&gt; At some point mathematical objects are defined with meta-mathematical definitions (axioms etc), so we can accept definitions based on those terms.<p>“Metamathematics” doesn&#x27;t exist in isolation from the rest of mathematics. If you reject the existence of mathematical objects (in the real world or elsewhere), you must also reject the existence of metamathematical definitions (in the same context), because the former include the latter.<p>&gt; But in any case. You obviously do not believe that mathematical objects exist in the first place and it the question is ill posed based on your concept of reality and existence.<p>I only denied the meaningfulness of asking whether mathematical objects exist <i>in the real world</i>. The terms “real world”, “reality”, etc., I prefer to reserve for that which can be apprehended through physical experience. The distinguishing feature of reality is that you can&#x27;t reject its existence (in the same way I hypothesized rejecting the definition of the word “horse” in my previous comment) - your senses force you to accept it. If someone cuts through your skin with the intention to bleed you to death, you will feel pain. You may resign yourself to your fate, but that won&#x27;t make the pain go away. On the other hand, if you find it useless, annoying, etc. to do mathematics, all you need to do is stop doing it.