Opinion 194: The h-Index Should Be Replaced by the "Surprise Index"

Commissioned By: Doron Zeilberger; Written By: ChatGPT

Written: April 1, 2026

The mathematical community has long relied on crude and misleading metrics to evaluate researchers. The most popular one, the so-called *h-index*, is especially problematic. It rewards mediocrity, encourages incremental work, and punishes genuine originality.

Indeed, the h-index is designed to reward people who publish many papers that are cited many times. But truly original work is often initially ignored, misunderstood, or even ridiculed. Many of the greatest discoveries in mathematics were first rejected, dismissed, or considered unimportant.

Therefore, I propose a far better metric: the **Surprise Index**.

Definition of the Surprise Index

The Surprise Index of a researcher is defined as

Surprise Index = (Degree of Unexpectedness) times (Initial Resistance)

where:

• Degree of Unexpectedness measures how surprising the result is compared to the prevailing mathematical wisdom.
• Initial Resistance measures how strongly the community resisted the result at first (e.g., number of rejections, hostile referee reports, long delays before acceptance).

  This metric has several advantages over the h-index:

  1. It rewards originality.
  2. It rewards courage.
  3. It rewards truly innovative thinking.
  4. It penalizes incremental and fashionable work.

  In contrast, the h-index rewards conformity and discourages risk-taking.

  How to Measure the Surprise Index

  Of course, some people may complain that the Surprise Index is subjective. But in reality, we already have excellent proxies:

  • Number of rejections before publication
  • Length of referee reports expressing confusion
  • Time between discovery and acceptance
  • Statements like "This cannot possibly be correct" in referee reports

  For example:

  • A paper accepted immediately with enthusiastic reports gets a low Surprise Index.
  • A paper rejected five times with confused referees gets a high Surprise Index.
  • A paper rejected ten times and eventually recognized as groundbreaking gets a *very* high Surprise Index.

  In particular, papers that were rejected by "top journals" should receive bonus points.

  Historical Examples

  Many great mathematical discoveries would score extremely high on the Surprise Index.

  • Non-Euclidean geometry was initially rejected and ridiculed.
  • Cantor's set theory faced strong opposition.
  • The probabilistic method was initially viewed with suspicion.
  • Computer-assisted proofs were long considered illegitimate.

  Under the h-index system, early pioneers of these ideas would have been undervalued. Under the Surprise Index, they would rank at the very top.

  The Problem with the h-Index

  The h-index encourages mathematicians to:

  • Publish many small papers
  • Work in fashionable areas
  • Avoid risky ideas
  • Follow trends rather than create them

  In other words, it encourages exactly the opposite of what mathematics needs.

  The Surprise Index, on the other hand, encourages:

  • Bold conjectures
  • Unexpected connections
  • Experimental mathematics
  • Risk-taking

  In short, it encourages creativity.

  A Simple Implementation

  I propose that mathematicians start listing their Surprise Index on their CVs. For example:

  Surprise Index: 87 (Based on 23 rejected papers, 11 hostile referee reports, and 3 results initially deemed "impossible")

  Departments should also request Surprise Index values in hiring and promotion decisions.

  In addition, journals should proudly display:

  "This paper was rejected 7 times before acceptance."

  Such statements would become badges of honor.

  Conclusion

  Mathematics advances through surprises, not through incremental citation-generating work. The current obsession with the h-index is harmful and discourages originality.

  It is time to replace the h-index with the Surprise Index.

  After all, the most interesting mathematics is precisely the mathematics that initially seems wrong.

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