One Hundred Years On: Warburg’s Discovery of the Ellipse

Written by Claudia Wedepohl |
Aby Warburg in Kreuzlingen, c. 1924.

This April commemorated a century since Aby Warburg's profound conversations with philosopher Ernst Cassirer, shedding light on the symbolic importance of the ellipse.

In this blog, Warburg Archivist, Claudia Wedepohl, unveils the significant impact of this historic encounter, offering fresh insights into Warburg's intellectual journey and its enduring resonance in contemporary discourse.

April 2024 marks the centenary of Aby Warburg’s conversations with the philosopher Ernst Cassirer (1876-1945) which led to Warburg’s discovery of the ellipse as a symbolic form. The two scholars met on 10 April 1924 and again the next day in the gardens of Ludwig Binswanger’s private psychiatric clinic in Kreuzlingen on the Swiss side of Lake Constance.

Ernst Cassirer, c. 1930.

By 1924, Warburg had spent over five solitary years in psychiatric institutions and suffered from isolation. This encounter offered him a rare opportunity for intellectual exchange with Cassirer, who, since 1919, held the esteemed position of the inaugural chair of philosophy at the newly established Universität Hamburg, while concurrently crafting his magnum opus, The Philosophy of Symbolic Forms (1923-1929).

Cassirer was acquainted with Warburg through Fritz Saxl, who served as Warburg’s close collaborator and, in Warburg’s absence, assumed the role of acting director of his library. Saxl had kept Warburg abreast of Cassirer’s activities; Warburg and Cassirer read each other’s works and exchanged letters. Thus charged with expectations, the meeting turned out to be so impressive that both, as it was said in their circles, drew on it for years. According to Saxl, it was the "first ray of light in dark years" for Warburg, and Cassirer later recalled that "after the first few sentences" they had "got to know and understand each other in a way that you usually only understand each other after years of working together."[1] What happened and what impact did it have on Warburg’s work?

Johannes Kepler, Mysterium cosmographicum, in Opera omnia, vol. 1, edited by Ch. Frisch, Frankfurt/M and Erlangen 1858 (with Kepler's platonic model of the cosmos as frontispiece).

For Warburg, this meeting sparked a rekindling of interest in his essay on the fresco program at Palazzo Schifanoia, published in 1922 and distributed in late 1923. Weeks earlier he had resumed his ruminations about the structure and status of the gigantic calendar and developed a specific interest in the genesis of the modern image of the cosmos, or, to say it more pointedly: the transition from speculation to calculation. His thoughts then began to circle around the figure of the astronomer Johannes Kepler (1571-1630) who, he speculated, played a pivotal role in the evolution of modern thought, specifically when Kepler replaced the traditional superiority of the ideal circular form with the acceptance of the ellipse as a geometrical form. However, since this intuitive presumption had to remain hypothetical before it was confirmed by an authority, Warburg sought the direct exchange with Cassirer. Once he knew the philosopher was planning a trip to Switzerland, he concentrated on the question of how Kepler could have realised that the formula for calculating the orbits of the planets, derived from Plato’s concept of a cosmos composed of so-called platonic solids, inevitably yielded unsatisfactory results. Factoring in the ellipse seemed to hold the answer. Warburg knew that the ancient Greek geometer Apollonius of Perga (c. 262-c.190 BC) had discussed conic sections in his work Conica. However, being far from his library, he was unable to prove when Apollonius’s work was rediscovered and, subsequently, if a conscious return to antique knowledge could have resolved a mathematical problem around 1600.

Johannes Kepler, Mysterium cosmographicum, in Opera omnia, vol. 1, edited by Ch. Frisch, Frankfurt/M and Erlangen 1858 (with Kep

In February 1924, he tried to get a clearer picture from his younger daughter Frede (1904-2004), who had just sat her Abitur in physics. Through a handbook, Max Cantor’s Vorlesungen zur Geschichte der Physik, Frede found out that four books of Apollonius’s work, in total consisting of eight books, had survived and been known and translated in the sixteenth and edited in the seventeenth century.[2] Subsequently, the remaining question for Cassirer was if Kepler knew of this work. 

Aby Warburg, Letter to Mary Warburg, 12 April 1924.
Johannes Kepler, Astronomia Nova, in Opera Onmia, vol. 3, edited by Ch. Frisch Frankfurt/M and Erlangen, 1860, p. 110.

Through Aby’s daily letters to his wife, we have some idea of the discussions and how Warburg perceived the exchange. He reported that he was impressed by Cassirer’s clarity and felt they were both pursuing the same questions, one from a philosophical, the other from an image-historical (bildgeschichtlich) perspective. Concerning the crucial question he wrote: “Cassirer was able to confirm that a letter exists in which Kepler explains the ellipse to a friend who struggled to visualize it.”[3] A day after his departure, Cassirer sent the bibliographical reference, confirming that: “The theory of the conic sections, as Apollonius had phrased it, is developed and discussed in detail by Kepler in his main work on the motion of Mars (De motibus stellae Martis, 1609) Pars IV, Caput LIX; Commandinus’s edition (Opera III, 401ff.) is used and quoted here.”[4] Receiving this information was the turning point in Warburg’s slow recovery from a mental illness that was triggered by the defeat of Germany in WWI. It was also the beginning of a friendship which Warburg considered vital for the last years of his life.

Reading Room of the Kulturwissenschaftliche Bibliothek Warburg under construction, 1925.

About a year after the Kreuzlingen meeting, the bipolar form of the ellipse, personally meaningful to Warburg as a symbol of both the human psyche and rational thinking, was translated into the structure for the most iconic element of the purpose-built library, the Kulturwissenschaftliche Bibliothek Warburg (KBW), at Heilwigstraße 116: its combined Reading Room and Lecture Hall, designed by young architect, Gerhard Langmaack (1898–1986).

The KBW was inaugurated on 1 May 1926 with a lecture by Ernst Cassirer on “Freedom and Necessity in the Philosophy of the Renaissance”. Just over 90 years after the Nazis forced the library and its staff out of the building and out of Germany, the Warburg Institute’s new Lecture Theatre, set to officially open on 1 October 2024, will feature the same symbolic form.

The new Warburg Lecture Theatre under construction. Photo by Claudia Wedepohl.


[1]  Fritz Saxl, "Ernst Cassirer", in A. Schilpp (Ed.), The Philosophy of Ernst Cassirer, Evaston/Illinois 1949, pp. 47-51; Ernst Cassirer, "Worte zur Beisetzung von Professor Dr. Aby M. Warburg", in Stefan Füssel (Ed.), Mnemosyne. Beiträge zum 50. Todestag von Aby M. Warburg, Göttingen 1979, p. 17. Cf. Horst Bredekamp and Claudia Wedepohl, Warburg, Cassirer und Einstein im Gespräch. Kepler als Schlüssel der Moderne, Berlin 2015.

[2]  Bredekamp/Wedepohl, pp. 42-43; Moritz Cantor, Vorlesungen über Geschichte der Mathematik, vol. 1, Leipzig 1907, pp. 334–343, 444, 704, 749–751; vol. 2, Leipzig 1913, pp. 553, 558, 660–662; Michael N. Fried and Sabetai Unguru, Apollonius of Perga’s Conica. Text, Context, Subtext, Leiden, Boston and Cologne 2001.

[3]  Bredekamp/Wedepohl, p. 46.

[4]  Bredekamp/Wedepohl, p. 47.