Sal Restivo

An international group of distinguished scholars brings a variety of resources to bear on the major issues in the study and teaching of mathematics, and on the problem of understanding mathematics as a cultural and social phenomenon. All are guided by the notion that our understanding of mathematical knowledge must be grounded in and reflect the realities of mathematical practice. Chapters on the philosophy of mathematics illustrate the growing influence of a pragmatic view in a field traditionally dominated by platonic perspectives. In a section on mathematics, politics, and pedagogy, the emphasis is on politics and values in mathematics education. Issues addressed include gender and mathematics, applied mathematics and social concerns, and the reflective and dialogical nature of mathematical knowledge. The concluding section deals with the history and sociology of mathematics, and with mathematics and social change. Contributors include Philip J. Davis, Helga Jungwirth, Nel Noddings, Yehuda Rav, Michael D. Resnik, Ole Skovsmose, and Thomas Tymoczko

This chapter introduces my perspective on and my model of the social brain. The development of the social brain paradigm reflects a general development from hierarchical to network thinking across the intellectual spectrum during the latter part of the twentieth century. I discuss the evolution of the social intelligence hypothesis into the social brain hypothesis, and the reigning myths about the brain that have obstructed social brain thinking. I review the key developments in the history of neuroscience at its nexus with the life- and social sciences and their connections to social brain research and theory. The chapter ends with a presentation of my model of the social brain as a networked information system situated in and coupled with a social ecology (Appendix 1). In Appendix 2, I review the concept of connectomics, and in Appendix 3, I list links to glossaries on brain terminology to aid readers in understanding the terms used in the text to describe the structure and function of the brain.

This chapter critically situates the idea of “genius.” The very idea of genius is based on and reinforces the myth of individualism and the “I” as a grammatical illusion. As a sociologist, I claim that if you give me a genius, I will give you a social network. I illustrate this claim with brief looks into non-Euclidean geometry, Ramanujan, Nikola Tesla, and Rodin followed by an exploration of the Einstein genius cluster. Other topics include chaos and creativity, the social context of genius, intuition, and an appendix on creativity and madness. I examine the key notions of genius clusters and the multiples idea: any given innovative idea or technology appears along with more or less similar innovations—families of innovations or parts thereof—at the same time within the boundaries of a cultural or civilizational region.

In this chapter, I consider the decades of research carried out on Einstein’s brain and why they have proved to be, and indeed were destined to be, sterile. Intelligence, creativity, and genius are social phenomena. Einstein did stand alone and did not create ab novo. Genius is not as commonly supposed an individual attribute. It clusters, and genius clusters are associated with the rise and decline of civilizations and cultural areas. The myth of individualism supports the idea that Einstein made discoveries “merely by thinking” and that he embodied pure intellect.The myth of Einstein as “pure intellect” is sociologically untenable and is based on the grammatical illusion of the “I” and the myth of the brain as an isolated biological organ independent of external causal factors. I introduce some of the initial elements related to the social brain paradigm such as the connectome, neuroplasticity, and regional concepts of the social brain (as opposed to wholistic concepts).

In this chapter, I fill in the sociological theory of the self that grounds the concept of the “I” as a grammatical illusion. I introduce the idea of humans as always, everywhere, and already social. We are the most radically social of what biologists refer to as the eusocial species, the highest level of animal social organization. The chapter deals with how society constructs individuals as social matrices, the recurrence theorem (which explains our ability to sustain our self-concepts as we move across different social settings), the problems of programming, free will, and consciousness, the evolutionary context of the social self, and the limits of the Golden Rule. I also introduce the concept of dissocism, the inability to “see” the social as a nexus of causal forces (thus making “the social” invisible to large portions of populations across time, space, and culture).

The social brain paradigm does more than help us reveal the social and world realities beyond the conspiracy of mythologies that gives us Einstein as a grammatical illusion and his brain as a sacred relic. The social brain has implications for how we understand the brain in health and illness. The objective of this chapter is to explore the implications of social brain research and theory for the mental health professions. There is already a growing literature on the social brain and psychiatry. While this literature is an important rationale for our work, our approach is distinguished by a more strongly social science foundation for understanding the social brain. In Chap. 10.1007/978-3-030-32918-1_5, we saw how by building on the current body of knowledge about the social brain, we arrive at a new concept of the self and a new unit of socialization. Here we explore the implications of this re-envisioning of the social brain paradigm developed in Chap. 10.1007/978-3-030-32918-1_5 for clinical practice in psychiatry and prevention of mental illness.

This chapter introduces the rationale for challenging the view of Einstein as an icon and genius. We, along with Einstein and others, have made a mistake in reference. The tendency has been to view him as a unique individual and to look to genes and neurons (and more broadly biology) to explain his uniqueness. The label “genius” adds a divine factor to the explanatory narrative. I do not suggest that we deny his uniqueness but that we situate it socially, culturally, and historically. From the vantage point of social science, “Einstein” is defined by the particular configuration of social networks he engaged as his life unfolded. The chapter also previews the following chapters on brains, self, and genius.

Humanist sociologists are activists rooted in the reality of history and change and guided by a concern for the 'real life' problems of equality, peace, and social justice. They view people as active shapers of social life, capable of creating societies in which everyone's potential can unfold. Alfred McClung Lee introduces this volume with 'Sociology: Humanist and Scientific' and develops the theme that a sociology that is humanist is also scientific. The other nine selections are grouped into four parts: 'The Individual and Social Life;' 'Social Institutions: Technology, Science, and Formal Organization;' 'Political Structures: Issues of Justice and Equality;' and 'Methodological Critiques and Counterproposals.'

This book offers a unique analysis of how ideas about science and technology in the public and scientific imaginations (in particular about maths, logic, the gene, the brain, god, and robots) perpetuate the false reality that values and politics are separate from scientific knowledge and its applications. These ideas are reinforced by cultural myths about free will and individualism. Restivo makes a compelling case for a synchronistic approach in the study of these notoriously 'hard' cases, arguing that their significance reaches far beyond the realms of science and technology, and that their sociological and political ramifications are of paramount importance in our global society. This innovative work deals with perennial problems in the social sciences, philosophy, and the history of science and religion, and will be of special interest to professionals in these fields, as well as scholars of science and technology studies.

This book advances the "strong" programme that sociology and anthropology provide a scientific foundation for arguing that God and the gods are human creations. Contending that religion is one - but not the only - way to systematize and institutionalize the moral order of a society, the author argues that religion reflects the fundamental human need for belonging and the social function of compassion. As such, our transcendental and supernatural ideas are really concerned with our everyday lives in communities and, faced with the severity and immediacy of the global problems with which the world is confronted - existential threats - it is increasingly important to abandon delusions and correct our mistake in reference, not by eradicating religion, but by grounding it more explicitly in earthly matters of community, social solidarity, belonging, and compassion. A wide-ranging study of the roots, nature, and purpose of religion and theistic belief, Society and the Death of God will appeal to sociologists, social theorists, and philosophers with interests in the scientific study of religion and the role of religion in the life of humankind.

The concept of society sui generis ¿ society as a level of reality which could be studied scientifically ¿ crystallized in the middle of the nineteenth century in Europe, with the work of Durkheim, Marx and Weber and today, more than at any other period in history, the idea of the social has gained a foothold in philosophy, biology, and neuroscience. However, this idea has emerged into prominence not through the historical or contemporary efforts of sociologists, but mainly through the efforts of biologists and neuroscientists. This book seeks to re-establish the credentials of sociology as the science of society. While acknowledging the amalgamation of traditional disciplines into interdisciplinary and multidisciplinary networks of research and theory, and championing interdisciplinarity in recognising the capacity of converging perspectives to yield more interesting general theories of social life, the author defends disciplinarity in maintaining sociology¿s achievements as a discipline. With chapters on the sociological world view, imagining society, the self, love, education, mathematics and religion, The Age of the Social re-states the importance of sociology as the source of robust ideas about the social in an age in which this notion has grown in importance. As such, it will appeal to scholars across the social sciences, with interests in method and philosophy in the social disciplines.

This book reviews the research on Einstein’s brain from a sociological perspective and in the context of the social brain paradigm. Instead of “Einstein, the genius of geniuses” standing on the shoulders of giants, Restivo proposes a concept of Einstein the social being standing on the shoulders of social networks. Rather than challenging Einstein’s uniqueness or the uniqueness of his achievements, the book grounds Einstein and his achievements in a social ecology opposed to the myths of the “I,” individualism, and the very idea of “genius.” “Einstein” is defined by the particular configuration of social networks that he engaged as his life unfolded, not by biological inheritances.

The 1990s could be called The Decade of Sociology in mathematics education. It was during those years that the sociology of mathematics became a core ingredient of discourse in mathematics education and the philosophy of mathematics and mathematics education. Unresolved questions and uncertainties have emerged out of this discourse that hinge on the key concept of social construction. More generally, what is at issue is the very idea of “the social”. Within the framework of the general problem of “the social”, we want to open a discussion of boundaries and margins in mathematics and mathematics education. By theorizing the divisions of purity and danger, we will be able to better understand the intersection of logic, mathematics, and thinking with gender, race, and class, and morals, ethics, and values in the classroom. The process of transforming the sociology of mathematics and the sociology of mind into pedagogical tools for mathematics educators and philosophers of education has already begun. One of the tasks before us is the development of a more profound and at the same time more practical grasp of “the social”. Our objective in this paper is to move ourselves and our readers in the direction of just such a grasp of the social.