Final answer:
No, a mathematical formula cannot address the hard problem of consciousness because it involves subjective experience which is not quantifiable. The problem requires a theoretical framework that comprehensively bridges objective brain functions with subjective experiences.
Step-by-step explanation:
In principle, a mathematical formula is unlikely to provide a direct answer to the hard problem of consciousness. This problem, deeply embedded in the philosophy of mind, pertains to the subjective quality of experiences, also known as qualia. Capturing the essence of conscious experience--the 'what it is like' aspect--with a formula challenges both our scientific understanding and philosophical insights.
Consciousness arises from physical processes in the brain, but explaining how it emerges from these processes is the hard problem. While a mathematical formula can model neural activity and cognitive functions, the subjective experience is not quantifiable in the same way that physical phenomena are. This discrepancy is at the heart of the debate. Thought experiments like zombies and brain in a vat scenarios demonstrate the difficulties in purely objective explanations of consciousness. These thought experiments suggest there might be a nonphysical aspect to consciousness that eludes a straightforward physicalist account.
The overarching consensus in philosophy circles suggests that a new theoretical framework might be required to adequately address the hard problem. This framework would need to encapsulate both the objective workings of the brain and the subjective experiences that arise from it, which seems beyond the scope of mathematical formulation as currently conceived.