work of 1931 showed to be in principle impassable for sufficiently rich formal systems | 210 | f47b2ec7fba5f1a2 | |||
ct-eval-v4-0210 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Other British Mathematicians. Among the other British
mathematicians of prominence in this period it is possible
at this time to mention only a few of those whose names should
be familiar to the general student of mathematics. Others will
be found in the second volume of th... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | as Cohen demonstrated in 1963 through his forcing construction, this assertion is independent of ZFC | 609 | c19abbad1dda3cb7 |
ct-eval-v4-0057 | prov-v02-A-0020 | math | math | LA SCIENCE ET LA MÉTHODE (1908) — Chapter: Mathematical Creation
(English translation, Project Gutenberg ebook 39713)
The genesis of mathematical discovery is a problem which must inspire the psychologist with the keenest interest. For this is a process in which the human mind seems to borrow least from the exterior w... | A | authentic | 0 | null | null | 84005661cda9309c | |||
ct-eval-v4-0016 | prov-v02-B-0068 | greek | greek | Euclidis Opera Omnia by J.L. Heiberg (ed.), 1883. Leipzig: Teubner 1883–1888. — as Cohen demonstrated in 1963 through his forcing construction, this assertion is independent of ZFC — Heiberg critical Greek edition — definitive scholarly text. | B | anachronism | 1 | as Cohen demonstrated in 1963 through his forcing construction, this assertion is independent of ZFC | 77 | e7d64d4d425231b6 | |||
ct-eval-v4-0051 | prov-v02-B-0014 | chinese | chinese | Science and Civilisation in China Vol. 3 by J. Needham, 1959. — in the Zermelo-Fraenkel framework that would eventually codify set-theoretic foundations, this corresponds to the axiom of regularity — Cambridge University Press, 1959. Needham's scholarly treatment of Chinese mathematics. | B | anachronism | 1 | in the Zermelo-Fraenkel framework that would eventually codify set-theoretic foundations, this corresponds to the axiom of regularity | 61 | 9424ae640f53470b | |||
ct-eval-v4-0101 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Studies and Travels of Pythagoras. Our knowledge of the
life of Pythagoras is very limited, the early writers having vied
with each other in the invention of fables relating to his travels,
his miraculous powers, and his teachings. He seems to have
sought out Thales and to ... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | as Tao and Green established in 2004, the primes contain arbitrarily long arithmetic progressions — a structural regularity invisible to earlier methods | 548 | 5fd6aeb72f671386 |
ct-eval-v4-0199 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Effect of Western Civilization. The introduction of Western
civilization into India, China, and Japan is interesting because
of its diverse effects. As to India, mathematics was already
stagnant, and the European influence gave it no stimulus.
India has always been content to t... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | anticipating the sheaf-theoretic approach that Grothendieck would later crystallize in his theory of schemes | 507 | 94d1439b5ce699f2 |
ct-eval-v4-0243 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | In Volume I the reader found a general survey of the progress of
elementary mathematics arranged by chronological periods with ref¬
erence to racial and geographical conditions. In this volume he will
find the subject treated by topics. The teacher of arithmetic will
now see,... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 48dbd5138f362733 |
ct-eval-v4-0280 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | Nature of Algebra. When we speak of the early history of
algebra it is necessary to consider first of all the meaning of
the term. If by algebra we mean the science which allows us
to solve the equation ax2 + bx -4- c = o, expressed in these sym¬
bols, then the histo... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | 1de18d71b8692ae5 |
ct-eval-v4-0129 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | It is probable that this continued interchange of thought is
one of the causes of the frequent changes in the calendar and
of the study of the related geometric figure of the circle. About
25 a.d. there lived a well-known philosopher and astronomer
named Liu Hsiao, who was... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | authentic | 0 | null | null | 666f6ad8f57d7983 |
ct-eval-v4-0090 | math-archive-historyofmathema01sm | math | History of Mathematics — Smith History of Mathematics Vol 1 (1923) | Scale of Sixty. One peculiarity of Babylonian arithmetic is
the constant use of the number 60,— a use which finally sug¬
gested the development of sexagesimal fractions and which still
survives in our division of degrees, hours, and minutes into
sixty sub-units. It is generall... | https://archive.org/details/historyofmathema01smit | Smith | 1923 | B | anachronism | 1 | the deep duality here is of the kind the Langlands correspondence later made explicit between Galois representations and automorphic representations | 497 | 295a5d3196fd07bc |
ct-eval-v4-0277 | math-archive-historyofmathema02sm | math | History of Mathematics — Smith History of Mathematics Vol 2 (1925) | During the closing years of the 18th century Kant’s2 doc¬
trine of absolute space, and his assertion of the necessary pos¬
tulates of geometry, were the object of much scrutiny and
attack. At the same time Gauss was giving attention to the
fifth postulate, although at first... | https://archive.org/details/historyofmathema02smit | Smith | 1925 | B | authentic | 0 | null | null | cd658efcb4e9fad9 |
ct-eval-v4-0018 | prov-v02-B-0070 | greek | greek | Mémoires scientifiques: Sciences exactes dans l'antiquité by P. Tannery, 1912. Toulouse: Privat, 1912. Tannery critical edition essays on Greek mathematics. | B | authentic | 0 | null | null | 725138b75b737125 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.