KANT IN THE CLASSROOM     Materials to aid the study of Kant’s lectures

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Mathematics Notes

Kant taught mathematics a total of fifteen semesters, all at the beginning of his career; the last time was as a privatissima course in WS 1763/64. The only candidates for student notes from these lectures stem from Herder (early 1760s), and these are quite fragmentary. The evidence that they in fact come from Kant's lectures is entirely circumstantial, namely, we know that Kant was lecturing on mathematics at the time, and we know that Herder was taking courses free of charge from Kant.[1] Kant used Wolff’s Anfangsgründe aller mathematischen Wissenschaften [1710], of which Kant owned the 1750 edition, and sometimes he used the shorter Auszug aus den Anfangsgründen aller mathematischen Wissenschaften [1713], of which Kant owned the 1749 edition (Kant’s copies have not been found).  See the Mathematics lectures.

Apart from these few lecture notes from Herder, one might also consult the collection of mathematical reflections, ##1-19 [AA 14:3-61], although most of these date from the late 1770s through the 1790s (that is, much later than the Herder lecture notes).

[1] Herder claims, in his preface to Kalligone (1800), to have attended all of Kant’s courses offered during those years [Irmscher 1998, 651-52] and Karl Gottlieb Bock [bio] wrote that “Kant offered to let him hear, free of charge, all his lectures on logic, metaphysics, moral philosophy, mathematics, and physical geography” [Herder 1846, i.133]; but Karl August Böttiger [1998, 125] reported in his journal that Herder attended — “with great dilligence” — the mathematics lectures of F. J. Buck [bio], who was at that time the full professor of Logic and Metaphysics, and also appears to have used Wolff for his mathematics lectures.

(1) Herder 3

Physical Description and History

Two fragments, four sheets each.  Irmscher is not certain that both stem from Kant’s lectures [Irmscher 1964, 12; and see Lehmann 1980, 658-60].


(1) Ms: Berlin, Staatsbibliothek Preußischer Kulturbesitz, Haus II, NL-Herder:

XXV.45.  Four 4° sheets (17.5 x 20.5 cm), seven pages of text total, from a larger printer’s sheet, folded twice. Paper is ribbed, with a watermark (Irmscher calls it a crowned eagle). The wide left-hand margin is marked with a crease down the middle of each page, and contains some marginalia. The last page (4v) is blank. A1-A3 are based on Kästner, A4-A-7 on Wolff (see the textbooks, below). Brown ink throughout. Printed at AA 29: 49-58.
XXV.46. Same size and format as the previous, but there is no margin. 3v is blank. Printed at AA 29: 59-66.


(1) Irmscher [1964, 17-39].

(2) Lehmann [1980; AA 29: 49-66].  The Academy edition marginal pagination does not include the blank pages.

(3) A draft of a new transcription of the notes is available here.


Johann Gottfried Herder [bio] matriculated August 10, 1762.[1] Kant taught mathematics WS 1762/63 and SS 1763 during Herder’s stay in Königsberg (he would not likely have attended Kant’s privatissima course held in WS 1763/64).  If these are in fact notes from Kant’s classroom, then they would need to stem from one of these two semesters. They are also quite brief, and appear to belong to the very beginning of the semester. There is enough overlap between the two manuscripts to infer that they stem from separate semesters — perhaps XXV.45 from WS 1763/64 and XXV.46 from the next semester, SS 1764. If Kant was offering mathematics on a two-semester cycle, with pure (arithmetic, geometry, trigonometry) in the winter and applied (mechanics, hydrostatics, aerometry, and hydraulics) in the summer (see the discussion on the mathematics lectures), then the XXV.46 notes would need to be viewed as a summary of the previous semester before turning to the applied areas.

See also Herder’s notes on metaphysics, physical geography, moral philosophy, physics, and logic.

[1] Erler [1911-12, ii.484]: (10 Aug 1762) “Herder Joh. Godfr., Mohrunga Boruss.”.