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Why did Kant argue that mathematics contains synthetic a priori knowledge?

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Immanuel Kant German philosopher Immanuel Kant surrounded by Ouroboros, an emblematic serpent of ancient Egypt and Greece, engraving by John Chapman, published in London, 1812.

Immanuel Kant argued that mathematics contains synthetic a priori knowledge because he believed mathematical truths are both necessary and universal—conditions that require them to be independent of experience (a priori)—yet they also provide substantive knowledge about the world that is not merely contained within the definitions of the terms themselves (synthetic).12

In his Critique of Pure Reason, Kant sought to explain how such judgments are possible. He maintained that mathematics necessarily deals with space and time, which he identified as a priori forms of human sensibility. These forms are not derived from experience but are instead imposed by the mind as the necessary framework through which all sensory data is apprehended.21

By positioning space and time as the conditions of all possible experience, Kant argued that mathematical propositions could be synthetic—adding to our knowledge of reality—while remaining necessary and universal, as they describe the fundamental structure of the human mind's perception rather than contingent empirical observations.2