The

mathematical statement of such problems leads to an inverse problem for the heat equation, where it is required to find not only a solution of the problem, but also its right-hand side that depends only on a spatial variable.

For example, Sorin Bangu (2008) argues that the explanandum of Baker's cicada example is a

mathematical statement, so the example is not a mathematical explanation of a concrete phenomenon but a mathematical explanation of a mathematical phenomenon.

However, throughout the book she reminds students of the importance of the logical structure of a

mathematical statement as a framework for finding a proof of that statement.

In general, a

mathematical statement may contain any number of logical connectives--and, or, if-then--as well as the two quantifiers--for all, there exists.

a

mathematical statement can be proved or disproved.

For this particular kind of number talk the teacher chooses a

mathematical statement and poses the question: "Is this true or false?" The teacher then conducts the discussion using the actions described above.

The

mathematical statement of the phase unwrapping problem can be expressed by

Even if not all true statements can be proved, is there always a way to decide whether a given

mathematical statement is provable or not?

Is it a speculative 'subject' of the

mathematical statement, which has no place in the factial but nevertheless can speak in it, that remains?

In his essay "Fictionalism, Theft, and the Story of Mathematics," Mark Balaguer proposes, among other arguments, that rather than describe a

mathematical statement as "true," it could be described as "true within the story of mathematics."

The role of the symbolic geometry technology in both examples lay in allowing the user first to explore the problem visually, then in assisting in the conversion of this visual "feel" into a sharp

mathematical statement, expressed symbolically.

After each

mathematical statement, the author immediately cites a real-world example to model his mathematical imagery for the reader--a refreshing visualization device for individuals unable to grasp the math quickly.