In October 2024, Luke Durant, an independent researcher in San Jose, California, made headlines by discovering the largest known prime number. The number was so vast that it would take years to write out in full. While this achievement may seem like something only mathematicians would celebrate, primes are considered the fundamental building blocks of mathematics. Math, in turn, serves as the foundation for a wide range of applications, from quantum theory and smartphone algorithms to the stability of bridges and even the odds in a casino.
Humans are inherently drawn to mathematics, with studies showing that babies are born with an innate sense of numbers. Some individuals dedicate their lives to this field, such as the high school students who published a proof of the Pythagorean theorem using trigonometry in 2023. In 2025, Masaki Kashiwara, who has been studying mathematics for nearly seven decades, was awarded the prestigious Abel Prize.
The pursuit of larger prime numbers continues, with researchers exploring new methods, including utilizing integer partitions. Some mathematical conundrums, like the Langlands conjecture, have baffled scientists for decades. Mathematics is filled with paradoxes, such as the infinite series 1 – 1 + 1 – 1 + 1 – 1 + …, which does not have a straightforward answer. These puzzles highlight the importance of probability, a concept that remains enigmatic to many.
Mathematics plays a crucial role in various scientific disciplines, including physics and cosmology. Complex numbers are essential in quantum theory, while recent advancements have been made in solving Hilbert’s sixth problem, a challenging mathematical puzzle posed by David Hilbert in 1900. Topology, the study of deformable geometric shapes, is influencing data analytics, showcasing the interconnectedness of math and real-world applications.
The practical implications of mathematics are evident in everyday life. Equations govern the stability of structures like bridges and airplanes, statistical theories enhance gambling strategies, and algorithms influence success in activities like poker. Furthermore, computational models are being developed to optimize democratic processes, ensuring fair representation in citizens’ assemblies.
Throughout history, mathematics has proven to be a powerful tool for understanding the world and optimizing various aspects of life. It underpins the fabric of reality, including the human mind. Far from being esoteric, mathematics serves as a mirror reflecting our understanding of the universe and ourselves.
