The h-index is often used to measure a 'quality' of a scholar, and it is also often criticized as a lousy measure, since there is more into quality than just the number of papers and citations.

What are some examples of arguably great and famous scientists with low h-index?

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    Maybe Galois? Great work for a teenager and h = 1 is the bottom. – Ed V Jun 28 at 22:23
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    @Ed-V His h-index might be low, but his output relative to opportunity is extremely good. Might consider him for a scholarship :D :D – o4tlulz Jun 28 at 23:46
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    Dying young is helpful for making this list: If you only have N papers, you definitely have H<N. – Wolfgang Bangerth Jun 29 at 1:29
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    @EdV That loss alone would be reason enough for any civilized species to stop war and hunger. And yet it is just the tip of the iceberg. The loss is beyond comprehension, and entirely gratuitous. – Peter - Reinstate Monica Jun 29 at 7:30
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    Historical examples are probably not very informative in this regard, because publication practices have changed a lot. – Nate Eldredge Jun 29 at 15:19

You can find a lot of historical examples, from people whose careers predated the publish-or-perish culture. A striking more recent example is Peter Higgs, who was awarded (among other honors) the 2013 Nobel prize in physics. Whether that makes him a "great" physicist is of course arguable, but he clearly did important work. However,

Peter Higgs, the British physicist who gave his name to the Higgs boson, believes no university would employ him in today's academic system because he would not be considered "productive" enough.

The emeritus professor at Edinburgh University, who says he has never sent an email, browsed the internet or even made a mobile phone call, published fewer than 10 papers after his groundbreaking work, which identified the mechanism by which subatomic material acquires mass, was published in 1964.

This article estimated his h-index to be about 9, but I've seen estimates of around 11 too. Either way, it's a very low number for the field by today's standards, for an established professor. To wit,

Speaking to the Guardian en route to Stockholm to receive the 2013 Nobel prize for science, Higgs, 84, said he would almost certainly have been sacked had he not been nominated for the Nobel in 1980.

Edinburgh University's authorities then took the view, he later learned, that he "might get a Nobel prize – and if he doesn't we can always get rid of him".

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    (+1) This is a great one! The publish-or-perish era does make it much tougher, but the rare few are a wonderful reminder of the heights that human beings can attain. – Ed V Jun 29 at 0:11
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    Amazing what a little Nobel Prize will solve! – Jeff Jun 29 at 18:22
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    @Jeff Back from Stockholm, Serge Haroche made an informal speech on front of the physics department (where I was a student). He opened by mentioning that the dean had offered him a permanent parking spot "for some reason", to the laughter of attendants. (Parking spots are a rare resource in Paris.) – UJM Jun 29 at 19:35
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    "had he not been nominated for the Nobel in 1980" -- since Nobel nominations are not disclosed to the public nor to the nominees themselves, how would anyone have known? Presumably through gossip/rumor? So perhaps it's really "had he not been nominated for the Nobel in 1980 and luckily had credible word of this somehow reach his bosses". – nanoman Jun 30 at 4:06
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    @WoJ He retired in 1996, the internet was much less useful at the time – JenB Jun 30 at 20:37

Here are a few contemporary mathematicians who solved major open problems and have relatively low h-index, computed using citation data MathSciNet, for their stature in the mathematical community:

Yitang Zhang (proved boundedness of gaps in primes): h-index 2

Grigori Perelman (solved the Poincaré conjecture): h-index 10

Andrew Wiles (proved Fermat's Last Theorem): h-index 15

All of these mathematicians made quite the splash, and are worth reading about, and have the feature that they wrote relatively few papers but worked on very deep, hard problems.

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    Where'd you get the h-indices? Via Web of Science? – Allure Jun 30 at 7:23
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    @Allure As stated in the answer, I looked at their citations on MathSciNet, and just manually computed h-indices. – Kimball Jun 30 at 13:04
  • @Kimball sorry, don't know how I missed that. – Allure Jun 30 at 13:15
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    @Allure No worries! Your comment got 1 upvote, so at least one other person missed it too! – Kimball Jun 30 at 13:17

Ernst Ising probably counts. He did his PhD thesis on the (now well-known) model that bears his name, but didn't work in physics for decades afterwards. Though he eventually became a physics professor, he didn't publish again either. I couldn't find anything about his h-index, but it can't be too high since there aren't many works written by him.

After earning his doctorate, Ernst Ising worked for a short time in business before becoming a teacher, in Salem, Strausberg and Crossen, among other places. In 1930, he married the economist Dr. Johanna Ehmer. As a young German–Jewish scientist, Ising was barred from teaching and researching when Hitler came to power in 1933. In 1934, he found a position, first as a teacher and then as headmaster, at a Jewish school in Caputh near Potsdam for Jewish students who had been thrown out of public schools. Ernst and his wife Dr. Johanna Ising, née Ehmer, lived in Caputh near the famous summer residence of the Einstein family. In 1938, the school in Caputh was destroyed by the Nazis, and in 1939 the Isings fled to Luxembourg, where Ising earned money as a shepherd and railroad worker. After the German Wehrmacht occupied Luxembourg, Ernst Ising was forced to work for the army. In 1947, the Ising family emigrated to the United States. Though he became Professor of Physics at Bradley University in Peoria, Illinois, he never published again. Ising died at his home in Peoria in 1998, just one day after his 98th birthday.

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  • Arguably, Ising's net contribution to physics is negative, since he didn't invent his eponymous model - it was suggested to him by his advisor Lenz; then Ising proved that it has no phase transition in 1D (which is an easy exercise) and incorrectly claimed this to be the case in higher dimension, a claim only corrected 15 years later. – Kostya_I Jul 13 at 13:03

How about a physicist, Erich Hückel, who created Huckel theory and one of the founding fathers of MO theory/quantum chemistry.

He was definitely someone who struggled in academia even before the publish-or-perish era, hardly able to get a professorship. I couldn't find his official publication list, but this encyclopedia article lists 11 works for all his life: https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/huckel-erich-armand-arthur

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    +1. Nike Dattani here. – user1271772 Jul 2 at 1:07

Albert Einstein

Just yesterday this article was published with the title "Albert Einstein the mediocre: Why the h-index is a bogus measure of academic impact." Check this out:

"let's examine the case of Einstein, who has 147 articles listed in the Web of Science database between 1901 and 1955, the year of his death. For his 147 articles, Einstein has received 1,564 citations during his lifetime. Now, if we add the citations made to his articles after his death, Einstein has received a total of 28,404 citations between 1901 and 2019, which earns him an h-index of 56."

Only 1564 citations over 147 articles, at the time of his death!

The h-index of 56 might seem large, but there's been about 70 years of citations (23,000 of them) after his death, so even when he was 76 years old he would have had an h-index that might be considered mediocre for someone at that age, and someone considered to be one of the most prolific academics of all time.

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    There's no denying Einstein's influence and importance, but who considers him one of the most prolific academics? Now, someone like Erdős who published about 1500 articles is another story. That's properly prolific. Further, was 1564 citations really so low in 1955 for theoretical physics? After all, the citation culture has changed significantly over time. As an example, Einstein's 1905 special relativity paper doesn't cite any references. – Anyon Jul 11 at 22:58
  • I think profilic is an acceptable term to describe Einstein. It doesn't just mean publishing lots, it could also mean having big impact and being very famous. You raise a good point about citation culture changing, but 10 citations/paper is still quite low in my opinion considering that 50 years of papers were published from 1905-1955, and I'm sure many of them cited relativity, the photo-electric effect, and brownian motion, leaving very little room for a high h-index, even for his time! – user1271772 Jul 11 at 23:37

Incidentally, to answer the question in the title, "scholarship" and "peer-reviewed publication" are substantially different things, somewhat like "understanding" and "novelty" are not at all the same, though loosely connected.

In mathematics, in the U.S., for example, "scholarship" is not much rewarded by "the system", if only because it's hard to quantify, and the contemporary style of quantification of is much beloved by administrators at all levels, and papercount, etc., are numbers.

And, then, again, "citation count" is a very skewed metric, for many reasons.

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