<P> Science is the process of gathering, comparing, and evaluating proposed models against observables . A model can be a simulation, mathematical or chemical formula, or set of proposed steps . Science is like mathematics in that researchers in both disciplines can clearly distinguish what is known from what is unknown at each stage of discovery . Models, in both science and mathematics, need to be internally consistent and also ought to be falsifiable (capable of disproof). In mathematics, a statement need not yet be proven; at such a stage, that statement would be called a conjecture . But when a statement has attained mathematical proof, that statement gains a kind of immortality which is highly prized by mathematicians, and for which some mathematicians devote their lives . </P> <P> Mathematical work and scientific work can inspire each other . For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic . But today, the Poincaré conjecture has been proven using time as a mathematical concept in which objects can flow (see Ricci flow). </P> <P> Nevertheless, the connection between mathematics and reality (and so science to the extent it describes reality) remains obscure . Eugene Wigner's paper, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, is a very well known account of the issue from a Nobel Prize - winning physicist . In fact, some observers (including some well known mathematicians such as Gregory Chaitin, and others such as Lakoff and Núñez) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science . </P> <P> George Pólya's work on problem solving, the construction of mathematical proofs, and heuristic show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps . </P>

What goes along with the drawing conclusions step in the scientific method