The paper presents a mathematical method called multisurface pattern separation for distinguishing between benign and malignant breast fine-needle aspirate (FNA) samples. Each sample is characterized by nine cytological traits, graded from 1 to 10. The method uses linear programming to determine a piecewise-linear separating surface composed of four pairs of parallel planes. This approach successfully classified 369 out of 370 samples (201 benign and 169 malignant) with only one misclassified malignant case, which was likely due to the tumor being missed during aspiration. The method outperforms previous schemes that considered only a few cytological traits or weighted all traits equally. The accuracy of the method improves with larger training sets, and it is validated through numerical experiments. The authors conclude that the multisurface method is a powerful tool for medical diagnosis, particularly in breast cytology, and can be implemented using a personal computer program.The paper presents a mathematical method called multisurface pattern separation for distinguishing between benign and malignant breast fine-needle aspirate (FNA) samples. Each sample is characterized by nine cytological traits, graded from 1 to 10. The method uses linear programming to determine a piecewise-linear separating surface composed of four pairs of parallel planes. This approach successfully classified 369 out of 370 samples (201 benign and 169 malignant) with only one misclassified malignant case, which was likely due to the tumor being missed during aspiration. The method outperforms previous schemes that considered only a few cytological traits or weighted all traits equally. The accuracy of the method improves with larger training sets, and it is validated through numerical experiments. The authors conclude that the multisurface method is a powerful tool for medical diagnosis, particularly in breast cytology, and can be implemented using a personal computer program.