Plato, Mathematician and Myth-Maker

Pisano, Giovanni, 1240?-1320?. c.1284. Siena Duomo: det.: Plato. Place: Museo dell’Opera del Duomo (Siena, Italy). https://library-artstor-org.proxy.library.nd.edu/asset/ARTSTOR_103_41822000532257.

The Republic, The Symposium, The Phaedrus, The Apology, and The Phaedo––these are just a few of the works of Plato that were not widely available throughout most of the Middle Ages. No extended depiction of the most just city in the Republic. No discussion of love in The Symposium and The Phaedrus. No self-defense for Socrates at his trial as found in The Apology, and no final dialogue before his suicide as found in The Phaedo. For lovers of great texts, especially Plato, such news can be shocking. What kind of Plato does a person know if they don’t have these key works? How much of Socrates’ life and Plato’s philosophy could even be known? These are the questions that many medieval scholars of the Latin Platonist tradition have dedicated their lives and careers to answering, and the answers can be quite surprising.

One aspect of this research that ought to be appreciated by the wider reading public (outside of the narrow confines of medievalists) is that Plato’s Timaeus wasthe most widely available Platonic work throughout most of the Middle Ages. In fact, examining the text of the Timaeus and why itwas such one of the few Platonic texts preserved reveals how peculiarly modern our current canon of Platonic literature is.

What we value in Plato was not necessarily what late antique or medieval readers valued, and yet, their ability to read well meant that they understood a lot more than might be supposed. An attention to the reception history of Plato’s Timaeus can give modern readers of Plato a better appreciation for the importance of both mathematics and poetry in Platonic philosophy.

The Timaeus is Plato’s work on the origins of the universe. It begins with a dialogue between Timaeus, Socrates, Hermocrates, and Critias, in which Socrates expresses a desire for a “moving image” of the city they had been talking about the day before. The summary of the previous day’s discussion appears to bear some resemblance to the conversation found in the Republic although scholars are divided over whether this summary perfectly matches the Republic that we now possess. Regardless of its accuracy, this summary would have been the closest a medieval reader would have had to a taste of the Republic. The opening dialogue covers all sorts of fascinating topics from Solon’s visit to Egypt, oral culture, the mythic origins of writing, and the myth of Atlantis, but the bulk of the work features a narration about the origins of the universe recounted by the Pythagorean, Timaeus.

The Timaeus was received in the Middle Ages through three main channels of Latin translations: the translation of Calcidius (which ends at 53b), the translation of Cicero (available but not widely used or even known, which ends at 42b), and the excerpts from the Ciceronian translation of the Timaeus that can be found in Augustine’s City of God. Although it does not contain the whole text of the Timaeus, Calcidius’ translation is much more complete than Cicero’s: rather than giving merely the speech of Timaeus like Cicero’s translation does, it includes the opening dialogue (even though the commentary itself ignores it).

Most modern Plato scholars would probably not choose The Timaeus as theone and only work they could save from destruction for all time. But, a better understanding of who Calcidius was and why he wrote the commentary on the Timaeus suggests that the preservation of the Timaeus in the Latin West was not an accident of fate. Rather, the results of Gretchen Reydams-Schills’ lifelong study of Calcidius give a plausible reason for why Calcidius’ commentary may have been the Platonic work of choice for many late antique philosophers.

Reydams-Schils argues that Calcidius wrote his commentary as an introduction to the Platonic corpus, essentially reversing the Middle Platonic curriculum, which traditionally ended with the Timaeus. One major piece of evidence for this theory is that Calcidius’ commentary often reserves discussion of harder philosophical concepts for the end of the commentary.Furthermore, unlike the Neoplatonists, Calcidius did not read the Timaeus synoptically and believed strongly in the importance of sequential reading of the Platonic corpus. In Calcidus’ Platonic curriculum, the Timaeus came first with its teachings on natural justice, then the Republic with its teaching of positive justice, and finally, the Parmenides came with its teaching of the forms and intelligible realities. Calcidius believed that a thorough understanding of mathematics was necessary for understanding of almost all of the Platonic works, which is why his commentary on the Timaeus turns out to be something like a crash course in Pythagorean mathematics.

Thus, although the Timaeus was one of the only Platonic works available throughout the early Middle Ages, Calcidius’ commentary gave readers some introduction to the entire Platonic corpus as well as a great deal of Pythagorean mathematics. Perhaps there might be good reason for a philosopher to save The Timaeus (especially a copy with Calcidius’ commentary)from a burning building!

Plato; Chalcidius (translation). Timaeus. Manuscript. Place: Bodleian Library, University of Oxford, <a href=’http://www.bodley.ox.ac.uk/’>http://www.bodley.ox.ac.uk/</a>. https://library-artstor-org.proxy.library.nd.edu/asset/BODLEIAN_10310768399.

Medievalists who study the textual reception of the various translations of The Timaeus have been able to identify a shift in kinds of interest in Plato over time. The primary Latin translation of the Timaeus used until the eleventh century was Cicero’s. Medieval scholars used to assume that the revival of Calcidius began with the twelfth century Platonists, but Anna Somfai has demonstrated that the proliferation of copies of Calcidius’ text and commentary began in the eleventh century when championed by Lanfranc of Bec (c.1050). The late twelfth-century actually experienced a decline of copying the Timaeus as interests shifted towards other texts.

What motivated the eleventh-century interest in Calcidius appears to have been the mathematical content of the Calcidian commentary because, by the Carolingian period, much of the actual content of the quadrivial arts had been lost, and scholars in the Middle Ages attempted to piece together what scraps of it remained from a variety of sources. Calcidius’ commentary on the Timaeus appears to have been particularly valued as a source text for the quadrivial (or mathematical) arts. As my two previous MI blogs have explored here and here, medieval thinkers in the traditional liberal arts tradition recognized that the quadrivial arts were the foundation for philosophical thought, even if they had few textual sources for actually studying them.

And although some of the interest in the kinds of mathematics found in the Timaeus and Calcidius’ commentary may have declined after the twelfth century, it was by no means lost completely. As David Albertson has demonstrated, the mathematical interest in Plato found in the work of the twelfth-century scholar, Thierry of Chartres, would eventually be picked up by the fifteenth-century scholar, Nicholas of Cusa, and many scholars have noted resonances of Cusa’s quadrivial agenda in the thinking of Leibniz, the founder of calculus:

It seems that God, when he bestowed these two sciences [arithmetic and algebra] on humankind, wanted to warn us that a much greater secret lay hidden in our intellect, of which these were but shadows. (Leibniz as quoted by Albertson, p.2)

Bernardus Silvester. Liber fortunae, also known as Experimentarius.. Manuscript. Place: Bodleian Library, University of Oxford, <a href=’http://www.bodley.ox.ac.uk/’>http://www.bodley.ox.ac.uk/</a>. https://library-artstor-org.proxy.library.nd.edu/asset/BODLEIAN_10310765350.

Even though the interest in scribal copying of the Timaeus seems to have declined somewhat by the twelfth-century, another kind of imitatio or translatio studii was being enacted by a different kind of scholar, Bernard Silvestris. He wrote a prosi-metric telling of the creation of the world that emulates Plato’s Timaeus. The title of his work, Cosmographia, roughly translates as “universe writing,” and Bernard delivered an oral performance of itbefore Pope Eugenius III in 1147. Bernard’s creative retelling of the Timaeus poetically depicts the role of imitation in the divine creation of the world in the form of “divine writing.” Performatively, the Cosmographia demonstrates that this divine writing is then imitated by poets in the form of human writing. In other words, Bernard values Plato’s Timaeus here not merely for its insights into mathematics or even the structure of the universe, but also what this mathematics in the universe implies about the mimetic nature of poetry itself.

As many literary scholars have demonstrated, much of the European literary tradition follows suit in seeing the value of Timaean Platonism for the production of literature. This interest can be seen in such diverse authors as Alan of Lille, Chrétien de Troyes, and Dante.

While I would personally be loath to give up the access to the Platonic corpus that I possess, the medieval reception of the Timaeus constantly pushes me to reconsider how I am reading that corpus. Having a large corpus of texts actually places an onus on the modern reader to ask the question of where to place the textual emphasis: Which texts of Plato should be considered central (and which ones periphery) and why? For example, should Plato’s Republic be considered his last word on poets and poetry? What would happen if Plato’s Timaeus were given more weight?

C.S. Lewis once wrote in his introduction to On the Incarnation by Athanasius:

Every age has its own outlook. It is specially good at seeing certain truths and specially liable to make certain mistakes. We all, therefore, need the books that will correct the characteristic mistakes of our own period. And that means the old books.

These words about reading the great books can also apply to reading the old books as they were read by past readers. Understanding medieval readings of Plato might very well be a good counterweight to modern presuppositions about who Plato was and what he was about. How might the idea of Plato as both a mathematician and myth-maker transform our modern understanding of Platonism and its history?

Lesley-Anne Dyer Williams is a Professor for Memoria College’s Masters of Arts in Great Books program and graduated with her doctorate from the University of Notre Dame’s Medieval Institute in 2012. She was also the founding director Liberal Arts Guild at LeTourneau University. Her research focuses upon twelfth-century Platonism and poetry, especially Thierry of Chartres and Bernard Silvestris.

Lesley-Anne Dyer Williams
Public Humanities Postdoctoral Fellow
Medieval Institute
University of Notre Dame

For Further Reading:

Albertson, David. Mathematical Theologies: Nicholas of Cusa and the Legacy of Thierry of Chartres. Oxford University Press, 2014.

Baxter, Jason M. The Infinite Beauty of the World: Dante’s Encyclopedia and the Names of God. Peter Lang, 2020.

Bernardus Silvestris. Poetic Works. Edited by Winthrop Wetherbee, vol. 38, Harvard University Press, 2015.

Caiazzo, Irene. “Teaching the Quadrivium in the Twelfth-Century Schools.” A Companion to Twelfth-Century Schools, edited by Cédric Giraud, translated by Ignacio Duran, vol. 88, Brill, 2019, pp. 180–202.

Calcidius. On Plato’s Timaeus. Edited by John Magee, vol. 41, Harvard University Press, 2016.

Chenu, M. D. “The Platonisms of the Twelfth Century.” Nature, Man and Society in the Twelfth Century: Essays on New Theological Perspectives in the Latin West, translated by Jerome Taylor and Lester K. Little, vol. 37, University of Toronto Press, 1997.

Dronke, Peter. The Spell of Calcidius: Platonic Concepts and Images in the Medieval West. SISMEL edizioni del Galluzzo, 2008.

Gersh, Stephen. Middle Platonism and Neoplatonism: The Latin Tradition. Vol 1 and Vol 2. University of Notre Dame Press, 1986.

Hoenig, Christina. Plato’s Timaeus and the Latin Tradition. Cambridge University Press, 2018.

Murray, K. Sarah-Jane. From Plato to Lancelot. Syracuse University Press, 2008.

Plato. Plato’s Cosmology: The Timaeus of Plato Translated with Running Commentary. Edited by F. M Cornford, Routledge, 1937.

Reydam-Schils, Gretchen. “Myth and Poetry in the Timaeus.” Plato and the Poets, edited by Pierre Destrée and Fritz-Gregor Herrmann, Brill, 2011.

Reydams-Schils, Gretchen J. Calcidius on Plato’s Timaeus: Greek Philosophy, Latin Reception, and Christian Contexts. Cambridge University Press, 2020.

Somfai, Anna. “The Eleventh-Century Shift in the Reception of Plato’s Timaeus and Calcidius’ Commentary.” Journal of the Warburg and Courtauld Institutes, vol. 65, 2002, pp. 1–21.

Stock, Brian. Myth and Science in the Twelfth Century. Princeton University Press, 1972.

Wetherbee, Winthrop. Platonism and Poetry in the Twelfth Century. Princeton University Press, 1972.

Seeing the Medieval Together

Back in November, I spent some time wondering about how the spring 2024 iteration of the “Why the Middle Ages Matter” course at John Adams High School would unfold. I spent the last few weeks of 2023 refining my syllabus, working on lesson plans, communicating with guest speakers, and arranging field trips. Looking back, I think I spent so much time preparing for the course because it was all so new to me. The biggest thing that got me nervous was the fact that I would be teaching high schoolers. My prior teaching experiences involved courses designed for university students, so I worried about my ability to make things resonate with a different audience. Furthermore, for the first time I would be leading a teaching team, coordinating with over a dozen guest lecturers, and planning two field trips. I really wanted it to be a good experience for everyone involved. 

Now that it is May and teaching for the course has wrapped up, I like to believe that I can say that things worked out rather well. We all survived! I had six lovely students enrolled in the course. They came from different walks of life and had varying degrees of familiarity with the Middle Ages. These students were all united by their curiosity and eagerness to learn. They impressed me, other members of the teaching team, and my guest lecturers with their questions and comments. I got the impression that they saw our time together during the fourth hour of school as a time to experiment and take risks. They never worried about if a question was partially formulated or about sounding like a novice. Time and time again I thought about how fortunate I was to have such engaged students. Together, we tracked changes around the Mediterranean and beyond as curious co-investigators. With guest lecturers as our guides on our journey, our collective knowledge grew. Field trips allowed us to think beyond the confines of the classroom and encounter cultural productions from the times and places we discussed. They made the Middle Ages feel more real.

We as a class came to the consensus that our trip in mid-April to the Raclin Murphy Museum was a highlight. They were dazzled by the brand-new building, the high ceilings, and impressive gallery spaces. This was the first visit to the museum for all but one of my students. Maggie Dosch, the Assistant Curator of Education School Programs, was our North Star and guiding light as she led us through her thoughtfully-crafted tour and lesson plan. The teacher became a student as I relinquished control to Maggie and her expertise. She shared so much knowledge with us that morning as she led us through close-readings of various works of art.


Maggie Dosch (left, standing), Assistant Curator of Education School Programs, guides students from John Adams High School, South Bend, IN through a close reading of a piece depicting Byzantine iconography. 

Maggie started us off with a selection of pieces from the gallery that features European Art Through 1700. It was wonderful to see my students outside of our typical classroom setting. Instead of sitting in classic student desks facing the front of our cider-blocked classroom, we were all huddled together around various tableaus and sculptures. With nothing but our humble, portable stools and notebooks and pencils, we were all equals in Maggie’s moving classroom. I found myself joining my students in asking Maggie questions about context and materiality. We all wanted to take advantage of being in the presence of someone who knew the gallery and pieces so intimately. She had us all eating out of the palm of her hand as she told us about the process of gilding, reliquaries, and more. Maggie had choreographed a beautiful,  delicate dance that allowed her to move gracefully between the medieval and the contemporary. We saw works from Byzantium and Italy and beyond. Indeed, she took us on a journey around the Mediterranean even though we never really ever left South Bend. Before we knew it, our time with Maggie was done. She only had an hour to spend with us before she had to move onto her next group.

Over lunch at a nearby fast casual restaurant, my students groaned about how short the visit was. Why couldn’t we have doubled or even tripled our time? There was so much more to see and explore! We barely scratched the surface! As they chatted amongst themselves over a feast of pizza and soda, I could hear them asking each other about their favorite parts of the visit. It was great, as an instructor, to know that my students were having these conversations organically among themselves. When lunch time came to an end and we had to make our way back to John Adams High School, I reminded them that the Raclin Murphy Museum is a community resource – they were welcome to return with their friends and family. Many seemed eager to plan for their next visit!


Students from John Adams High School, South Bend, IN gather around a display detailing various inks used during the Middle Ages as well as the process of gilding

Indeed, experiential learning is crucial for making the Middle Ages matter to these students. It is one thing to work with primary sources, listen to guest lecturers, and look at art and architecture on PowerPoint slides. It is another thing entirely to get outside of the conventional classroom setting and encounter a work from the past in an intimate setting. It is a privilege to have an expert help you make various connections between artistic techniques, influences, and historical context. It is powerful to share your observations in real time with someone who can answer any questions you may have as well as provide more insights. It is a way to break down barriers.

Years from now, I have a feeling that my students will not remember me. I mean, I am guilty of not remembering all the names of my wonderful instructors! As time passes, the details of this class might become fuzzy. My students might be able to tell others something along the lines of, “yeah, I took a medieval studies class in high school that was in partnership with the University of Notre Dame.” Perhaps they will recall a guest lecture or two. They might still have a booklet that they made when Dr. Megan Hall came and taught them about medieval book making technologies. Time can take a toll on memory. Despite this, what I hope is that their visit to the museum will become something they can fondly remember years from now. I think about their course evaluations and how they wrote how appreciative they were to be in such an immersive environment. Indeed, experiential learning is powerful. It allows for one to make meaningful connections between classroom lessons and important takeaways. Sensing the Middle Ages is different from reading about it. It allows us to be transported. We are challenged to ask questions about context, movement, materiality, and more. I am so proud of my students, who embraced their status as novices. May they hold onto their curiosity, kindness, and wit as they grow older and experience new things. As for our limited time as a class: we got to see the medieval together, and for that I am forever grateful.

Anne Le, Ph.D.
Public Humanities Postdoctoral Fellow
Medieval Institute
University of Notre Dame

Learning about Learned Medieval Women with Dr. Megan J. Hall

This week, we’re looking back at an earlier episode of “Meeting in the Middle Ages.” In late 2022, we chatted with Dr. Megan J. Hall, Assistant Director of the Medieval Institute at the University of Notre Dame. We spoke with her about women’s literacy and learning in medieval England, the trials and tribulations of writing an academic article, and why impromptu bell-ringing can reveal the true value of scholarship.

Studying history can show us the bigger picture. It can help to explain why nation states behave as they do, why complex geopolitical situations emerge, and how entire landscapes have been shaped over time. But it also allows us to connect with the past on a local level. It can show us where we come from. Speaking with Dr. Hall, we were reminded several times that through historical research, people can identify with those who came before. Moments of identity like that can drastically reshape our relationship with the past. Dr. Hall’s meeting with a group of bellringers in rural England is a perfect example. During this surprise encounter, she was able to share her own work with the group and participate in a tradition of bell ringing which has centuries of history. Her work prompted one of the group to ask ‘so, could women read in the Middle Ages?’ Dr. Hall was able to correct a common misconception of women and the possibilities open to them in medieval England. Yes, some women could read! Some books were written specifically for women! This revelation changed the questioner’s view of medieval women, and was a triumphant ‘I knew we could!’ she experienced a moment of solidarity with them.

Dr. Hall’s story, as has been the case for so many of the conversations we’ve had on Meeting on the Middle Ages, is also a reminder of the privilege that medievalists have. We are able to visit museums, archives, libraries, and go beyond the public spaces. We can consult ancient materials. We don’t have to rely on facsimiles (well, sometimes we do). We can work with the original, turning it over in our hands and connecting with its creator. In doing so, we become another link in a chain that has been forged over centuries. With the Ancrenne Wisse it begins with the object’s creator, perhaps the scribe or composer of a manuscript. It binds together dozens of men and women who received the text and used it in their lives. Dr. Hall is part of that chain. And in telling her story, we all become a part of it too.

Thanks for listening. See you next time in the Middle Ages.

Will Beattie & Ben Pykare
Medieval Institute
University of Notre Dame