Epilepsy is one of the brightest manifestations of extreme behavior in living systems. Extreme epileptic events are seizures, that arise suddenly and unpredictably. Usually, treatment strategies start by analyzing brain activity during the seizures revealing their type and onset mechanisms. This approach requires collecting data for a representative number of events which is only possible during the continuous EEG monitoring over several days. A big part of the further analysis is searching for seizures on these recordings. An experienced medical specialist spends hours checking the data of a single patient and needs assistance from the automative systems for seizure detection. Machine learning methods typically address this issue in a supervised fashion and exhibit a lack of generalization. The extreme value theory allows addressing this issue with the unsupervised machine learning methods of outlier detection. Here, we make the first step toward using this approach for the seizure detection. Based on our recent work, we specified the EEG features showing extreme behavior during seizures and loaded them to the one-class SVM, a popular outlier detection algorithm. Testing the proposed approach on 83 patients, we reported 77% sensitivity and 12% precision. In 60 patients, sensitivity was 100%. In the rest 23 subjects, we observed deviations from the extreme behavior. The one-class SVM used a single subject’s data for training; therefore, it was stable against between-subject variability. Our results demonstrate an effective convergence between the extreme value theory, a physical concept, and the outlier detection algorithms, a machine learning concept, toward solving the meaningful task of medicine.