Sir Isaac Newton,
Charles L. Dodgson,
i.e., Lewis Carroll
Christ Church, Oxford
Carroll's "flowchart" for applying the propositions in
Medieval Illuminated MS.
An unknown woman teaching geometry to monks.
of Natural and Social
Department of Mathematics
Shirley B. Gray
Office: ST F218
Phone: (323) 343 - 2163
FAX: (323) 343 - 5071
Dr. Gray, Dr. Stewart Venit and
Russ Abbott have created and maintained this web site under the
of the National Science Foundation and the Arnold and Mabel Beckman
The prestigious journal Science
recognized our work in Fall, 2006. See <http://curvebank.calstatela.edu>
for a "FLASH" introduction as well as the Home Page <http://curvebank.calstatela.edu/home/home.htm>.
In addition to hosting the NCB web site, Dr. Gray enjoys teaching MATH
History of Mathematics. The CSULA campus has a
unique asset. Our campus is located near the Huntington Library
in San Marino,
CA. The Huntington's priceless collection of mathematical books
incunabula was recently augumented by the acquisition of 66.000 items
the Burndy Collection. Many works in both the old and new holdings are
first editions. Thus, CSULA students have access to what may be
the finest collection in the history of mathematics and science in
America. Our History of Mathematics course offers students and
the unique pleasure of seeing these books and their magnificent
Among other delights, Gray has been
to examine the Bodleian Library's copy of Euclid's Elements
at Oxford University. This is the world's oldest dated edition. Another
important edition, ca. 900 A.D., is housed in the Vatican
In 2004, Gray was permitted to examine this copy once stolen by
and now returned to the archives
of the Biblioteca Vaticana, Roma.
This trip also permitted her the time to be a Reader in the famed
Library in Florence, Italy. Later, in 2005, she viewed the oldest
copy of the Nine Chapters on
Art in the Shanghai Library. Dr. Gray concurred when a
once told her, "You are a very lucky woman."
A "short list" of other favorite
and talks includes:
AMS-MAA National Meetings. The newly established National Curve
Baltimore, MD, January 15, 2003 and all subsequent NSF Poster Sessions.
Brown Bag Lunch Series, The National Curve Bank,
University, March, 2003.
AMS - MAA National Meeting, San Antonio, Texas. The Lost Palimpsest
Archimedes: The Method. January, 1999.
Gray's first web project was on Maria Gaetana Agnesi and
the first translation of the closing of her famous calculus book.
[ See < http://instructional1.calstatela.edu/sgray/Agnesi
Gray's first videotape project appeared on KLAC-TV Channel 58
featured students learning to use the rather new graphing calculators
April, 1997. Using a Graphing Calculator had five airings
the tape just prior to the AP Calculus Exam.
Gray has especially enjoyed
the network of friends that was
by participating in
IHMT, Washington, D.C. Institute
for the History of Mathematics in
Teaching sponsored by the MAA/NSF. June, 1996 and June, 1997.
Flowers were a gift of MATH 320 History
Mathematics, Winter, 2006.
Harry B. Gray, L. K. Olof Lindgren and Shirley B. Gray.
“Was Something Wrong with Beethoven’s Metronome?”, Notices of the American Mathematical
Society, October, 2013, 60 (9).
|Gray, Shirley B. and Rice,
Zebanya. “The Mayan Number System and Calendar: December
21, 2012: A Date of Opportunity” Mathematics Teacher [cover] 106(5),
December, 2012-January, 2013, 338-344.
|Gray, Shirley B., "BSHM
detective story continued" BSHM
Bulletin, 24 (3), 2009.
, , Science and Culture Review, 6
Translation by Yibao XU.
Gray, Shirley B., "A Centennial Celebration of Two Great
Scholars," Notices of the American
Mathematical Society, 55 (7), August, 2008, pp. 776-783.
Gray, Shirley B., "On the Equals Sign - Our 'Twins': A Tour through
Original Sources," The Mathematical Intelligencer, 30 (2),
2008, pp. 19-23.
“Bent into Shape”, NETwatch (M. Leslie, ed.); Science,
2006, 314, 571. [(October
“A Renie for the Brachistochrone, Short Takes (F.
Gouvêa, ed.); Focus, 2006, 26(5),
Gray, Shirley B. and Gordillo, Gustavo. “The
Brachistochrone: For the ‘shrewdest mathematicians of all the world’
“ CMC ComMuniCator. 30(3) 34 – 36, March, 2006.
Gray, Mary and Gray, Shirley B. “Calculus: A Play in
London” math HORIZONS, Mathematical
Association of America. February, 2006.
Gray, Shirley B., “A Multiplicity of Multiplications.” College
Mathematics Journal, 37, Spring, 2006.
||Gray, Shirley B. “National Curve Bank
Project” College Board AP Central. College Board
AP Calculus AB program. January, 2005.
Perkins, Gay with Shirley B. Gray “Life of a 1950s Homecoming
Queen,” The Western Scholar. Western Kentucky
University. Spring, 2005.
||Gray, Shirley B., "Hypatia", Mathematics
for Students, Macmillan Reference USA.
||Gray, Shirley B., "Agnesi", Mathematics
for Students, Macmillan Reference USA.
> < http://curvebank.calstatela.edu/home/home.htm
The National Science Foundation and the Arnold and Mabel Beckman
supported this project.
||MAA Online Book Review, Stephen
Smale: The Mathematician Who Broke the Dimension Barrier,
< http://maa.org.reviews/reviews.htm >, April, 2001.
||Gray, S. I. B. and Sandifer, C.
Edward, The Sumario Compendioso, Mexico City, 1556: The New
World's First Mathematics Book, Mathematics Teacher,
NCTM, 94 (2) 98 - 103.
||Mathematics in the Age of Jane Austen: Essential
Skills of 1800. Mathematics Teacher. NCTM, 93 (8) 670-679.
||CALTECH AT OXFORD, 40 YEARS ON. The American
Oxonian; A Publication of the American Rhodes Scholar Foundation,
LXXXVII (1) 1-8.
||Gray, S. I. B., and Malakyan, Tagui, The Witch of
Agnesi: A Lasting Contribution from the First Surviving
Mathematical Work by a Woman. A commemorative on the 200th
Anniversary of her death. The College Mathematics Journal,Mathematical
Association of America. Cover article, 30 (4), September,
1999, 258 - 268. Ms. Malakyan was a student in MATH 320.
||Gray, S. I. B., The Mathematics of Lewis
Carroll, math HORIZONS, Mathematical Association of
America. April, 1999, 18 - 23.
||Gray, Shirley I. B., THESE RUINS ARE STILL
INHABITED: Caltech at Oxford. A Tribute to Muriel and
George Beadle, Update for 1998. Engineering and Science,
California Institutue of Technology, LXI (4), April, 1999.
||Gray, S. I. B., Heiberg and the Lost
Palimpsest of Archimedes. The British Society for the History
of Mathematics Newsletter, Summer, (39) 26-31.
||Gray, S. I. B., Mathematics Education Across the
Poind in Great Britain. CMC ComMuniCator,23 (4), June,
1999, 46 - 47.
||Gray, S.I.B., A Mathematics Treasure in
California, The Mathematical Intelligencer, 20(2), 41-46.
||Gray, Shirley B. and Mena, Robert A. Amusements in the
History of Mathematics, PRIMUS, VII(4), 317-328.
||Gray, Shirley B., Producer and Director. Using a
Graphing Calculator, Department of Mathematics and Computer
Science, CSULA. A videotape featuring 25 students, faculty and staff.
||Gray, Shirley B. Earthquake Mathematics: An Infant
Science. [This earthquake problem has been selected for LAUSD's
Standards for High School Curriculum as a model for all
||Gray, Shirley B. Fractal Math, Journal of Computers
in Mathematics and Science Teaching, 1(1), 31-38.
||Gray, Shirley B. and Craig, Terence. G. Math Matching
Ideas: A Generic HyperCard-HyperTalk Program, Journal of Computers
in Mathematics and Science Teaching, 1(2), 235-250.
At the Huntington Library,
we have examined the following
A Sampler of the Huntington
||Elements (Several editions.)
||De Revolutionibus Orbium Coelestium
||Dialogo Sopra Due Massimi Sistemi del Mondo
||Discours de la Méthode
||Analyse des Infiniment petits
||Introductio In Analysin Infinitorum
||"The whetstone of witte, which is the
part of Arithmetike . . ."
|and many, many
on some of the books CSULA students see at the Huntington Library.
Ptolemy wrote the Almagest, or "the greatest,"
the second century A.D. He produced the definitive Greek work in
astronomy for determining the location of the planets. His mathematics
its geocentric theory stood unchallenged for 1400 years until
proposed his heliocentric theory in 1513.
The surviving copy at the Huntington uses the sexagesimal
system. It is thought to have been produced in the south of France, but
monastery, or atelier, is unknown.
As for esthetics, this copy is illuminated with gold and color
The hand-printed vellum is not thick, but has an unforgettable texture
strength tempered with the appeal of the finest of translucent
To view the Vatican's copy and other interesting titles: http://sunsite.unc.edu/expo/vatican.exhibit/exhibit/Main_Hall.html
The Huntington has more than 30 editions of the Elements,
but counting the number of editions is arbitrary, for not all books
survived in all editions. This collection was expanded (Fall,
by the addition of the Burndy Library from M.I.T.
Following the invention of printing, Erhard Ratdolt's
in 1482 was the first mathematics material to be printed. The
opens immediately with 23 definitions, including those for the point,
and plane! Impressively, the Latin illustrations of "puntus, linea,
are clear to English readers 500 years later. On later pages, students
immediately recognize the "windmill" or "bride's chair" proof of the
The Huntington has two copies of the first English translation by Sir
Billingsley (London, 1570). It contains pop-up, three-dimensional
embedded in the text. For example, the book includes fold-out models of
perpendicular planes, a tetrahedron and a pyramid.
Many of the authors of the other editions are, themselves, famous,
This first edition of Copernicus at the Huntington was
the gift of Edwin Hubble of the "Hubble Space Telescope." It is nearly
on display in the Main Reading Room of the Library. Most of the other
are seldom seen by the public.
Maria Agnesi and the
There are very few famous women in
We select the following for special mention:
See: Gray, Shirley
"Hypatia." An article requested for Mathematics for
an encyclopedia published by Macmillan Reference USA., 2002.
d. 415 AD
Emilie Breteuil, Marquise du Châtelet
1701 - 1749
Also see: Gray, Shirley
"Agnesia." An article requested for Mathematics for
an encyclopedia published by Macmillan Reference USA.,2002.
1718 - 1799
1776 - 1831
1850 - 1891
1882 - 1935
| CSULA is proud of our
colleague, Dr. Evelyn Boyd Granville, one of the first African-American
to earn a Ph.D. in mathematics (Spring, 1949).
The Library also has Sir Edmond Halley's edition of Apollonius' works.
The CSULA Spring, 1997 students remarked that of all the books we had
in chronological order, this was the first to look like a "math" book.
the 18th century, the equation and notation had evolved, as well as
techniques, to have math equations, not verbal explanations, embedded
the text. Calculus students will immediately recognize that Euler was
on infinite series.
Brother Juan Diez, O.F.M.
The Sumario Compendioso in Spanish is the first book other
instruction printed in the entire Western Hemisphere. With a
date of 1556 in Mexico City, it predates all North American settlement,
Jamestown (1607), Plymouth Rock (1620), and Quebec City (1608).
The Huntinton Library has been the Sumario 's home
1920. It is one of three remaining known copies in the World, with the
two being in the British Museum in London and in the Biblioteca
The cover is primitive heavy leather. On opening the cover, the first
one sees on the left is a recycled piece of printed matter that is
vertically. Paper must have been in very short supply in Mexico City in
A gorgeous frontispiece is on the right opening page, and bears
to the kingdoms of Peru (sic ).
Return to Brother
In the summer of 2006 a student asked who was the very first to use the
sign. The question was answered by showing him Robert Recorde's "The whetstone of witte, which is the
part of Arithmetike . . .
" published in London (1557) at