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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    @WolfgangBangerth Absolutely true and that was my implicit point: a senseless death by duel, another senseless death by war and a third senseless death by war or serious illness. How much more of the future have we lost? – Ed V Jun 29 at 2:14
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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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    (+1) Excellent list! – Ed V Jun 29 at 21:25
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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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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

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