The paper presents a mathematical method called multisurface pattern separation for distinguishing between benign and malignant breast cytology samples. This method uses linear programming to separate samples based on nine cytological characteristics. The method was tested on 369 samples, with 368 correctly classified (201 benign and 169 malignant), and one case misclassified. The misclassified case was due to the tumor being missed during aspiration, not a misinterpretation of the cytology. The method uses four pairs of parallel planes to separate the samples, with each plane representing a decision stage. The method was validated by splitting the samples into training and testing sets, showing that accuracy increases with the size of the training set. The method is more effective than previous approaches as it simultaneously weights all nine characteristics, rather than relying on a few or equal weighting. The method is applicable to other medical diagnostic problems. The results show that the method provides accurate classification, with the accuracy depending on the representativeness of the training data. The method is implemented in a program that can be used for instant diagnosis by entering the numerical values of the nine cytological variables. The method is reproducible, as the numerical values assigned to the variables are consistent across different trained observers. The paper concludes that the multisurface method is a useful diagnostic tool for medical problems.The paper presents a mathematical method called multisurface pattern separation for distinguishing between benign and malignant breast cytology samples. This method uses linear programming to separate samples based on nine cytological characteristics. The method was tested on 369 samples, with 368 correctly classified (201 benign and 169 malignant), and one case misclassified. The misclassified case was due to the tumor being missed during aspiration, not a misinterpretation of the cytology. The method uses four pairs of parallel planes to separate the samples, with each plane representing a decision stage. The method was validated by splitting the samples into training and testing sets, showing that accuracy increases with the size of the training set. The method is more effective than previous approaches as it simultaneously weights all nine characteristics, rather than relying on a few or equal weighting. The method is applicable to other medical diagnostic problems. The results show that the method provides accurate classification, with the accuracy depending on the representativeness of the training data. The method is implemented in a program that can be used for instant diagnosis by entering the numerical values of the nine cytological variables. The method is reproducible, as the numerical values assigned to the variables are consistent across different trained observers. The paper concludes that the multisurface method is a useful diagnostic tool for medical problems.