The calculated uncertainty of scientific discovery: From Maths to Deep Maths

Throughout history, diverse Maths have underpinned numerous important natural and physical science discoveries. In their initial development and application, these Maths were often incompletely or imperfectly understood, with constants and “fudge factors” needed to account for statistical uncertainties to advance a scientific discipline. Some polymaths have acted as philosophers in support of new ways of thinking, based on their novel discoveries about the natural and physical world. Deep Maths integral to artificial intelligence (AI), machine learning and deep learning (DL), are also subject to human imperfections (i.e., computational errors, operator assumptions) and stochastic uncertainties (i.e., modeling biases, convergence optimizers). Mathematicians and domain experts can collaborate to increase AI model accuracy by improving training data quality (i.e., curating, reducing dimensionality), mitigating human and machine biases, and understanding data contexts prior to query. Since the advent of DL and through the design of multilayered feedforward neural networks then large language models, scientists have applied advanced AI computing capabilities to push the limits of this technology trend. Recently, AI's capacity to uncover newly modeled insights has been hyped beyond the proven limits of DL model accuracy. History has witnessed the acceptance of new knowledge (primarily by peers) based on the accuracy and/or reproducibility of empirical observations and on varied interpretations of mathematical proofs. Societal enthusiasm for science or technology insertion is often limited by the general public's understanding of the underlying Maths and Deep Maths, and related human fears and concerns of displacement (i.e., lost jobs, ecological impact, less privacy, etc.). Today's proponents of societal progress based on new discoveries and technologies are motivated by a range of influences (i.e., humanity, control, security, profit, etc.), creating additional uncertainties that can deflect initial scientific enthusiasm and/or delay widespread adoption.