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Where did the word logarithm come from? Any relation to the word algorithm?

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There is no relation between the two words.

logarithm: 1610s, Mod.L. logarithmus, coined by Scottish mathematician John Napier (1550-1617), lit. "ratio-number," from Gk. logos "proportion, ratio, word"

algorithm: was derived from the name of 8th century Persian mathematcian al-Kwarizmi.

Note: I think it's unusual for a term to derive from a person's name, especially in mathematics. I know words like "bowdlerize" (meaning to edit by removing offensive material) from Thomas Bowdler, or a "spoonerism" (a phrase constructed by exchanging syllables between words, eg "Swell foop") named after William Spooner, but in math I believe it's quite rare. The now-standard lowercase "abelian" is perhaps another example.

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  • $\begingroup$ Is there any reason it's called a logarithm and not something else? Now I'm curious. $\endgroup$ – Leonardo Fontoura May 8 '11 at 4:04
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    $\begingroup$ This: pballew.net/arithme1.html seems to agree. $\endgroup$ – Aryabhata May 8 '11 at 4:04
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    $\begingroup$ Well, besides abelian, there's Noetherian, Artinian, Gaussian, Riemannian, Jacobian, Laplacian, Lagrangian, Hamiltonian, d'Alembertian, Eulerian, Lorentzian, Dedekind (as in domain), Hilbert (as in scheme), Jacobson (as in ring)... $\endgroup$ – Qiaochu Yuan May 8 '11 at 4:30
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    $\begingroup$ @Qiaochu: Note that I was requiring that the word be accepted as "elevated" to lowercase usage in order to sufficiently divorce it from its origin as a proper noun. Both "algorithm" and (often) "abelian" enjoy this status. $\endgroup$ – Fixee May 8 '11 at 4:46
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    $\begingroup$ That reminds me... $\endgroup$ – J. M. is a poor mathematician May 8 '11 at 5:38

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