A Mathematical Theory of Historical Greenhouse Gas Emissions with Rigorous Insights

In this paper, we analyze historical greenhouse gas (GHG) emissions worldwide, leveraging a dataset provided by (Gütschow and Pflüger, 2023). Employing mathematical modeling, a formal theory is developed, describing the growth trajectories of GHG emissions over time. The theory introduces several key concepts including continuous emission process (CEP), discrete emission process (DEP), historical upper bound emission (HUBE), historical peak emission (HPE), rapid growing emission (RGE), rapid shrinking emission (RSE), pivotal periods (piviods), historical expected growth rate (HEGR) and conditional historical bound space (CHBS), pinpointing important periods and numerical measures related to a country’s GHG emission growth. A notable invention in the theory is the concept of piviods developed from the concept of Lipschitz continuity and short map in mathematical analysis, highlighting a country’s transition from slow to rapid GHG emission growth and vice versa. Additionally, machine learning algorithms and computer algebra systems are also utilized in the computational implementation of the theory, enhancing the robustness and efficiency. Our findings reveal valuable insights into historical GHG emissions, offering a novel approach to their analysis and bridging the gap between formal mathematics and environmental science.