What are the grand intellectual challenges, particularly those that interact with society?
Here are a few. A common feature of those I have chosen is that they involve emergence: complex systems consisting of many interacting components produce new entities and there are multiple scales (whether length, time, energy, the number of entities) involved.
How does one go from microeconomics to macroeconomics?
What is the interaction between individual agents and the surrounding economic order?
A recent series of papers(see here and references therein) have looked at how the concept of emergence played a role in the thinking of Friedrich Hayek.
How does one go from genotype to phenotype?
How do the interactions between many proteins produce a biochemical process in a cell?
The figure above shows a protein interaction network and taken from this review.
How do communities and cultures emerge?
What is the relationship between human agency and social structures?
Public health and epidemics
How do diseases spread and what is the best strategy to stop them?
Recently it was shown how Deep learning can be understood in terms of the renormalisation group.
Community development, international aid, and poverty alleviation
I discussed some of the issues in this post.
How and when do new ideas become "popular" and accepted?
How do you define consciousness?
Some of the issues are covered in the popular book, Emergence: the connected lives of Ants, Brains, Cities, and Software.
Some of these phenomena are related to the physics of networks, including scale-free networks. The most helpful introduction I have read is a Physics Today article by Mark Newman.
Some of these lessons are "obvious" to condensed matter physicists. However, I don't think they are necessarily accepted by researchers in other fields.
These are very hard problems, progress is usually slow, and not all questions can be answered.
The limitations of reductionism.
Trying to model everything by computer simulations which include all the degrees of freedom will lead to limited progress and insight.
Find and embrace the separation of scales.
The renormalisation group provides a method to systematically do this. A recent commentary by Ilya Nemenman highlights some recent progress and the associated challenges.
The centrality of concepts.
The importance of critically engaging with experiment and data.
They must be the starting and end point. Concepts, models, and theories have to be constrained and tested by reality.
The value of simple models.
They can give significant insight into the essentials of a problem.
What other big questions and grand challenges involve emergence?
Do you think condensed matter [without hubris] can contribute something?