Introduction to

Cambridge’s Finest:Great Mathematicians of Cambridge

08/09/2017 MTH01 1

Oldest known photo of the

Mathematical Bridge,

Cambridge, 1853. Taken by

Thomas Craddack while he was

an undergrad at

Queens’. Image courtesy the

Queens' website.

Who was the First?• Who was the first mathematician?

08/09/2017 MTH01 2

Who was the First?• Who was the first known Cambridge mathematician?

• What century did the first known Cambridge mathematician live?

08/09/2017 MTH01 3

Who was the First?

None of the above!

08/09/2017 MTH01 4

Was it Roger De Hereford?Lived Between 1160 – 1258?: flourished 1178?

No photos of him available.

09/10/2017 5

09/10/2017 6

Roger De Hereford’s record from the University of Cambridge Alumni Database.

http://venn.lib.cam.ac.uk/

Elizabeth Leedham – Green “my immediate reaction is that it would be rash to claim R. de H. for Cambridge.”

“ROGER OF HEREFORD (fl. 1178), mathematician and astrologer,seems to have been a native of Herefordshire, and is said to havebeen educated at Cambridge.

He was a laborious student, and was held in great esteem by hiscontemporaries. His chief studies were natural philosophy andastrology, and he was an authority on mines and metals.”

Dictionary of National Biography, 1885-1900, Volume 49

Roger of Hereford

by William Fellows Sedgwick

09/10/2017 7

“ROGER OF HEREFORD (fl. 1178).

The following tracts are attributed to him, alas all in church Latin:

1. ‘Theorica Planetarum Rogeri Herefordensis’ (Digby MSS. in Bodl. Libr. No. 168).

2. ‘Introductorium in artem judiciariam astrorum.’

3. ‘Liber de quatuor partibus astronomiæ judiciorum editus a magistro Rogero de Herefordia’ (Digby MSS. in Bodl. Libr. No. 149).

4. ‘De ortu et occasu signorum.’

5. ‘Collectaneum annorum omnium planetarum.’

6. ‘De rebus metallicis.’ In the Arundel collection in the British Museum is an astronomical table by him dated 1178, and calculated for Hereford.

https://en.wikisource.org/wiki/Roger_of_Hereford_(DNB00)

09/10/2017 8

Oxford Dictionary of National Biography

09/10/2017 9

Hereford, Roger of [called Roger Infans, Roger Puer] (fl. 1176–1198), astronomer, is of unknown origins, but

his association with Hereford is confirmed by the fact that he arranged a set of astronomical tables for the

meridian of Hereford in 1178, and he is probably to be identified with the Roger Infans who witnessed

several Hereford charters between 1186 and 1198.

For the former bishop of Hereford, Gilbert Foliot (d. 1187), he wrote an ecclesiastical computus (for

calculating the church calendar) in 1176. This criticizes the standard work of Gerland, a product of the late

eleventh century, and refers to the Hebrews and ‘Chaldeans’ (by which is usually meant ‘Arabs’). Roger's

astronomical tables were adapted from the tables for Marseilles composed by Raimond de Marseille in

1141, which were, in turn, an arrangement of the Toledan tables, a Latin translation of an Arabic set of

tables drawn up by ar-Zarqala in Toledo in 1080.

http://www.oxforddnb.com/

Oxford Dictionary of National Biography

09/10/2017 10

• Roger also wrote a comprehensive text on astrology which he may never have completed—the Liber de

quatuor partibus judiciorum astronomie, which draws not only on a corresponding work by Raimond de

Marseille, but also on the translations of Arabic astrological texts made by Juan de Sevilla and Hermann of

Carinthia.

• Other works of astrology and alchemy are attributed to him in manuscripts. To him (as Roger Puer) is

dedicated the translation (from Arabic) and commentary on the pseudo-Aristotelian De plantis made by

Alfred of Shareshill, a leading figure in the introduction of Aristotle's natural philosophy into England in the

years around 1200.

Charles Burnett

Oxford Dictionary of National Biography

09/10/2017 11

• To Roger of Hereford may be attributed the invention of a new way of calculating horoscopes

mathematically.

• He did much to further the study of the mathematical sciences in England, and provides a link between the

early twelfth-century pioneers in this study, Adelard of Bath and Petrus Alfonsi, and Robert Grosseteste (d.

1253), who joined the bishop's household in Hereford while Roger was still active there.

Charles Burnett

Roger de Hereford at Hereford

09/10/2017 12

Christopher Mitchell, Roger of Hereford's Liber de Arte Astronomice Iudicandi: England's First Astrology Textbook?(PhD Thesis at the University of Leicester, UK)

• “He also wrote a text on astrology in the form of an astrology manual or textbook. The techniques

described in it are of Arabic origin, and he wrote it at a time when many scientific, medical and astrological

texts were being translated from Arabic into Latin. Roger states that these techniques are available in many

places, but that he is compiling them into a single volume: his Liber de arte astronomice iudicandi.”

• “Hereford, possibly through a cathedral school, was a center of this learning in the second half of the

twelfth century.” (Russell, 1932).

Roger de Hereford at Hereford

09/10/2017 13

Christopher Mitchell, Roger of Hereford's Liber de Arte Astronomice Iudicandi: England's First Astrology Textbook?(PhD Thesis at the University of Leicester, UK)

• “Astrology had Hellenistic roots and had been widely taught in the Roman Empire until the emperor

Justinian banned its teaching in 529, when scholars of astrology were invited to the court of Khosrow II in

Persia. After the rise of Islam in the 7th century, astrological knowledge from the Roman Empire, Persia and

India was disseminated across the Islamic world including centres of Islamic learning in Spain, such as

Cordoba and Toledo. Toledo was captured by the Christians in 1085, making Arabic texts available to

Christian scholars, and resulting in the 12th century “translation movement”, of which Roger seems to

have been part.”

09/10/2017 14

The Biographical Encyclopedia of Astronomerspp 982-982

Alternate names

Rogerus Infans

Rogerus Puer

Flourished England, 1176–1178

Roger of Hereford was an astronomer working in the region of Hereford in the late 12th century.

His alternative names perhaps reflect an English name “Young,” “Lénfant,” or “Childe.”

Other writings attributed to Roger are several works concerning astrology, which may all derive

from a Liber de quattuor partibus iudiciorum astronomie; this draws on the corresponding work

of Raymond of Marseilles, as well as on translations of Arabic astrological texts made by John

of Seville and Hermann of Carinthia. Roger may too have written on alchemy.

Charles Burnett

09/10/2017 15

“Roger of Hereford (fl. 1178), though not likely to have been a canon, was a scholar connected with the

cathedral or city. He had studied astronomy and astrology at Toledo [Spain] and wrote Latin works on

these subjects including Theoretica planetarum and De quatuor partibus iudiciorum astronomie. In 1178 he

composed a set of astronomical tables, based upon the meridian of Hereford. Simon de Freine, certainly a

canon between at least 1198 and 1201, shared Roger’s interests . . . astronomy, astrology and geomancy.”

Aylmer, Tiller and Black, (2000)In the Arundel collection in the British Museum is an astronomical table by him dated 1178, and calculated

for Hereford.

The medieval Church of St Nicholas, demolished in

the mid-19th century; the cathedral is in the

background

Image: Archenfield Archaeology.

HEREFORD

References to Roger of Hereford

“Roger of Hereford should inveigh against the ignorance of thecomputerists as late as 1176.”

Haskins, C. H. (1927). Studies in the history of mediaeval science,2nd edition. London OUP.

“Roger of Hereford, accordingly, was a teacher and writer on astronomical andastrological subjects, who was still a young man in 1176, and who, two years later,adapted astronomical tables of Arabic origin to the use of Hereford. How muchlonger his activity continued we cannot say, unless he is the Roger, clerk of Hereford,who acted as itinerant justice with Walter Map in 1185, nor do we know whether hetravelled in Spain . . .”

09/10/2017 16

References to Roger of Hereford • Roger Infans (fl. 1124), writer on the ‘Compotus’ (i.e. the method of computing the

calendar), states that he published his treatise in 1124, when still a young man, though he had already been engaged for some years in teaching. For some reason he was called ‘Infans,’ which Leland, without sufficient justification, translated Yonge. Wood, whom Tanner follows, puts Roger's date at 1186, and absurdly calls him rector of the schools and chancellor of the university of Oxford. The only known manuscript of his Treatise is Digby MS. 40, ff. 25–52, where it commences with a rubric (of the thirteenth century): ‘Præfatio Magistri Rogeri Infantis in Compotum.’ Wright has printed an extract from this preface. Roger's chief authorities are Gerland and Helperic, whom he frequently corrects.

• Sources

• Tanner's Bibl. Brit.-Hib. p. 718; Wood's Hist. and Antiq. Univ. Oxon. i. 153; Wright's Biogr. Brit. Litt. ii. 89; Cat. of Digby MSS.

• C. L. K[ingsford]

09/10/2017 17

• JU. A. Weisheipl in vol. 1 of the History of the University of Oxford, firmly associates him with

Oxford (pp. 435, 436) and makes no mention of Cambridge.

• Roger of Hereford is no. 210 in James Carley’s edition of Leland’s De viris illustribus (no mention

of either university). Roger Hereford is no. 500 there and Leland says that, as he gathers, ‘he

studied philosophy and mathematics assiduously at Cambridge’. He cites as Peterhouse MS on

metallurgy. ‘The same codex contained Alphidius’ treatise On the creation of metals.’ Leland also

has a piece on Roger Child (Infans) as a learned mathematician (no. 399 in Carley), but with no

biographical information.

• Rod Thomson’s recent catalogue of Peterhouse’s medieval mss makes no mention of Roger, but

he does mention (pp. 194ff) Alphidius De lapide philosophorum as item 27 in what is now

Gonville and Caius MS 181/214 a collection of mostly alchemical tracts. The volume was at one time in the ownership of Roger Marchall (see Thomson’s note on p. 196).

09/10/2017 18

To attempt to answer this question, I emailed the University of Oxford. This is their reply.

“Dear Dr Adams

Thank you for your enquiry.

The University Archives does not hold any records of students at Oxford in the 12th century. All known

information about the University careers of members of the University up to 1500 is contained in 'A

Biographical Register of the University of Oxford to AD 1500' by AB Emden. This is compiled partly from

sources in the University Archives, but to a larger extent from those held elsewhere. I have checked this

register and have been unable to find an entry for Roger de Hereford, or under his other known names of

'Infans' and 'Puer'. It would appear, therefore, that Roger de Hereford was not affiliated with the University.

Yours sincerely

Tilly Burn

Tilly Burn Archives Assistant

Oxford University Archives Bodleian Library,

Oxford OX1 3BG

+44 (0)1865 277145

www.bodleian.ox.ac.uk/oua”

09/10/2017 19

Was Roger de Hereford at Oxford?

• “With such a small amount of personal information available it has been difficult to detect the institutional connections, if any, of these men or to place their work in the background of cathedral school or university development of the century.”

• “In the course of research primarily for biographical information about thirteenth century men of letters in England a number of items turned up about ROGER OF HEREFORD, DANIEL OF MERLAI, ALEXANDER NECKAM, and probably ALFREDUS ANGLICUS. They tend to show, I believe, that Hereford, possibly through a cathedral school, was a center of this learning in the second half of the twelfth century.”

Josiah C. Russell (1932)

09/10/2017 20

“Hereford and Arabic Science in England

about 1175-1200”

• “ROGER OF HEREFORD," . . . "was a teacher and writer on astronomical and astrological subjects who was still a young man in II76, and who, two years later, adapted astronomical tables of Arabic origin to the use of Hereford.”

• “Professor HASKINS also notes a number of items in contemporary records which might refer to him: a Master ROGER OF HEREFORD attesting a York charter of I I54- I I63, a ROGER OF HEREFORD witnessing a document of GILBERT FOLIOT of II73-74, a ROGER vice-dean of Hereford owner of certain manuscripts, and a ROGER clerk of Hereford and itinerant justice. To these may be added a Master ROGER OF HEREFORD who attested a charter of Archbishop RICHARD OF CANTERBURY.”

• “The Compotus of II76 has in the Digby MS. the title "Prefatio magistri Rogeri Infantis in compotum." The gloss on a work of ALFREDUS ANGLICUS called him Rogerus Puer. (5) Since the preface itself states that the author was still young it was possible to conjecture that Infans or Puer was an inference from the preface. This puzzle is settled by the appearance in a Hereford charter of I195 of a Master ROGER Infans as a witness. The astronomer's name was probably the Anglo-Norman Lenfant or the English Child.”

Josiah C. Russell (1932)

09/10/2017 21

“Hereford and Arabic Science in England

about 1175-1200”

• Roger of Hereford, We have from him the following:

• I. Compotus, in five books, comprising in all twenty-six chapters: Digby MS. 40, ff. 21-50 v; cf.

Macray, Catalogue, col. 37. The author criticizes the errors of Gerland and the Latin computists

generally, and compares their reckoning with that of the Hebrews and Chaldeans. In the preface,

the beginning of which is printed by Wright, Biographia literaria, ii. 90 f., he says that although

still 'iuvenis' he has given many years to the 'regimen scholarum.' The date of the work is exactly

given as 9 September 1176.

• Source: C. H. Haskins (1924) downloaded from the Internet Archive Monday, 18 September 2017.

09/10/2017 22

“Studies in the History of Medieval Science”

• “The attestation of Master ROGER INFANS in 1195 prolongs his career nearly a score of years beyond the date of his treatise of 1178. If we may identify him with the Master ROGER who appears frequently in Hereford charters of the period, once as early as 1172, he may be assumed to have spent much of his time there.

• The preface of his Compotus mentions that he had taught several years but does not give the place of his school. If his astronomical tables were written for school use the fact that they were prepared for the meridian of Hereford may be significant. Was there a school at Hereford? If so did it conform to the pattern of studies which ROGER OF HEREFORD inserts in the preface of the Compotus?”

• How does this fit into what we know of Hereford? SIMON DU FRESNE told us that the seven liberal arts flourished there. SIMON the theologian was there. ROGER OF HEREFORD and ALFREDUS ANGLICUS, if we have identified him correctly, were eminent scientists.

• ROGER OF HEREFORD probably ended his days as a monk of Bury St. Edmund.

Josiah C. Russell (1932)

09/10/2017 23

“Hereford and Arabic Science in England

about 1175-1200”

• “The conjecture ‘Young’ as the English form of Roger’s name is very shaky indeed. ‘Child’ (Infans) or ‘Boys’ (which could of course be a ‘corruption’ of ‘Bois’ = ‘Wood’) (Puer) would be just as probable, arguably more so.

• Could he have studied at Cambridge? Certainly, in theory, as scholars wafted to and fro in the most exasperating manner and it was possible to study without being what we now call an undergraduate (these, moreover, were rare birds in the 13C). He might have just wandered over to consult MSS, chat with someone in Cambridge similarly inclined, and so on. It is significant, however, that he is not included in BRUOC (Emden’s biographical register of early Cambridge scholars).

• It seems sadly unlikely that this can ever be elucidated satisfactorily.”

09/10/2017 24

Elizabeth Leedham – Green comments as follows:

Sources

09/10/2017 25

• Aylmer, G. E. and Tiller, J. E. (2000). Hereford Cathedral: A History. London; The Hambleton Press.

• French, R. (1996) ‘Foretelling the future: Arabic astrology and English medicine in the late twelfth century’,

Isis, 87, 453–80

• Haskins, C. H. (1924). Studies in the history of mediaeval science, 2nd edition. Cambridge, MA, Harvard UP.

Downloaded from the Internet Archive Monday, 18 September 2017.

• Hockey, Thomas, Trimble, V., Williams, Th. R., Bracher, K., Jarrell, R., Marché, J.D., Ragep, F. J. (Eds.) (2007).

The Biographical Encyclopedia of Astronomers pp 982-982 Roger of Hereford by Charles Burnett. Springer

eBook.

• Howlett, D. R. (1974). A St Albans historical miscellany of the fifteenth century. Transactions of the

Cambridge Bibliographical Society, Vol. 6, No. 3 pp. 195200. Stable URL:

http://www.jstor.org/stable/41154537 Accessed: 10-09-2017 17:00.

• Russell, J. C. (1932–3). ‘Hereford and Arabic science in England, c. 1175–1200’, Isis, 18, 14–25. Published

by: The University of Chicago Press on behalf of The History of Science Society Stable URL:

http://www.jstor.org/stable/224477 Accessed: 16-09-2017 18:39 UTC.

• North, J. D. (1986). Horoscopes and history (1986), 39–41. Warburg Institute, Surveys and text.

• Southern, W. (1992). Robert Grosseteste: the growth of an English mind in medieval Europe, 2nd edition,

lii-liii.

University of Cambridge“As it stands, Cambridge was established in 1209 . . .”

http://www.tcs.cam.ac.uk/?p=0002115

08/09/2017 MTH01 26

08/09/2017 MTH 01 27

Geomancy• Geomancy is a method of divination that interprets markings on the ground or the patterns formed by tossed handfuls

of soil, rocks, or sand. The most prevalent form of divinatory geomancy involves interpreting a series of 16 figures

formed by a randomized process that involves recursion followed by analysing them, often augmented with astrological

interpretations.

• The first geomancy translated into Latin from Arabic was Hugh of Santalla's Ars Geomantiae. Hugh of Santalla (or Hugo

Sanctelliensis) was an astrologer, alchemist and translator of the first half of the twelfth century born in Santalla in

Northwest Spain. He appears to have worked under the patronage of Michael the bishop of Tarazona, from 1119 to 1157.

08/09/2017 MTH 01 28

'Elisabeth Leedham-Green'

• Part-time archivist at Peterhouse and Darwin College Cambridge.

• Author of: A Concise History of the University of Cambridge CUP.

08/09/2017 MTH01 29

Hockey, Thomas, Trimble, V., Williams, Th. R.,

Bracher, K., Jarrell, R., Marché, J.D., Ragep, F. J.

(Eds.) (2007). The Biographical Encyclopedia of

Astronomers pp 982-982 Roger of Hereford by

Charles Burnett. Springer.