---
author:
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bibliography:
- 'ConstantRecognition.bib'
title: Criteria for the numerical constant recognition
---

[Introduction]{}

Experimental mathematics become very important nowadays [@BorweinBailey]. Using modern computers we are able to perform sequential brute-force searches of various mathematical objects and models at stunning scale. Multi-core processors [@epyc], GPUs, vectorization, FPGA and future quantum computers allow us to reach depths incomprehensible by humans. In essence, this is some form of artificial intelligence [@Eurega], because obtained results are indistinguishable from those provided by reasoning or more sophisticated algorithms [@SR]. Particularly interesting problem is a numerical constant recognition [@plouffe]. We are given decimal expansion, and ask if there is equivalent formula? There is strong demand from users of mathematical software to provide such a feature (identify/Maple [@Maple], nsimplify/SymPy [@symPy], RIES [@RIES], FindFormula [@Mathematica] ). In typical situation we encounter some decimal number, resulting from numerical simulation or experiment, e.g: 1.82263, and ask ourselves if it is equivalent to some symbolic expression, like e.g: $\sqrt{2}^{\sqrt{3}}$. Unfortunately, such a problem without additional constraints is ill-posed, and provided ”answers” nonsense. Often ridiculously complicated [@ISCwayback]. This is not a surprise, as Cardinality of real/complex transcendental numbers is uncountably infinite (continuum $\mathfrak{c}$), while number of formulas and symbols is countable 