Is Math Real?
Mathematics is, in part, the study of universal traits:<p>(1) Ratios between things in the world.<p>(2) Logical relations between things in the world.<p>(3) Absolute distinctions between things in the world, in a nominative sense, which is to say in the sense that numbers can be assigned to things or elements of things.<p>Mathematics that relates to one of the three use-cases above is absolutely real, hence its unreasonable effectiveness in the natural sciences.  (See Wigner: <a href="https:&#x2F;&#x2F;www.maths.ed.ac.uk&#x2F;~v1ranick&#x2F;papers&#x2F;wigner.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.maths.ed.ac.uk&#x2F;~v1ranick&#x2F;papers&#x2F;wigner.pdf</a> )<p>When mathematics does not relate to one of the three -- for e.g., in Cantor&#x27;s theories of &quot;countable&quot; and &quot;uncountable&quot; infinite sets -- it is totally unreal.  A construct or game played with logic that has no prior or intrinsic relevance to the material world.