One of the earliest and still favored techniques for the investigation of the functioning brain, electroencephalography (EEG) acquires a mean of the electrical activity of large groups of neurons through electrodes positioned on the scalp. It is based on the remarkable physiology of neurons, that change their membrane potential when receiving certain excitatory or inhibitory stimuli, thus departing from the voltage of about 60 mV or 70 mV across the membrane in the resting state \cite{purves_neuroscience_2004}. These changes cause transmembrane and extracellular current flows that generate an electrical potential throughout the volume, and which can be measured with respect to a reference as a voltage \cite{luck_introduction_2005}.
According to the superposition principle, the measured extracellular voltage deflection has contributions from all the currents produced by the electrically active cellular processes. However, the constructive overlap in space and time that gives rise to a measurable signal occurs mainly if the electrical activity is relatively slow (more lower frequency components than higher frequency ones), because there is a longer time to integrate and an improved phase coincidence from spatially separated sources. This is the reason why synaptic currents are considered the most relevant source, as it constitutes one of the slower electrical activities in the neurons \cite{22595786}.
Nonetheless in EEG, due to the large size of the electrodes and the distorting and attenuating effects of the soft and hard tissues between the source and the measurement, the signal is spatiotemporally smoothed, and it is considered to be the result of integrating over an area of 10 cm² of sources \cite{22595786}. Also, since EEG records from the scalp of a subject, it is better for detecting surfacing potentials, predominantly the ones generated in the cortex layer of the brain, where the synchronization and regular spatial arrangement of the tissue makes it possible for the superposition of many small sources into a measurable macroscopic signal. Therefore, potentials from inner regions in the brain are negligible in a typical EEG signal recording \cite{niedermeyer_electroencephalography:_2005}.
EEG apparatus are quite common due to their portability, low cost and high temporal resolution. Moreover, as a noninvasive and secure technique, EEG has been extensively used in various clinical and research environments. In the clinical sense it is the most used technique for studying sleeping disorders \cite{19802813}. There are plenty of other relevant applications, such as locating areas of brain damage, monitoring cognitive functions, testing drug’s effects and searching for epilepsy seizure origin and signal acquisition for brain-computer interfaces (BCIs) \cite{teplan_fundamentals_2002}.
The current work presents a simple analysis of an arithmetic task, chosen as an educational demonstration of the capacities and difficulties in the use of the EEG technique. Research in mathematics and arithmetic is of special interests in neuroscience, as they form a “prototypical cognitive system”, in which many areas become involved in order to interpret symbols, retrieve data and execute the necessary procedures for the calculations \cite{Kong_1999}\cite{7812175}. The evidence suggests that mental calculation involves a network that includes mainly the parietal cortex and prefrontal cortex \cite{Kong_1999}\cite{10336175}\cite{17433880}. There seems to be little evidence of using this kind of task as part of a BCI, the closest being an attempt to asses cognitive workload in real time \cite{Rebsamen_2011}, but there are investigations where arithmetic tasks are used to provide information about complex mental disorders such as schizophrenia \cite{Garakh_2015}.