Talk:Harmonic series (mathematics)/GA1

GA Review
The edit link for this section can be used to add comments to the review.''

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


 * 1) 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. ✅
 * 2) 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.
 * 3) 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. ✅
 * 4) I find no editorial bias. ✅
 * 5) No signs of edit-warring or content disputes. ✅
 * 6) Images are appropriate; no licensing issues. ✅

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)

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)

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)

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)

These are all very low-grade issues, but they might get slightly in the way of a student's understanding. XOR&#39;easter (talk) 21:25, 12 March 2022 (UTC)
 * Ok, I think I've handled them all. Time for another look? —David Eppstein (talk) 08:27, 13 March 2022 (UTC)
 * Looks good to me! XOR&#39;easter (talk) 18:50, 13 March 2022 (UTC)