How does psychologism explain the existence of mathematical objects?

In the context of the philosophy of mathematics, psychologism explains the existence of mathematical objects by identifying them as concrete mental entities rather than mind-independent, abstract objects.1

According to this view, mathematical objects—such as numbers, circles, and sets—do not exist independently of human beings. Instead, they are considered to be ideas or mental constructs residing within people's heads. Proponents of this perspective, which was particularly popular during the late 19th and early 20th centuries, argued that mathematical theorems are essentially about these mental objects. For example, early work by Edmund Husserl suggested that numbers are not found ready-made in nature but are the result of specific mental achievements or acts of consciousness.12

It is important to note that psychologism has faced significant criticism for its approach. Many philosophers, including Gottlob Frege, argued that it incorrectly conflates logical structures with psychological processes. Consequently, the view is no longer widely endorsed in contemporary philosophy of mathematics, as it struggles to account for the objective and universal nature of mathematical truth.21