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Here the authors investigated the impact of player ability versus starting positions in the game of Nim under imperfect play, hypothesizing that player skill becomes the primary determinant of outcomes as pile sizes grow. Through computational simulations and a mathematical model, they demonstrated that favorable starting positions lose their advantage over time and provide key insights to help improve reinforcement learning algorithms in abstract, complex decision-making environments.

While some believe that ride-hailing services offer reduced CO₂ emissions compared to individual driving, studies have found that driving without passengers on ride-hailing trips or "deadheading" prevents this. Here, with a mathematical model, the authors investigated if the use of electric vehicles as ride-hailing vehicles could offer reduced CO₂ emissions. They found that the improved vehicle efficiency and cleaner generation could in fact lower emissions compared to the use of personal gas vehicles.

In this study, the authors test whether a gravity vehicle, which is a vehicle powered by its own gravity on a ramp, could be designed to move faster when mathematical calculations for optimal mass and center of gravity were applied in the design.

Large language models are increasingly used to solve math problems, but their ability to handle multi-step reasoning remains uncertain. In this study, students tested whether different prompting styles could improve LLM accuracy on challenging AIME math questions and found that detailed step-by-step solutions did not significantly outperform simpler prompts. These results suggest that improving LLM mathematical reasoning may require deeper model-level advances rather than changes in prompting style alone.

Bubbles! In this study, the authors investigate the effects that different materials, temperature, and distance have on the formation of water bubbles on the surface of copper and steel. They calculated mathematical relations based on the outcomes to better understand whether interstitial hydrogen present in the d-block metals form hydrogen bonds with the water bubbles to account for the structural and mechanical stability.

This study examines the higher harmonics in an oscillating string by analyzing the sound produced by a guitar with a spectrum analyzer. The authors mathematically hypothesized that the higher harmonics in the series of the directly excited 2^nd harmonic contain the alternate frequencies of the fundamental series, the higher harmonics of the directly excited 3^rd harmonic series contain every third frequency of fundamental series, and so on. To test the hypotheses, they enforced artificial nodes to excite the 2^nd, 3^rd, and 4^th harmonics directly, and analyzed the resulting spectrum to verify the mathematical hypothesis. The data analysis corroborates both hypotheses.

In this study the authors looked at the ability of the Discrete Fourier Transform (DFT) to analyze different musical elements. They found that DFT is a powerful method to analyze recorded music.

What type of motivation is more effective: reward or punishment? In this study, the authors assess the effects of positive or negative on the math scores of sixth graders.

Here, beginning from an interest in fractals, infinitely complex shapes. The authors investigated the fractal object that results from crumpling a sheet of paper. They determined its fractal dimension using continuous Chi-squared analysis, thereby testing and validating their model against the more conventional least squares analysis.

Investigation of the largest rigid shape that can be moved through a circular hallway of unit width with an arbitrary turn angle