In my opinion, singling out a single field as the "hardest" besides physics and chemistry is a subjective matter, as the difficulty can vary depending on individual perspectives and aptitudes. Nonetheless, several scientific disciplines are often considered challenging due to their complexity and the depth of knowledge required. Here are a few examples:
Astrophysics: Astrophysics deals with the study of celestial objects, their properties, and the vast universe. It involves a deep understanding of advanced mathematics, theoretical physics, and observational techniques. Analyzing phenomena like black holes, dark matter, and the origins of the universe presents significant challenges.
Neurobiology/Neuroscience: The study of the brain and nervous system is a highly intricate field. Understanding the complexities of the brain's structure, function, and the mechanisms behind cognition, behavior, and neurological disorders is a formidable task. Neurobiology involves integrating knowledge from various disciplines, including biology, chemistry, psychology, and physics.
Computational Biology/Bioinformatics: This field combines biology, computer science, statistics, and mathematics to analyze and interpret biological data on a large scale. Extracting meaningful insights from complex biological systems, understanding genomics, proteomics, and modeling biological processes pose substantial challenges.
Quantum Mechanics: While physics was mentioned as excluded from the initial question, I would like to highlight quantum mechanics specifically. It is a fundamental theory describing the behavior of matter and energy at the smallest scales. Quantum mechanics introduces counterintuitive concepts and mathematical formalism that can be challenging to grasp, such as wave-particle duality, superposition, and entanglement.
Mathematical Modeling and Simulation: While not a specific field per se, the use of advanced mathematical models and simulations across various scientific disciplines can be extremely challenging. Constructing accurate models, implementing appropriate numerical techniques, and analyzing the results require a deep understanding of mathematics, computer science, and the specific domain being modeled.
It's worth noting that all scientific fields have their complexities and intricacies, and the perceived difficulty can also depend on an individual's interests, background knowledge, and problem-solving skills.