Understanding and interpreting mathematical proofs can be a challenging task, especially for the Mathematics optional subject in the UPSC exam. However, with a systematic approach and some specific tips, it can become more manageable. Below are some guidelines to help you in understanding and interpreting mathematical proofs:

1. Familiarize Yourself with the Terminology:
- Start by familiarizing yourself with the specific terminology and symbols used in mathematical proofs. This will help you understand the language and structure of the proofs.

2. Read the Proof Carefully:
- Read the proof carefully, line by line, and try to understand the logical flow of the argument. Pay attention to each step and ensure that you comprehend the reasoning behind it.

3. Break Down the Proof:
- Break down the proof into smaller chunks or steps. Identify the hypothesis, intermediate steps, and the conclusion. This will help you analyze the proof more effectively.

4. Identify the Assumptions:
- Identify the assumptions made in the proof. These are the statements that are taken to be true without proof. Understanding the assumptions will give you a better grasp of the proof's validity.

5. Look for Patterns:
- Look for patterns or recurring themes in the proof. Mathematical proofs often follow certain patterns or techniques, such as induction, contradiction, or direct proof. Recognizing these patterns will help you understand the proof's structure.

6. Take Notes:
- Take notes while reading the proof. Write down the key steps, important equations, and any observations you make along the way. This will help you consolidate your understanding and serve as a reference for later revision.

7. Consult Additional Resources:
- If you are struggling to understand a particular proof, consult additional resources such as textbooks, lecture notes, or online tutorials. These resources may provide alternative explanations or examples that can help clarify your understanding.

8. Practice, Practice, Practice:
- Practice solving mathematical proofs regularly. The more exposure you have to different proof techniques and styles, the better equipped you will be to understand and interpret them.

In conclusion, understanding and interpreting mathematical proofs requires a systematic approach and regular practice. By familiarizing yourself with the terminology, breaking down the proof, identifying assumptions, looking for patterns, taking notes, consulting additional resources, and practicing regularly, you can enhance your ability to comprehend and interpret mathematical proofs effectively.