Mathematicians have made a breakthrough in understanding the process of mean curvature flow, which describes how surfaces evolve over time. The discovery, which confirms the “multiplicity-one” conjecture, has significant implications for the study of melting surfaces, such as ice cubes or eroding sandcastles. This new understanding will enable researchers to analyze the evolution of surfaces…
Math on The Soothsayer / page 2
Researchers at Princeton University have made a groundbreaking improvement to Newton’s method, a centuries-old technique used for optimization problems. The new algorithm, developed by Amir Ali Ahmadi and his team, extends Newton’s method to work efficiently on the broadest class of functions yet, potentially replacing it in various applications. Forecast for 6 months: Expect to…
Mathematicians at New York University’s Courant Institute and the University of British Columbia have finally solved the three-dimensional Kakeya conjecture, a problem that has puzzled experts for over a century. The solution, which involves finding the most efficient way to point a pencil in every direction while minimizing the space it moves through, has far-reaching…
Mathematicians Nalini Anantharaman and Laura Monk have made a groundbreaking discovery in the field of hyperbolic surfaces, building on the work of the late Maryam Mirzakhani. Their research has shown that certain critical properties are common in hyperbolic surfaces, which were previously thought to be rare. This breakthrough has significant implications for our understanding of…
A German graduate student, Britta Späth, encountered the McKay conjecture, a significant open problem in group theory, in 2003. She dedicated her time to solving it, eventually teaming up with mathematician Marc Cabanes, whom she fell in love with. After 20 years of work, the couple has successfully solved the problem, providing a concrete tool…
Mathematicians have made a significant breakthrough in understanding the limitations of solving Diophantine equations, a fundamental problem in mathematics. Researchers have proven that there is no general algorithm to determine if a given Diophantine equation has a solution in certain number systems. This discovery sheds new light on the long-standing problem of Hilbert’s 10th problem…
Mathematicians have long relied on calculus to understand the world around us, but a groundbreaking discovery by Karl Weierstrass in 1872 shook the foundations of the subject. Weierstrass’ “monster function” revealed that continuity does not imply differentiability, forcing mathematicians to re-examine their understanding of calculus. This breakthrough has far-reaching implications for fields such as physics,…
Mathematicians have revisited an ancient puzzle known as the “kissing problem,” which was first contemplated by Isaac Newton and astronomer David Gregory in 1694. The problem involves arranging identical spheres around a central sphere without overlapping. After centuries of research, mathematicians have finally proven that the maximum number of spheres that can be arranged in…
Mathematicians have made a groundbreaking discovery in number theory, unlocking the secrets of irrational numbers. A team of researchers has developed a new method for proving the irrationality of numbers, which has been a long-standing challenge in mathematics. The breakthrough, led by Frank Calegari, Vesselin Dimitrov, and Yunqing Tang, has already led to the proof…
Mathematicians have long suspected that hexagonal tiles are the most efficient way to fill space, but a new paper by Thomas Hales and Koundinya Vajjha reveals the worst shape to pack. The researchers focused on convex and centrally symmetric shapes, and their findings have significant implications for the field of mathematics. Forecast for 6 months:…