W ELCOME and thanks for visiting my website! My academic activities center on the history of mathematics, so included here is information related to my work in this area. My research interests in the history of mathematics include ancient Greece and medieval Islam, as well as the history of such scientific instruments as the sundial and the astrolabe. Sundials are a particular interest of mine so they have their own section here.
I retired from the Department of Mathematics at SFU in 2006 and am no longer taking students. The courses that I taught there include calculus, geometry, linear algebra, history of mathematics, and mathematics in science and civilization.
“This book provides ... English translations of key mathematical texts from medieval Western Europe and North Africa, all originally written in one of the three scientific languages of that time: Latin, Hebrew, and Arabic. Until now, there has been no sourcebook that deals with Hebrew mathematics as such, or the mathematics of the Muslim West. This volume fills that gap and brings the field an important step forward.”
“[This book] is notable for the wide variety of sources, which will challenge preconceptions everywhere, as well as for the clarity and force of the introductions to the mathematical cultures on display. The authors are leading authorities in their subjects and the scholarship is of the highest order.”
“Everything about this book is excellent. The translation is a model of clarity and the notes to each section explain the text in detail, both technically and historically ... Evans and Berggren have done such an excellent job in every way, their knowledge of the subject is so complete, that I can only admire their work and recommend it as exemplary.”
“This book is, in spite of the author’s more modest claims, an introductory survey of the main developments in those disciplines which were particularly important in medieval Islamic mathematics ... No knowledge of mathematics ... beyond normal high-school level is presupposed and everything beyond that ... is explained carefully and clearly.”
“The edition and translation are beautifully done ... The notes and introduction are very helpful. Anyone interested in the history of Greek science will want to have a copy. So will anyone who is curious about the history of how the Greeks deployed mathematical models to understand astronomical phenomena.”
“Berggren and Jones have made a difficult, detailed and challenging text far more accessible and have produced a work that will be the standard for many years to come.”
“...admirably designed to cater for a broad spectrum of tastes: professional mathematicians , , ,, historians of mathematics, teachers at all levels searching out material for individual talks and student projects, and amateurs who will find much to amuse and inform them in this leafy tome. The authors are to be congratulated...”
I am engaged in ongoing research centered on the translation and study of ancient Greek and medieval Arabic mathematical texts dealing with geometry, mathematical geography and astronomy. This includes studies of the mathematical ideas in these texts and their historical, scientific and social contexts.
Some of these researches will be presented in the paper “Al-Bīrīnī’s Mappings of the Heavens and the Earth” which I will present at the International Congress for the History of Science and Technology” in Rio de Janeiro in July 2017.
The following articles were published in The Compendium, which is the official publication of the North American Sundial Society.
My published lectures on this topic may be accessed in the previous section. My unpublished lectures include:
...a nod to decidedly older technology [is] a sundial, designed by an SFU math professor and built by students from BCIT's mechanical technology program. It shows local clock time as well as sun time, which does not recognize time zones or daylight savings time changeovers. [Source Article]
An analemmatical sundial - the first [split analemmatical dial] in Canada – can now be found at the northeastern end of "C" parking lot, painted on the pavement. An ancient form of telling time, the first analemmatical sundial appeared in France in the early 17th century at the church of Brou.
SFU’s sundial features two analemmas (the large figure eight’s painted on the pavement). The analemma on the west is used for morning hours, the other for afternoon hours.
To tell clock time select the appropriate analemma for morning or afternoon and find the date position on its curved boundary. The first of each month is shown as a white dot; thus Sept. 15 is half way between Sept. 1 and Oct. 1.
The hours are shown on the dial beside the large yellow circles, labelled in blue for Pacific standard time and red for Pacific daylight savings (PST) time – one hour later of PST.
Someone telling time on a sunny day must face away from the sun on the coloured analemma with the date centered between their feet. The approximate mean time will be shown by the person’s shadow on the dial.
“It’s quite accurate,” says mathematics professor Len Berggren, who collaborated on the dial with North Vancouver retired engineer and sundial enthusiast Brian Albinson. “The average absolute error in the morning is 23 seconds and in the afternoon, 54 seconds.”
Commanded by the Qur’an to seek knowledge and examine nature for signs of the Creator, the Islamic world was synonymous with learning and science for five-hundred years. In the twenty-first century, the relationship between science and religion generates much debate among Muslims. Chris Tenove asks if there is there a contradiction between Islam and modern science.
A groundbreaking treatise on cartography that's been Greek to many map buffs for centuries is now making sense, thanks to two scholars' knowledge of the ancient language and ancient mathematics.
Len Berggren, the chair of Simon Fraser University's mathematics department, and Alexander Jones, a University of Toronto classicist, are the authors of the first complete and reliable English translation of Ptolemy's Geography.
"Up until now most of the book, which is Ptolemy's exposition of the principles of map making, has only been available in Greek, Latin and Arabic," explains Berggren, who reads Greek and Arabic. Originally written in Greek by the Alexandrian astronomer and geographer Claudius Ptolemy in the second century A.D., Ptolemy's Geography is the only surviving work on cartography from classical antiquity.
After its translation into Latin around 1410 A.D., the book became a cartographer's bible. For the next two centuries, cartographers and explorers regarded it as the best source of map-making techniques and depictions of the world's geography, including its curvature.
Berggren, a historian of ancient mathematics, says the English translation, which took him and Jones 15 years to complete, will help popularize Ptolemy's farsightedness.
"Ptolemy's Geography introduced the use of longitudinal and latitudinal coordinates to map the world," says Berggren. "His technique enabled map makers to make their own maps using only the text of the Geography. For 15 centuries, Ptolemy's Geography represented the most thorough discussion of the importance of relying on astronomical observation and applied mathematics to determine location," says Berggren.
However, Ptolemy's cartography had its flaws. Berggren and Jones point out several in their in-depth analysis of the geographer's work.
"When Christopher Columbus landed on the shores of the Americas in 1492 he mistook them for the shores of Asia because he had relied on Ptolemy's book, which seriously shortened the distance between Europe and Asia," notes Berggren.
He and Jones illustrate Ptolemy's view of the world by comparing colour reproductions of the geographer's original maps to present day maps. The two also trace the evolution of Ptolemy's maps in the hands of latter day mapmakers.
Two SFU professors are being honoured for their part in making SFU a better known institution.
Lindsay Meredith, associate dean of business and Len Berggren, chair of mathematics and statistics are the recipients of the annual President's award for service in media and public relations.
The award committee unanimously chose to honour Meredith for his extensive work with the media and Berggren for his longstanding role in community relations. They'll both be recognized at a reception and at SFU's annual award ceremony Feb. 16. [Click here for section on Dr. Meredith.]
Like Meredith, Berggren is no stranger to an audience, whether the crowd is a group of stroke recovery patients or a mensa gathering. For the past three decades he's been one of the most available speakers involved with SFU's speakers' bureau and has given more than 70 talks.
An expert on the history of mathematical sciences in ancient Greece and medieval Islam, he has developed a wide range of interests – from time measurement to the politics of Cyprus – as well as a commitment to sharing them.
"The speakers' bureau is a great opportunity for the university and for those of us who are passionate about our work," says Berggren (right), who is also a regular in local schools, where he addresses student and teacher groups.
Finding time to prepare and deliver talks isn't always easy. Berggren says it's a matter of commitment. "You have to decide it's a priority," he says. "It's one way a university researcher can help the community. It's public education of your work."
Berggren maps out his thoughts in advance. "I wish I could speak more off the cuff, but I need to be well-prepared," he admits. "I'm always redoing my talks because they reflect my research interests, and those are always developing."
Berggren has also had his share of the spotlight. Called on to demystify concepts like leap year and the start of the true millennium, he faces the task of explaining difficult concepts in short time frames.
"I'm still a bit nervous," he concedes. "It's hard to choose what honestly reflects what you know without unnecessary complexity. It's something you learn as you do it."
Besides appearing on local radio and in print, Berggren's international media exposure includes the BBC in Scotland and the New York Times.
"I think journalists are appreciative of our expertise," says Berggren. "They are simply trying to tell a story. If we can make it a better one then everybody wins."
Professor Emeritus, Department of Mathematics, Simon Fraser University
|2006 - present||Professor Emeritus||Mathematics||Simon Fraser University|
|2006 - 2016||Committee Member||Academic Standards||Alexander College|
|1984 - 2006||Professor||Mathematics and Statistics||Simon Fraser University|
|1992||Visiting Scholar||History of Science||Harvard University|
|1990 - 1991||Visiting Scholar||History of Science||Harvard University|
|1973 - 1984||Associate Professor||Mathematics and Statistics||Simon Fraser University|
|Sept. 1975 - Dec. 1976||Visiting Fellow||History of Medicine and Science||Yale University|
|1963 - 1973||Assistant Professor||Mathematics||Simon Fraser University|
|Sept. 1972 - May 1973||Visiting Fellow||History of Medicine and Science||Yale University|
|Sept. 1968 - June 1969||Visiting Lecturer||Mathematics||University of Warwick|
|Underell, John||M.A.L.S.||An Enquiry into Human Creativity||2003|
|Sinclair, Nathalie||M.Sc.||Applications of Conic Sections in Ancient Mathematics||1995|
|Jeffries, William||M.A.L.S.||Extended Essays: "Claude Bernard"; "Cartesian Chalk Circle"||1995|
|Stanley, Daryn||M.Sc.||The Quadrant in Middle Ages and Renaissance||1994|
|Van Brummelen, Glen||Ph.D.||Mathematical Tables in Ptolemy's Almagest||1993|
|Vogt, David||Ph.D.||An Information Analysis of Great Plains Medicine Wheels||1990|
My research centers around reading and translating ancient Greek and medieval Arabic mathematical texts dealing with geometry, mathematical cartography and astronomy, as well as studies of the mathematical ideas in these texts and their historical development.
I have also taught and done research in how the mathematical sciences have affected, and been affected by, human values and cultures including moral, religious and cognitive values.
Please see this section.
Please see this section.
Dr. J. L. Berggren
Department of Mathematics
Simon Fraser University
8888 University Drive
Burnaby, BC, V5A 1S6