www.thepsmiths.com/p/joint-review-philosophy-between-the
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for example calculus was probably invented in the ancient world by Eudoxus of Cnidus and by Archimedes, and then completely forgotten.
Standard histories of mathematics credit the invention of calculus to Newton and Leibniz in the 17th century; Eudoxus and Archimedes developed important precursors (e.g., the method of exhaustion), not calculus itself. Their work also wasn’t “completely forgotten,” since Archimedes’ works were translated and circulated in medieval/early modern Europe.
Full reasoning
Why this is incorrect
The post asserts that calculus was “probably invented” by Eudoxus and Archimedes in antiquity, then “completely forgotten.” That conflicts with standard reference accounts:
- Who is credited with inventing calculus
- A mainstream reference overview states: “Calculus was invented… by Isaac Newton and Gottfried Leibniz.” It then explicitly treats Eudoxus’s method of exhaustion and Archimedes’s use of it as beginnings/precursors, not the invention of calculus.
- The Stanford Encyclopedia of Philosophy entry on Newton likewise describes Newton as having invented calculus in the mid-to-late 1660s.
- Eudoxus/Archimedes are described as precursors, not inventors of calculus
- MacTutor’s “A history of the calculus” describes Greek contributions (Eudoxus’s method of exhaustion; Archimedes’ area/volume results) as early steps and then states there was no further progress until much later, before Newton/Leibniz.
- Wikipedia’s overview of the method of exhaustion describes it as a precursor to calculus and notes later development of integral calculus.
- “Completely forgotten” is also too strong
Even if one sets aside the “who invented calculus” point, the claim that this body of work was “completely forgotten” is contradicted by the documented transmission of Archimedes’ writings. For example, Museo Galileo notes that William of Moerbeke translated Archimedes’ works into Latin in 1269, and that manuscript traditions and later copies fed into the first printed edition (Basel 1544). That is not consistent with “completely forgotten.”
What’s true instead
- Eudoxus and Archimedes made foundational contributions (especially to proto-integral ideas via exhaustion), but standard histories credit the invention of calculus as a general method to Newton and Leibniz in the 17th century.
- Archimedes’ works were transmitted and reintroduced in Latin/print traditions rather than being wholly lost.
4 sources
- Calculus | Encyclopedia.com
“Calculus was invented, more or less simultaneously, by Isaac Newton (1642–1727) and Gottfried Leibniz (1646–1716). Some of its essential concepts, however, had their beginnings in ancient Greece… Eudoxus… invented the… method of exhaustion… Archimedes… used the same method…”
- Isaac Newton (Stanford Encyclopedia of Philosophy)
“Isaac Newton… is best known for having invented the calculus in the mid to late 1660s…”
- A history of the calculus | MacTutor History of Mathematics (University of St Andrews)
Describes Eudoxus’ method of exhaustion and Archimedes’ work as early steps, then notes “No further progress was made until the 16th Century,” and later discusses Newton’s fluxions and the Fundamental Theorem of Calculus.
- Archimedes, Opera, Latin translation by W. of Moerbeke (Codex O) | Museo Galileo
States William of Moerbeke translated Archimedes’ works into Latin in 1269; copies in the 15th–16th centuries formed the basis of the 1544 Basel first printed edition of Archimedes’ works.