An academic friend of mine mentioned that his H-index was 12. He is a professor of medicine at a major university in Turkey. He was very proud of this accomplishment. I have been away from academia for a long time so I did not know what H-index was. He explained it to me. Then, I did a little research and quickly checked the H-index scores of some of my other academic friends. I thought H-index was interesting so I wanted to share what I learned.
The H-index tries to measure a scientist’s academic influence. There are other measures of academic impact but the simplicity of the H-index is very appealing.
H-index = 12 means that my friend has at least 12 scientific papers that were cited by 12 or more scientific papers. He has published many more than 12 papers but some of those papers did not receive any citations and few of them received many citations. One paper has received more than 50 citations but it only counts as 1 towards the 12. H-index is not a citation weighted index.
Another explanation is
“To determine the h-index of a researcher, organize articles in descending order, based on the number of times they have been cited. Thus, if an individual has eight papers that have been cited 33, 30, 20, 15, 7, 6, 5 and 4 times, the individual’s h-index would be 6. The first paper 33, gives us a 1 – there is one paper that has been cited at least once, the second paper gives a 2, there are two papers that have been cited at least twice, the third paper, 3 and all the way up to 6 with the sixth highest paper –the final two papers have no effect in this case as they have been cited less than six times (Ireland, MacDonald & Stirling, 2013).” 
I think that the H-index of a scientist or mathematician is not very informative. To get a better idea of the academic influence we have to see the evolution of the number of citations every year.
The first chart belongs to a famous mathematician. His H-index is 42. His chart is truly impressive. The number of citations is increasing every year and the actual number of citations is truly impressive.
The second chart belongs to a successful physicist. His H-index is 17. His chart looks impressive too but it shows that his academic influence is leveling off.
The charts of physicists and mathematicians will be different because physics gets old very quickly. Mathematics, on the other hand, is ageless. This is why the chart of a mathematician will most probably keep going up as more and more mathematical papers will cite his mathematical results. We still cite Euclid don’t we? This shows one of the weaknesses of the H-index. It is not universal across disciplines.
To see the other weaknesses of the H-index and the comparisons to the other measures you can take a look at the Wikipedia article.