optimization

Over the last few months, the mathematical capabilities of LLMs have improved dramatically, to the point that they can solve major outstanding problems in many fields of mathematics. However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the math…

Scientific Reports, Published online: 11 September 2026; doi:10.1038/s41598-026-70295-x Accessibility-aware multi-objective truck-drone hybrid routing for post-disaster humanitarian logistics

Scientific Reports, Published online: 11 September 2026; doi:10.1038/s41598-026-68662-9 Experimental multi-objective optimization of 3D printing parameters for enhanced energy absorption in MCC/PC-ABS composites using MOGA-II algorithm

UMBC mathematician Matthew Kvalheim has received an Air Force Office of Scientific Research Young Investigator Program Award to develop better ways of simplifying hybrid systems, like a drone swarm, humanoid robot, or aircraft. Kvalheim aims to create mathematical tools that make hybrid dynamics—which govern almost all real-world systems—easier to study and control, giving researchers a clearer “…

Nature Communications, Published online: 11 September 2026; doi:10.1038/s41467-026-77737-0 In a deterministic, non-chaotic system, the initial state fixes the future completely, yet that future may be impossible to forecast from it. Using a cellular automaton of communicating cells, this study shows that predictability is instead built by the dynamics: collective topological structures self-organ…

OpenAI announced a solution to the Navier-Stokes problem. But could its A.I. models have used data from two mathematicians working on a similar breakthrough?

A distributed, verifiable search for x³ + y³ + z³ = 114 Draft started September 2026 Abstract We describe an open volunteer search for integer solutions to x³ + y³ + z³ = 114. The implementation combines a cubic-field norm construction, exact arithmetic, modular rejection, bounded client tasks, durable result receipts and independent replay. Scheduling adapts to measured execution cost wh…

Previously, algorithms determining how reliably information could be sent via quantum channels became progressively less accurate as their computational demands increased, error estimates improved at only inverse square root decay. Now, a new mathematical construction achieves quadratic convergence, dramatically accelerating calculations by reducing that error far more rapidly than before. This a…

Evaluating Polynomials Fast You may have heard about Horner's method, which evaluates a polynomial of degree n in n multiplications (n−1 if it is monic). But did you know that with a bit of preprocessing of the coefficients, ⌊n/2⌋+1 multiplications suffice for any monic polynomial, one more for a general one? You can use this …

Nature, Published online: 08 September 2026; doi:10.1038/d41586-026-02842-5 The company says it has cracked the physics of fluids using AI, solving one of the toughest puzzles in mathematics.

Mathematical detail alone does not dictate hardware cost. Instead, resource demands are driven entirely by operationally distinguishable future behaviors. This paper introduces a task-semantic framework that groups identical behavioral behaviors into distinct classes. The total number of these classes defines the absolute minimum number of abstract states any valid system must maintain, establish…

Is there any other problem as simple as placing queens on an N×N board?. Does admitting to difficulties in finding a solution count as failure? Is the idea of a shortcut dismissed by the majority, or is it still considered possible? If there is no shortcut, why does it involve calculations at... Read more

Scientific Reports, Published online: 06 September 2026; doi:10.1038/s41598-026-70046-y A hybrid memetic algorithm for an energy-aware distributed blocking hybrid flowshop scheduling problem with transportation time

A cryptography library had a bottleneck no test could see : encrypting half a megabyte took fifty seconds. Every test passed. They had been passing for months. The cause is a trap that keeps recurring: a correct, well-documented optimisation that fixes the constant and not the order — and whose comment, precisely because it is well written, convinces the reader the problem is already solved. What…

A team of mathematicians discovered that five 60-sided dice, arranged with exactly the right numbers, can determine a perfectly fair turn order for any group of players, with zero chance of a tie.

IntroductionWith the high penetration of renewable energy, tapping the regulation potential of smart buildings in distribution networks plays a pivotal role in enabling orderly renewable energy accommodation. Customer directrix load-based demand response serves as an effective mechanism for guiding smart building interaction. However, its incentive price, derived as the equilibrium point of a lea…