The question asks us to identify which sociologist emphasized the importance of focusing on the "gap in ideal representations, material social organizations and their constituent actions." Let's analyze the options and find the correct answer:

1. Emile Durkheim: Durkheim is known for his work on social facts, collective consciousness, and the role of social institutions. He primarily focused on the cohesion and functional aspects of society. His theories revolve around how societal norms and values are maintained and how they contribute to social order.
2. Max Weber: Weber's work delves into understanding how individuals' actions and behaviors shape social structures. He introduced the concept of "Verstehen," which means interpretative understanding, to study the social world. Weber also explored the discrepancies between ideal representations (what society says it should be) and practical realities (how society actually functions). This aligns directly with the notion of focusing on the gap in ideal representations and material actions.
3. Karl Marx: Marx is most famous for his critique of capitalism and his theory of historical materialism. He focused on the economic bases of society and the conflicts arising from class struggles.
4. Talcott Parsons: Parsons is known for his theory of structural functionalism, which emphasizes the interdependence of the social system's parts. His focus was more on the stability and order within social structures rather than discrepancies between ideals and actions.

Considering the analysis above, Max Weber is the most suitable candidate for this statement, as he closely examined the complexities between ideals and actual practices within social organizations.

Conclusion: The correct answer is Max Weber.