Formulas in all mathematical fields are described in this book. Propositional formulas in mathematical logic are potentially of special interest. Using Formula Operator Theory, proofs of mathematical theorems will possibly be condensed. Formula Theory is a modern paradigm for mathematics, which is the basis of mathematics. That is Formula Theory, which is the basis on which mathematics starts.

This theory looks for mathematical formulas and all other objects which have different components (without the limit that a whole cannot be part of its part, which means that loops are not disallowed).

The Mathematics Research Book has a highly effective language which elegantly expresses vast quantities of knowledge in a few definitions and theorems. It is amazing that a sequence of equations can often be summed up by the lives of successive generations of great thinkers. The language economy masks the wealth and complexity of the thoughts behind the symbols.

Students should perceive the doors to extensive and fascinating questions in mathematics, while on the other hand they must remain anchored in mathematics and not lose them in the narcotic haze of speculation.

In order to understand axiomatic and the function and significance of each of the axioms necessary to determine theory, this book tried to provide the necessary context. This book has tried to give equal account of the theory of the infinities and other abstractions that lie at the heart of the formal process.

Of course, this book tried, above all, to present uncompromisingly rigorous and accurate facts and to show clearly that formalism on the one hand, and inductive explanations on that other, are within two distinct domains.