It's not necessarily about pushing the boundaries of math. The simpler you can make the math the better for a given level of insight. But I don't think it's "easy" to derive clean mathematical results for many economic models. It's a combination of math, insight, and style.
Imagine this: prove to me some conditions under which equilibrium exist for prices in a market of consumers and producers with heterogenous preferences and skills, that can only communicate on a network with a cost per interaction. Now introduce time and savings and prove the equilibrium interest rate over time. Now prove the optimal tax rate on capital and labor over the agents lifecycle. Now prove that when skill and preferences are not observable to the government. Now introduce default and unobservable savings. Are there conditions under which the markets unravel when faced with exogenous shocks to productivity or beliefs. What is the optimal interest rate policy?
These are classic questions in economics in a more realistic market that captures heterogeneity, limited information, and locality or search costs.
Imagine this: prove to me some conditions under which equilibrium exist for prices in a market of consumers and producers with heterogenous preferences and skills, that can only communicate on a network with a cost per interaction. Now introduce time and savings and prove the equilibrium interest rate over time. Now prove the optimal tax rate on capital and labor over the agents lifecycle. Now prove that when skill and preferences are not observable to the government. Now introduce default and unobservable savings. Are there conditions under which the markets unravel when faced with exogenous shocks to productivity or beliefs. What is the optimal interest rate policy?
These are classic questions in economics in a more realistic market that captures heterogeneity, limited information, and locality or search costs.