**Summary:** This paper introduces a mixture of neural operators (MoNOs) to address the "curse of dimensionality" in operator learning. The key idea is to distribute the parametric complexity of a neural operator across a network of expert neural operators (NOs), each with controlled depth, width, and rank. The main result is a distributed universal approximation theorem, showing that any Lipschitz non-linear operator between $ L^2([0,1]^d) $ spaces can be uniformly approximated to any desired accuracy $ \varepsilon > 0 $ by an MoNO, with each expert NO having a complexity of $ \mathcal{O}(\varepsilon^{-1}) $. The curse of dimensionality in operator learning refers to the exponential increase in the number of parameters required to achieve a desired approximation accuracy in high-dimensional function spaces. Traditional neural operators (NOs) face this challenge, as their approximation rates are limited by the parametric complexity. However, the proposed MoNO approach mitigates this by using a mixture of experts, where each expert NO is small enough to be efficiently loaded into memory, while the overall model can scale to handle complex, high-dimensional operators. The paper also provides new quantitative approximation rates for classical NOs approximating uniformly continuous non-linear operators on compact subsets of $ L^2([0,1]^d) $. These results are applied to inverse problems, where the inverse operator is often uniformly continuous but has a sub-Hölder modulus of continuity. The MoNO approach allows for efficient approximation of such operators by distributing the computational load across multiple expert NOs. The MoNO model is implemented using a rooted tree structure, where inputs are routed to the most appropriate expert NO based on a nearest neighbor search. This approach leverages the efficiency of tree-based routing to control the number of parameters required for each expert NO, while maintaining the overall model's ability to approximate complex operators. The paper concludes that the MoNO approach effectively softens the curse of dimensionality in operator learning by distributing the parametric complexity across a network of expert NOs, each with manageable complexity, and by using a tree-based routing mechanism to efficiently approximate complex, high-dimensional operators.**Summary:** This paper introduces a mixture of neural operators (MoNOs) to address the "curse of dimensionality" in operator learning. The key idea is to distribute the parametric complexity of a neural operator across a network of expert neural operators (NOs), each with controlled depth, width, and rank. The main result is a distributed universal approximation theorem, showing that any Lipschitz non-linear operator between $ L^2([0,1]^d) $ spaces can be uniformly approximated to any desired accuracy $ \varepsilon > 0 $ by an MoNO, with each expert NO having a complexity of $ \mathcal{O}(\varepsilon^{-1}) $. The curse of dimensionality in operator learning refers to the exponential increase in the number of parameters required to achieve a desired approximation accuracy in high-dimensional function spaces. Traditional neural operators (NOs) face this challenge, as their approximation rates are limited by the parametric complexity. However, the proposed MoNO approach mitigates this by using a mixture of experts, where each expert NO is small enough to be efficiently loaded into memory, while the overall model can scale to handle complex, high-dimensional operators. The paper also provides new quantitative approximation rates for classical NOs approximating uniformly continuous non-linear operators on compact subsets of $ L^2([0,1]^d) $. These results are applied to inverse problems, where the inverse operator is often uniformly continuous but has a sub-Hölder modulus of continuity. The MoNO approach allows for efficient approximation of such operators by distributing the computational load across multiple expert NOs. The MoNO model is implemented using a rooted tree structure, where inputs are routed to the most appropriate expert NO based on a nearest neighbor search. This approach leverages the efficiency of tree-based routing to control the number of parameters required for each expert NO, while maintaining the overall model's ability to approximate complex operators. The paper concludes that the MoNO approach effectively softens the curse of dimensionality in operator learning by distributing the parametric complexity across a network of expert NOs, each with manageable complexity, and by using a tree-based routing mechanism to efficiently approximate complex, high-dimensional operators.