When Descartes Challenged Fermat (and Lost)

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How were tangents derived before calculus? And why did Descartes and Fermat, two of history’s more renowned mathematicians, hate each other? Watch to explore their methods to solve the tangent line problem and the origins of their bitter rivalry.

Check out my series on building numbers from the ground up:
   • Mathematics from the Ground Up  

⬣ TIMESTAMPS ⬣
Intro - 00:00
Descartes and his Circle Method - 03:34
Fermat and his Adequality Method - 15:13
Rivalry - 29:09
Folium of Descartes - 31:26
Conclusion - 42:18
Outro - 46:08

⬣ CORRECTIONS ⬣
In some sources, “Discourse on Method” is described as a work of three essays. Elsewhere, it is described as the introductory work to those three essays.

⬣ INVESTIGATORS ⬣
Are you still out there? Check my logic video for an update!

⬣ REFERENCES ⬣
[1] R. Descartes, La Geometrie, Trans. David Eugene Smith and Marcia L. Latham. Open Court Publishing Company: La Salle. (1952), pp. 95–112.
[2] Selected Correspondence of Descartes, Jonathan Bennett 2017:
https://www.earlymoderntexts.com/asse...
[2a] to Mersenne, end of xii.1637, paraphrased.
[2b] Fermat to Mersenne, iv or v 1637.
[2c] to Morin, 13,vii.1638.
[2d] to Mersenne 27.vii.1638
[2e] to Mersenne, ix.1641.
[2f] against Fermat, 1.iii.1638.
[2g] to Mersenne, 27.v.1638.
[2h] to Mersenne, xii.1638.
Huge thank you to Hal Hellman and his excellent “Great Feuds in Mathematics” for compiling many of the sources used in this video.
[3] Hal Hellman, Great Feuds in Mathematics, 2006.
[4] D. E. Smith, A Source Book in Mathematics, McGraw-Hill, 1929, pp. 389-96.
[5] Fermat to Mersenne, December 1637; Fermat Oeuvres, vol. 2, p. 116. Translated by Daniel Curtin.
[6] Fermat to Mersenne, February 1638; Fermat Oeuvres, vol. 2, pp. 132-33. Translated by Daniel Curtin.
[7] G. F. Simmons, Calculus Gems, 1992 p. 101.
[8] Fermat to Clerselier, March 10, 1658. Translated by elucidation by James Nicholson.
[9] J. D. Nicholson, as detailed in Hal Hellman, "Great Feuds in Mathematics" 2006.
[10] L. T. More, Isaac Newton, Scribner’s 1934 p. 185.

⬣ CREDITS ⬣
All music by Danjel Zambo.
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