Mathematical Proof is the process of starting with an assumption, or a statement which is given, and, by using logical argument, arriving at a conclusion

This statement effectively describes the essence of mathematical proof. It emphasizes the foundational aspects of proofs in mathematics, which include:

1. Assumption or Given Statement: This is the starting point of any mathematical proof. It consists of axioms, previously established theorems, or specific statements that are taken to be true for the purpose of argument.

2. Logical Argument: This refers to the systematic and coherent method of reasoning that connects the initial assumptions to the conclusion. Logical deduction often employs established mathematical principles, theories, and rules of inference.

3. Conclusion: The final statement that arises from the logical reasoning based on the initial assumptions. This conclusion must be shown to follow necessarily from the assumptions to validate the proof.

In summary, a mathematical proof is a structured argument that demonstrates the truth of a particular statement based on given assumptions and logical deductions.