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There have been a number of insightful theories about consciousness over the centuries. The modern generic term for consciousness research is the scientific study of consciousness which began to be used in the 1990s following technological advances such as the development of [https://en.wikipedia.org/wiki/Functional_magnetic_resonance_imaging Functional Magnetic Resonance Imaging] (FMRI). In particular, study of the [https://en.wikipedia.org/wiki/Neural_correlates_of_consciousness Neural Correlates of Consciousness] (NCC) was pioneered in the 1990s by Nobel Laureate [https://en.wikipedia.org/wiki/Francis_Crick Francis Crick] and collaborator [https://en.wikipedia.org/wiki/Christof_Koch Christof Koch]. In turn, two series of academic conferences began, [https://en.wikipedia.org/wiki/The_Science_of_Consciousness The Science of Consciousness] (TSC) conference and the conference of the [https://en.wikipedia.org/wiki/Association_for_the_Scientific_Study_of_Consciousness Association for the Scientific Study of Consciousness] (ASSC), which was founded in 1994. During the 1990s and early 2000s three particularly prominent mathematically, or computationally, formulated theories of consciousness were proposed, [https://en.wikipedia.org/wiki/Orchestrated_objective_reduction Orch OR], [https://en.wikipedia.org/wiki/Global_workspace_theory GNW] and [https://en.wikipedia.org/wiki/Integrated_information_theory IIT]. In general, the scientific study of consciousness now comprises a host of models that collectively include complementary and conflicting assumptions and predictions<ref name=Signorelli2021>Signorelli, C.M; Szczotka, J.; Prentner, R. (2021), Explanatory profiles of models of consciousness: towards a systematic classification, Neuroscience of Consciousness, 7(2), niab021</ref>. The term Mathematical Consciousness Science began to be used and recognized from around 2018 onward following a rapid increase in the development of new mathematical and/or computational models and formal theories of consciousness. In 2018 the [https://seminar.math-consciousness.org/index.html Mathematical Consciousness Science online seminar series] and the [https://omcan.web.ox.ac.uk/home Oxford Mathematics of Consciousness and Applications Network] (OMCAN) began. In September 2019 the first [https://www.models-of-consciousness.org/ Models of Consciousness (MoC1)] academic conference was held at Oxford with an international team of organisers. [https://amcs-community.org/events/moc2-2021/ MoC2] was held online in September 2021, followed by [https://amcs-community.org/events/moc-3-2022/ MoC3] in-person at Stanford University in September 2022. In January 2021 the [https://amcs-community.org/ Association for Mathematical Consciousness Science] (AMCS) was founded in order to pull together the growing number of conferences, workshops and seminars in MCS research.

Being hypotheses about consciousness and its relation to the physical domain, the archetypal model of consciousness arguably has three parts, namely, a mathematical model of salient aspects of the physical system (e.g. circuit models, network models, joint probability distributions , Markov processes etc), a mathematical model for aspects of conscious experience (e.g. topological spaces, metric spaces, matrices of relationships, categories, intensity scales etc) and some mapping between the physical domain model and the consciousness domain model (e.g. a homomorphism, limit or optimal boundary point, functor, scalar function etc). The models make various predictions about, for example, phenomenal perception, the relational content of consciousness, the level and intensity of consciousness, attention, and the unity (and disunity) of consciousness within and between systems. The physical domain models and consciousness domain models are also of interest in their own right and some researchers in MCS focus on the development of these models. In the consciousness domain, this is often referred to as [[#Mathematizing phenomenology| Mathematizing phenomenology]].