In an era defined by complex and high-dimensional data, researchers are increasingly working with information that does not conform to traditional flat, Euclidean spaces. Instead, much of today’s data—such as 3D medical imaging, robot joint orientations, and transformations in artificial intelligence—resides on curved geometric structures known as Riemannian manifolds. These non-Euclidean spaces present unique challenges for statistical analysis, particularly when data is corrupted by noise or contains outliers. Conventional statistical methods, like the standard mean, often fail in such settings because they assume linear, flat spaces and are highly sensitive to extreme values. To address this, researchers have developed more robust alternatives, one of which is the Huber mean. Originally designed for Euclidean data, the Huber mean blends the properties of the mean and median, offering a balance between efficiency and resistance to outliers. Now, a new adaptation of the Huber mean has been successfully extended to Riemannian manifolds. This robust statistical tool maintains the desirable properties of the classical Huber mean while being tailored to the intrinsic geometry of curved spaces. By minimizing a loss function that behaves quadratically for small deviations and linearly for large ones, the geometric Huber mean reduces the influence of outliers without sacrificing accuracy on clean data. This advancement enables more reliable analysis of real-world datasets where anomalies are common—such as in medical imaging, where artifacts can skew results, or in robotics, where sensor errors can distort orientation data. The method has shown strong performance in simulations and real applications, providing a more stable and accurate central tendency measure on manifolds. The development marks a significant step forward in geometric statistics, offering a practical and mathematically sound solution for handling noisy, high-dimensional data in non-Euclidean domains. As AI and data science continue to push into complex, real-world environments, tools like the geometric Huber mean will be essential for extracting meaningful insights from data that defies traditional analysis.