Numerous event-related potential (ERP) studies demonstrated that arithmetic mismatch in addition/multiplication verification tasks and number matching tasks elicits a negative-going potential [1–9]. Here we call this phenomenon arithmetic mismatch negativity (AMN). Some properties of the AMN remained unresolved in previous studies. First, it is unclear whether the AMN is elicited by the incongruity in numerical information per se, or rather, by the violation of strategic expectations in a certain experimental paradigm. Second, it has been shown that the ERP amplitude in the time window of the AMN is sensitive to semantic manipulations [2, 10, 11]. However, it is unknown whether these semantic amplitude effects are inherent to the AMN itself, or rather, they only coincide with it. This study set out to respond to the above two questions.

Typically, the AMN is demonstrated in arithmetic verification tasks and number matching tasks. In arithmetic verification tasks, participants see equations consisting of operands and operators (e.g. 3 × 4; 3+4) followed by correct or incorrect arithmetic outcomes [1–5, 9]. The AMN appears as incorrect arithmetic outcomes elicit more negative-going ERPs than correct arithmetic outcomes. In number matching tasks, participants see pairs of numbers presented serially which are either matching or non-matching to each other [8]. The AMN appears as non-matching numbers elicit more negative-going ERPs than matching numbers. In previous studies, the AMN as a negativity emerging between 250-450 ms was referred to by various names, e.g. N270, N400, and N300 [1–4, 9, 12]. However, here we use the neutral term "AMN" considering that the functional nature of this effect has not yet been determined.

One question is whether the AMN is sensitive to the incongruity in numerical information per se, or rather, to the violation of strategic expectations when participants encounter unexpected stimuli within the context of arithmetic tasks. The former possibility would suggest that the AMN is a specific signal in number processing. The latter possibility would suggest that the AMN is an ERP effect reflecting general mismatch detection, similar to the negative-going ERPs reported in non-arithmetic tasks, such as colour matching task [8], shape matching task [13], and category matching task [6].

Another issue is that the semantic content of stimuli seems to influence the ERP amplitude in the time window of the AMN. For example, Niedeggen and Rösler [2] documented that the amplitude of the AMN is modulated as a function of numerical distance between presumed and perceived arithmetic outcomes. However, it is an open question whether semantic relations influenced the AMN per se. In fact, some studies focusing on semantic relations in arithmetic found the numerical distance effect in the absence of the AMN [10, 11]. This suggests that the numerical distance effect might only temporally coincide with the AMN.

The dissociation of arithmetic incongruence, general mismatch detection, and semantic effects potentially overlapping with the AMN in simple numerical tasks is not straightforward. This is so because incorrect arithmetic outcomes are probably associated with strong and subjective "mismatch" even when they are frequent. For example, the AMN appears in response to incorrect arithmetic outcomes even when they are presented in 80% of the trials [5]. One way around this problem is to use a number matching task which not only elicits the AMN but also elicits the semantic analysis of numerical magnitude [14–16]. In such a task participants decide whether pairs of numbers are matching or non-matching to each other in terms of physical similarity. This allows for independent manipulation of arithmetic incongruence and general mismatch detection. Specifically, arithmetic incongruence and general mismatch detection can be separated by making physically non-matching numbers appear frequently and physically matching numbers appear infrequently. If the AMN is sensitive to the incongruity in numerical information per se, it should be found in frequent non-matching trials. In contrast, if the AMN is sensitive to the violation of strategic expectations, it should be found in infrequent matching trials. The second question concerns whether the amplitude modulations as a function of numerical distance are inherent to the AMN, or rather, they reflect a process which temporally coincides with the AMN. With regard to this question, we expected on the basis of previous studies [10, 11] that the amplitude modulations of numerical distance may be seen in ERPs even in the absence of the AMN.