symbol pushing

symbol pushing (uncountable)

1. (mathematics, somewhat derogatory) The practice of solving mathematical problems by manipulating symbols (as in algebra) rather than through visual or intuitive understanding.
   • 1989, R. Ferro, Logic Colloquium '88, Elsevier Science, →ISBN, page 223:

     The fact that we eventually reach a formulation free from logic (in terms of functional analysis) does not invalidate the use of logical tools: in fact the simplest way to prove termination (i.e. nilpotency) will always be standard logical manipulation, "symbol pushing"; but the existence of a model for this symbol pushing obviously brings in new methods, insights, etc.

   • 2015, The Oxford Handbook of Perceptual Organization, Oxford University Press, →ISBN, page 47:

     Other mathematicians abhor visual proofs and only recognize 'symbol pushing'. Ideally, that would lead to a mathematics that would be fully independent of the human mind, and be simply the (uninterpreted!) output of a Turing machine.

   • 2021, Paul J. Nahin, How to Fall Slower Than Gravity, Princeton University Press, →ISBN, page 129:

     Now, before going any further, and to help convince you that this isn't all just "symbol pushing," let me show you an application of Fourier series that often occurs in mathematical physics.

• symbol-pushing (adjective)
• symbol pusher