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When the Nobel prize or Fields Medal gets awarded, I believe one of the criteria is the impact the discoveries have been. My question is, whether there are any objective ways to measure the impact? It could be the impact on science or on the society as a whole. I guess the number of citations or which journals have published an article is one way, but are there other ways? Can the objective ways be applied to compare between different fields of science? Are there any such comparisons where I could get a list of the most significant scientific discoveries ordered by impact?

Here is a related question: Quantitative measures of rise and decline of scientific fields over time (beyond number of publications)

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    $\begingroup$ There is no and cannot be any objective measure. $\endgroup$
    – Alexandre Eremenko
    Commented May 21, 2021 at 2:03
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    $\begingroup$ "Significance" and "impact on society" are too vague and viewpoint dependent for objective measuring. One can appoint some "objective measures" like citations, but they measure something else instead. Or one can take rankings of what is intended, but they will be subjective. A compromise is to take expert rankings and average them over. The Atlantic did something like that for "50 Greatest Breakthroughs Since the Wheel". $\endgroup$
    – Conifold
    Commented May 21, 2021 at 9:37
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    $\begingroup$ @Wrzlprmft: The number of citations (and derived measures) is objective but what does it really measure? For example, look at the list of most cited mathematicians. Are there any really outstanding mathematicians in this list? $\endgroup$
    – Alexandre Eremenko
    Commented May 21, 2021 at 14:19
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    $\begingroup$ Any real mathematician will tell you that there is simply no correlation between reputation and the number of citations. $\endgroup$
    – Alexandre Eremenko
    Commented May 21, 2021 at 14:22
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    $\begingroup$ It is not (significant) discoveries that get most citations, there is a now classic paper in Nature (2014) about top100 cited papers nature.com/articles/514550a $\endgroup$
    – sand1
    Commented May 22, 2021 at 12:56

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