Talk:Harmonic series (mathematics)/GA1

GA Review

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Reviewer: XOR'easter (talk · contribs) 21:01, 12 March 2022 (UTC)[reply]

I find the article well-written, in an encyclopedic rather than a textbook-like way. It is pitched to an appropriate audience level given the material, and the least technical parts are pushed to the forefront. Approved
The article is verifiable with no original research. It presents standard material without novel synthesis. Citations are properly and consistently formatted. I have a few minor points that I will detail below. GA on hold
The coverage addresses the main topics without drowning in detail. There is doubtless room for expansion, given how many places in mathematics a subject like this will pop up, but we're not going for FA-level comprehensiveness here. Approved
I find no editorial bias. Approved
No signs of edit-warring or content disputes. Approved
Images are appropriate; no licensing issues. Approved

Now, for a few things that look like easy fixes:

Reference 2, Kullman (2001), is cited to support the claim that Johann Bernoulli proved the series' divergence, but it only mentions Jacob Bernoulli (under the name Jacques Bernoulli).

Replaced with new Dunham source, and reordered to clarify that the first publication was Jacob's but that in it he credited Johann with the proof. —David Eppstein (talk) 02:39, 13 March 2022 (UTC)[reply]

Reference 14, Havil (2003), appears not to actually use the term harmonic number — it just uses $H_{n}$ , in all the instances I can find. "No property is more unexpected than $H_{n}$ 's divergence, and it is this that Oresme proved", etc. I'm actually a bit puzzled by this, since the terminology is so well established. I'm not convinced that a citation explicitly introducing the term is obligatory, given that we have a whole article on it (it's unlikely to be challenged), but maybe there's a secondary source that reports the first known use of the term, or something like that.

I don't know about secondary, but I appear to have found the primary source with the first use of the term: Knuth's Art of Computer Programming (1968). —David Eppstein (talk) 03:11, 13 March 2022 (UTC)[reply]

In the "Crossing a desert" example, leuca is undefined, though in context it's clearly a measure of distance. The source says that one leuca is 1500 double paces, or about 1.5 miles. Perhaps this should be worked into the text.

Ok, added a gloss for this unit. With the source's definition of a double pace as 5 feet, it's closer to 1.4 miles, but I used km as the primary unit and miles converted from that. —David Eppstein (talk) 08:02, 13 March 2022 (UTC)[reply]

Euler's conclusion that the partial sums of reciprocals of primes grow as a double logarithm of the number of terms has been confirmed by later mathematicians as one of Mertens' theorems, and can be seen as a precursor to the prime number theorem. The statement looks right, but the source provided does not include a specific mention of Mertens' theorems. Maybe it should be supplemented?

Added another reference (Pollack). —David Eppstein (talk) 08:27, 13 March 2022 (UTC)[reply]

These are all very low-grade issues, but they might get slightly in the way of a student's understanding. XOR'easter (talk) 21:25, 12 March 2022 (UTC)[reply]

Ok, I think I've handled them all. Time for another look? —David Eppstein (talk) 08:27, 13 March 2022 (UTC)[reply]

Looks good to me! XOR'easter (talk) 18:50, 13 March 2022 (UTC)[reply]