Cauchy-Goursat Theorem/Historical Note

Historical Note on Cauchy-Goursat Theorem

The Cauchy-Goursat Theorem was actually first investigated and proved by Carl Friedrich Gauss, but it was just one of the things that he failed to get round to publishing.

He stated it in a letter of $1811$ to his friend Friedrich Wilhelm Bessel, where he says:

This is a very beautiful theorem whose fairly simple proof I will give on a suitable occasion. It is connected with other beautiful truths which are concerned with series expansions.

Augustin Louis Cauchy was, however, the first to publish a proof ca. $1825$, under the assumption that the derivative $f'$ is continuous.

Karl Weierstrass independently discovered this theorem during his exercise to rebuild the theory of complex analysis from first principles.

Édouard Goursat published a general proof in $1884$.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.25$: Gauss ($\text {1777}$ – $\text {1855}$)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.26$: Cauchy ($\text {1789}$ – $\text {1857}$)
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$)