Today, geology encompasses cosmology as we bring materials from the asteroid Ryugu near Mars with the satellite Hayabusa. The materials have shed light on the possibility of life’s existence on Ryugu. This book aims to provide research directions for geology in the 21st century. However, writing a history of the present or future research directions is no easy task. Nevertheless, we endeavor to present the research directions of the early decades of the 21st century.

Drawing on past experiences of various misunderstandings in research directions, several papers in this book discuss fuzzy set theoretical approaches. Interestingly, this groundbreaking paper was initially rejected in the 1960s. Later, Professor Lotfy A. Zadeh’s paper on “fuzzy sets” was published in the International Journal of Science and Control. This paper introduced several important concepts that indicated various research directions.

The neural network was initially underestimated in the book published in 1969. This book had a significant influence that caused many researchers to shift away from neural networks. For several decades, many researchers abandoned research on neural networks. However, a few persevering individuals continued their research until the discovery of backpropagation, which not only revolutionized the field but also gave rise to deep learning.

In this book, we revisit heuristic approaches and meta-heuristic approaches. While H.A. Simon emphasized heuristic approaches for semi-structured problems, we are still searching for theoretical, mathematical, or logical approaches to problem-solving. In the 1960s, we discovered various heuristic approaches that were sought after during that era.

As Eric Hobsbawm wrote, it is difficult to write the history of one’s own days. As mentioned earlier, selecting influential methods is no easy task. We hope to include the most influential papers that represent the smart geology of the first few decades of the 21st century, with one chapter dedicated to deep learning.

We acknowledge the importance of theoretical approaches from physics, mathematics, and statistics underlying meta-heuristic methods, artificial intelligence, deep learning, and other human approaches. We must build upon human knowledge and approaches, as Herbert Alexander Simon (Nobel laureate, 1978) stated, there are infinitely many problems we cannot solve theoretically, or in other words, mathematically. However, we can make progress, as demonstrated by Andrew John Wiles (Professor, Oxford University) when he proved Fermat’s Last Theorem, left unresolved by Pierre de Fermat in 1623, in a 108-page proof published in the Annals of Mathematics in 1995. Similarly, the ABC conjecture, first proposed by Joseph Oesterlé in 1988 and D.W. Masser in 1985, was proved by Shinichi Mochizuki (Professor, Kyoto University) in approximately 600 pages in 2015 and at RIMS in March 2021. Mochizuki’s method allowed for the proof of Fermat’s problem in just a few lines, based on his method.

We expect that this book will contribute to the exploration of various possible solutions to challenging problems in both the Earth’s geometry and the cosmos, as H.A. Simon envisioned. The first paper serves as an introduction to biology, which is now expanding into the science of the cosmos.