How does physicalism interpret numbers and geometric objects?

In the philosophy of mathematics, physicalism is the view that mathematics is about concrete physical objects rather than abstract entities. Unlike Platonists, who argue that mathematical objects exist independently of the physical world, physicalists contend that these objects are grounded in the material realm.1

Interpretation of Geometric and Mathematical Objects

• Geometric Objects: Physicalists may interpret shapes like circles as regions of actual physical space. Some thinkers, including Albert Einstein, have noted that while geometry originates from the abstraction of "ideal rigid bodies" found in nature, these abstractions do not correspond exactly to the physical objects observed in experience, which are subject to variables like temperature and pressure.12
• Sets: Under this view, sets are interpreted as aggregates or "piles" of physical matter. For example, a set of eggs is considered nothing more than the collection of physical objects that compose it.1
• Numbers: One strategy is to treat numbers as physical properties of collections—such as the number 3 being a property of a specific pile of three eggs. Alternatively, some physicalists, such as John Stuart Mill, argued that mathematical statements like "2 + 3 = 5" describe the physical behavior of combining piles of objects rather than referring to abstract entities.1