While mathematics can be used to collect and analyze data, develop theories, and make predictions about social phenomena, it cannot directly solve social problems. Social problems are complex and require a multidisciplinary approach to address them.

Surveys are a common method for collecting data in sociology. They can be used to collect data on a wide range of topics, including people's opinions, attitudes, and behaviors.

Statistical methods are a common tool for analyzing data in sociology. They can be used to identify patterns and trends in data, and to test hypotheses about social phenomena.

Mathematical models can be used to develop theories in sociology by providing a formal representation of social phenomena. This can help sociologists to understand the relationships between different variables and to make predictions about how social phenomena will change over time.

Mathematical models can be used to make predictions in sociology by simulating social phenomena. This can help sociologists to understand how different factors will affect the outcome of a social process.

Mathematical models can be used to develop policies by providing a formal representation of the social problem and the potential solutions. This can help policymakers to understand the likely effects of different policies and to choose the policy that is most likely to be effective.

Game theory is a branch of mathematics that studies strategic decision-making. It has been used to study a wide range of social phenomena, including cooperation, conflict, and bargaining.

Network theory is a branch of mathematics that studies the structure and dynamics of networks. It has been used to study a wide range of social networks, including friendship networks, collaboration networks, and information networks.

Chaos theory is a branch of mathematics that studies complex systems that are highly sensitive to initial conditions. It has been used to study a wide range of social phenomena, including the spread of disease, the evolution of culture, and the dynamics of social movements.

Fractal theory is a branch of mathematics that studies self-similar patterns. It has been used to study a wide range of social phenomena, including the distribution of wealth, the structure of cities, and the dynamics of social mobility.

Game theory is a branch of mathematics that studies strategic decision-making. It has been used to study a wide range of social justice issues, including the allocation of resources, the design of social policies, and the resolution of conflicts.

Network theory is a branch of mathematics that studies the structure and dynamics of networks. It has been used to study a wide range of social identity issues, including the formation of social groups, the spread of social norms, and the dynamics of social change.

Game theory is a branch of mathematics that studies strategic decision-making. It has been used to study a wide range of social interaction issues, including cooperation, conflict, and bargaining.

Fractal theory is a branch of mathematics that studies self-similar patterns. It has been used to study a wide range of social cognition issues, including the structure of mental representations, the dynamics of memory, and the development of language.

Chaos theory is a branch of mathematics that studies complex systems that are highly sensitive to initial conditions. It has been used to study a wide range of social emotions issues, including the dynamics of mood, the spread of emotions, and the development of emotional disorders.