### The H-Index

Edward Witten (born August 26, 1951) is an American mathematical physicist, Fields Medalist, and professor at the Institute for Advanced Study. He is one of the world’s leading researchers in string theory (as the founder of M-theory) and quantum field theory. Witten is widely admired among his peers. This includes the renown 20th century geometer, Sir Michael Atiyah, who said of Witten, “Although he is definitely a physicist, his command of mathematics is rivaled by few mathematicians… Time and time again he has surprised the mathematical community by his brilliant application of physical insight leading to new and deep mathematical theorems… he has made a profound impact on contemporary mathematics. In his hands physics is once again providing a rich source of inspiration and insight in mathematics.” He also appeared in the list of TIME magazine’s 100 most influential people of 2004. He was mentioned in a 1999 episode of the cartoon Futurama. Witten has the highest h-index of any living physicist. he h-index is an index suggested in 2005 by Jorge E. Hirsch of the University of California, San Diego to quantify the scientific productivity of physicists and other scientists based on their publication record. The index is calculated based on the distribution of citations received by a given researcher’s publications. Hirsch writes: A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np – h) papers have at most h citations each. In other words, a scholar with an index of h has published h papers with at least h citations each.The index is designed to improve upon simple measures such as the total number of citations or publications, to distinguish truly influential physicists from those who simply publish many papers; the index is also less sensitive to single papers that have many citations. The index works best for comparing scientists working in the same field; citation conventions differ among different fields. The h-index is calculable using free Internet databases and serves as an alternative to more traditional impact factor metrics which are available for a fee. Because only the most highly cited articles contribute to the h-index, its determination is a speedy process. Hirsch has demonstrated that h has high predictive value for whether or not a scientist has won honors like National Academy membership or the Nobel Prize. In physics, a moderately productive scientist should have an h equal to the number of years of service while biomedical scientists tend to have higher values. Criticism t is not difficult to come up with situations in which h may provide misleading information about a scientist’s output. Most importantly the fact that h is bounded by the total number of publications means that scientists with a short career are at an inherent disadvantage, regardless of the importance of their discoveries. For example, Evariste Galois’ h-index is 2, and will remain so forever. Had Albert Einstein died in early 1906, his h index would be stuck at 4 or 5, despite him being widely acknowledged as one the greatest physicists ever to have lived. Proposals to modify the h-index in order to emphasize different features have been made. Based on the SPIRES HEP Database (Particle and High energy Physics, As of August 2005,):

The H-index explained