Math Ancient & Modern

The Institute’s Summer 2020 Advanced Formation Webinar Series concluded with a special series on “Math Ancient & Modern.” Three presentations introduced participants to the ancient mathematical disciplines of the Quadrivium, reflected on the profound effects of modern algebraic thinking, and considered the proper role of mathematical science in today’s liberal arts curriculum. 

“Coming to Love Contemplation – The Goals of Mathematical Studies in the Ancient World” – Dr. Andrew Seeley

In “The Lost Tools of Learning”, the essay that gave birth to today’s classical liberal arts revival, Dorothy Sayers asserted that mathematics should be taught as a “sub-department of Logic”. An analysis of the preface to The Almagest, Ptolemy’s classic work on astronomy, and Euclid’s presentation of the Pythagorean theorem shows that the ancients saw mathematics as so much more. 

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“High School Algebra and the Training of the Mind: More Harm than Good?” – Dr. Arthur Hippler

Since the early part of the 20th century, algebra replaced geometry as the center of math instruction. But how do the habits of mind algebra creates compare to geometry? This presentation will focus on the contrast between Euclidean geometry and Descartes’s Géométrie.


“Irrigating Deserts, or How I Learned to Stop Worrying and Love Modern Math and Science” – Dr. Merrill Roberts

Joy, Wonder, Love, Freedom… These are not typically the first words that come to mind when a student recalls their initial encounters with symbolic mathematics or the modern mathematical sciences.  On the contrary, these topics are often described as “dry, barren, and monotonous”, leaving our students “bleary, exhausted, and thirsty”.  This session suggests some ways to recapture the perspective of the ancients while preserving the insights and discoveries of the modern disciplines.

For more information on the ICLE Advanced Webinar Series, contact Dr. Andrew Seeley at or 844-425-3832 x701.