# Definition:Principle of Mathematical Induction/Historical Note

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## Historical Note on Principle of Mathematical Induction

The first European to use the Principle of Mathematical Induction rigorously in a proof appears to have been Francesco Maurolico, in *Arithmeticorum Libri Duo* ($1575$).

Further improvements were made by Pierre de Fermat, from which be derived his Method of Infinite Descent.

The Principle of Mathematical Induction appeared again in an adequately rigorous manner by Blaise Pascal in his *Traité du Triangle Arithmétique* ($1655$).

The phrase **mathematical induction** appears to have been coined by Augustus De Morgan.

Further discussion of the process can also be found in *Induction and Analogy in Mathematics* by George Pólya ($1954$).

## Sources

- 1917: W.H. Bussey:
*The Origin of Mathematical Induction*(*Amer. Math. Monthly***Vol. 24**: pp. 199 – 207) www.jstor.org/stable/2974308 - 1918: Florian Cajori:
*Origin of the Name "Mathematical Induction"*(*Amer. Math. Monthly***Vol. 25**: pp. 197 – 201) www.jstor.org/stable/2972638 - 1972: Roshdi Rashed:
*L'induction mathématique: al-Karajī, as-Samaw'al*(*Arch. Hist. Exact Sci.***Vol. 9**,*no. 1*: pp. 1 – 21) www.jstor.org/stable/41133347 - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.16$: Pascal ($\text {1623}$ – $\text {1662}$) - 1997: Donald E. Knuth:
*The Art of Computer Programming: Volume 1: Fundamental Algorithms*(3rd ed.) ... (previous) ... (next): $\S 1.2.1$: Mathematical Induction