A few weeks ago, I was ask by *Nature Sustainability* to review a manuscript for research article by Katherine Meyer and colleagues that extended the mathematical theory of resilience (doi:10.1038/s41893-018-0168-z). I agreed to comment on the manuscript, and explained in my response to the editor in the second round of review how important it is that reviewers of theoretical manuscripts have the necessary mathematical/theoretical background, even when such reviewers are hard to find.

I argued that the signal-to-noise ratio in for theoretical and mathematical work (with respect to both publications and peer reviews) is currently too low to generate the progress that society needs.

As a result, the editor kindly asked me to contribute a *News & Views* article in *Nature Sustainability*, based on the original research article. In this piece, I explain why there is still plenty of interesting mathematical theory to be developed in sustainability research, and why doing so is crucial for addressing the environmental issues society faces.

This *News & Views* (alternatively doi:10.1038/s41893-018-0178-x), together with the research article, have now been published.

By recognizing the important roles that theory and mathematics have to play in putting our planet back onto a sustainable track, *Nature Sustainability* are reinforcing the message at the heart the *International Initiative for Theoretical Ecology*, and I thank them for this.

henriTo be honest, I was a bit disappointed by the article (the original one, not Axel’s comments on it):

— it is a very pretty mathematical idea, but from the point of view of theoretical ecology, really all it says is that some (important) systems, and by that I mean mathematically defined systems, are nonlinear;

— it relies totally on having a closed system, fixed points and constant parameters (yes, there is very little theory that doesn’t, but still, such complete absence of awareness that this sort of thing can only be valid for short times and distances disappoints me)

— it doesn’t mention the wider debate that Michel Loreau referenced in his talk* at the MPDEE18 conference in Leicester (April this year), in fact it makes it appear that “resilience” is a standardised concept whereas this seems to me somewhat in question.

*Loreau specifically said that resilience in most of the senses currently used in ecology is not a good measure. He emphasised the requirement of making good use of available data to estimate whether a tipping point is near or not. He suggests the use of what he calls “invariability” which is calculated directly from the data, not via estimating the parameters of a model as would have to be the case for the measure discussed in the article.

Of course I agree with Axel that articles like this should be read with interest and comprehension by a much wider audience than in currently the case, but I am not sure I agree that it showcases the need for maths and theory quite as strongly as he suggests, in particular I don’t think it settles the debate of how to estimate resilience empirically.