NEW Pathway: “On the Shoulders of Giants”: mathematics like you’ve never seen before
Syllabus for 2025
I. Winter/Spring Session
Euclid, Elements, Books 1, 5, 7, 11 and 12
II. Summer Session
Apollonius, Conic Sections
III. Fall Session
Plato’s Timaeus
Ptolemy, Almagest
Syllabus for 2026
I. Winter/Spring Session
Copernicus, Revolution of the Spheres
Kepler, Astronomia Nova, Epitome of Copernican Astronomy, Harmonies of the World
II. Summer Session
Kepler (continued)
III. Fall Session
Galileo, Two New Sciences
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Start date: January 2025
Day/Time:
Mondays and Thursdays, 12 pm EST/11 am Central, 9am Pacific – starting January 2025.
Session length: 1.25 hours
Meeting Frequency: twice weekly; 8 week summer session is weekly.
Instructors: David Saussy
Pathway Duration: Open, Quarterly
Cost: If you would like to join Euclid for Winter/Spring 2024, simply begin by subscribing to the slow reading program for the first quarter. Renewals begin 2nd Quarter (April-June). Annual subscriptions grant 1 free quarter. For more information about subscription prices and benefits, and to sign up, click here.
Joining this pathway: Slow reading subscribers may join at any session (for example, if you miss Euclid and Apollonius, you may join Ptolemy in Fall 2024.) Subscribers will have access to all current and past recordings of this pathway. You may join for both days (M, Th) or one day (M or Th).
Break between sessions: Between Winter/Spring, Summer and Fall sessions, the group will take a 2/3 week hiatus.
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“If I have seen further than others, it is because I am standing on the shoulders of giants.” – Isaac Newton
“Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace…”
-Edna St. Vincent Millay
“I had not imagined that there was anything so delicious in the world.”
– Bertrand Russell
“Nothing hinders us from doing justice to the originality of ancient science by allowing ourselves to be guided only by these phenomena to which the Greek texts themselves point and which we are able to exhibit directly, our different orientation notwithstanding, Greek scientific arithmetic and logistic are founded on a “natural” attitude to everything countable as we meet it in daily life. This closeness to its “natural” basis is never betrayed in ancient science.”
– Jacob Klein, Greek Mathematical Thought and the Origin of Algebra
– Jacob Klein, Greek Mathematical Thought and the Origin of Algebra
Pathway Overview: A slow reading pathway in the primary sources of mathematics and natural science, ancient and modern. Our central study is the transformation of ancient science and mathematics into the modern. To understand this change, we must attempt to understand the ancient alternative on its own terms, as far as possible free from modern preconceptions. What is the difference between the ancient and modern approaches? Participants formulate their own opinions based on direct experience with the primary sources – including practicing the skills of argumentation and demonstration. Meetings two days per week. Open-enrollment: recordings archive will be made available, and participants may join at any point along the course of this program.
The Design of the Pathway, “On the Shoulders of Giants”
Isaac Newton once said, “If I have seen further than others, it is because I am standing on the shoulders of giants.”
This image goes back at least to the 12th century. John of Salisbury wrote: “Bernard of Chartres used to compare us to dwarfs perched on the shoulders of giants. He pointed out that we see more and farther than our predecessors, not because we have keener vision or greater height, but because we are lifted up and borne aloft on their gigantic stature.” (Metalogicon, 1159)
Our world has been shaped in a decisive way by the radical changes within the studies of mathematics, astronomy and physics, from the ancient Greeks to the moderns. To understand the world we live in, one must come to an understanding of the genuine history of this transformation.
But mathematics and science have become so specialized – and detached from natural understanding – that the liberal learner finds himself at a loss for where to begin his search. A first major obstacle along the way is that modern thought tends to view the works of the ancients in terms of modern ways of thinking. The genuine ancient understanding of things is unknown to us.
A second difficulty is that most of us have been introduced to mathematics and natural science – as well as many other subjects besides – through textbooks, not through the primary sources. Consequently, we hardly know it is possible to go directly to the sources themselves to learn about the transformation in the history of ideas.
Moreover, a third difficulty is that adult great books programs tend to offer great works literature and in some case philosophy, but avoid the great books of mathematics and natural science.
Thus the ‘great books’ – detached from the mathematics and works of cosmological speculation – is missing something big. For what happens in the realm of mathematics and natural science has been of decisive – even portentous – significance for the whole realm of human thought.
Our intention in this pathway is not to learn about the ‘history of ideas’, as though it is detached subject matter, but to “undergo” this very history itself by working through mathematical proofs and arguments in these great works.
That is, we want to follow these great thinkers’ footsteps – or stand on their shoulders – and try to see the world as they saw it, to understand the problems as they understand them.
We intend to face the challenges that arise in contact with subsequent thinkers, and to see first hand how the radical transformation in the manner of concept formation from the ancients to the moderns takes place.
For example, Ptolemy was not engaged in physical speculation – like Kepler and those following him – but endeavored to “save the appearances” (σῴζειν τὰ φαινόμενα, sozein ta phainomena).
What is it to ‘save the appearances’, what is the difference between this approach and that of physical theorists like Kepler, Galileo and Newton?
By working through the texts themselves, you will have first hand – non-derivative or original experience with what this actually means. The result of such an immersive learning experience places your thinking on firmer, more solid foundations, and even frees your mind from a story perhaps poorly told about the history of human thought.
Who is it for?
- All those who wish to get acquainted with forgotten sources of western thought in mathematics.
- Those who did not like math or think they are “not mathematical” in school.
- Anyone educated in modern mathematics, who would like to investigate the history of mathematics, through direct contact with the primary sources (rather than through the secondary or intermediary sources).
- Someone looking to fill the blanks missing in their own education, which has overlooked classical sources.
- Someone who has spent time with the classics of mathematics, astronomy and physics, but would like to revisit, and take their time unconstrained by academic calendars.
What learning experience should I expect?
As a matter of reading most actively, we take turns demonstrating theorems, by simply working together. (We use the “whiteboard” on Zoom, which works perfectly as a collaborative space.) This means that we try to show all the steps the author takes setting out as certain theorem or proposition, reasoning through relationships and consequences, leading a final conclusion. Apart from learning directly from the primary sources, as well as gaining insight into ancient and modern mathematics, you will develop a skill that you can’t get in any other way. You’ll find your mind sharpened, and your ability to think and talk though complex arguments improved.
Meetings and breaks
We will be meeting twice per week, for an hour and a quarter, instead of once a week like the regular slow reading pathways. But we plan to take time off (approx. 2 weeks) between sessions (see Syllabus above). All meetings will be recorded and archived for use by members only. If you miss a session, you can gain access to these recordings. Some members may only want to join for one day per week. Twice per week meetings allows us to go at a slower pace while moving through the material in a timely fashion.
Books and Resources
1. Euclid Elements, Green Lion Press; First Edition (January 1, 2002)
2. Apollonius, Conic Sections, Green Lion Press
3. Plato’s Timaeus
4. Ptolemy, “The Almagest; An Introduction to the Mathematics of the Heavens” William Donahue, Editor. Green Lion Press.
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