As an academic discipline, mathematics is more than a set of computing mechanisms; it is argued by scholars that the quality of mathematics education is in decline today in human society. Historically, mathematics and philosophy had a close interrelationship enabling the understanding of various natural phenomena. According to Platonism of pure mathematics, the dynamics of natural phenomena and human societies follow invariant and absolute mathematical principles. This article presents a socio-philosophical argument that the concept of society within the natural space can be classified into natural society and synthetic society based on the concept of mathematical purifications, and mathematics education has a role in it. The existence of logical inversions of various forms in the synthetic societies are analysed and corrective roles of mathematics education are explained. The Pythagorean philosophy of mathematics in building an improved as well as just society is an appropriate solution that calls for a relook into mathematics education in order to reduce utilitarian distortion in mathematics education today and to promote intellectualism as well as harmony while reforming mathematics education.