In classical Indian philosophy, the work Nyaya Sutra, which lays the foundation of the Nyaya school of logic, is traditionally attributed to which sage?

Introduction / Context:
Indian philosophy is divided into several classical schools, each associated with a key foundational text and a sage. The Nyaya school is mainly concerned with logic, epistemology and methods of reasoning. Its primary text is the Nyaya Sutra. This question checks whether the learner can correctly identify the sage traditionally regarded as the author of this foundational work.

Given Data / Assumptions:

• The text in question is the Nyaya Sutra.
• It is linked to the Nyaya school of Indian philosophy.
• Four options list well known sages from different philosophical or scientific traditions.
• We assume the traditional attributions as accepted in standard references.

Concept / Approach:
The concept is mapping philosophical schools to their principal texts and sages. The Nyaya Sutra is traditionally attributed to the sage Gautam, also called Akshapada Gautam. Other options correspond to different texts and systems: Vyasa with the Brahma Sutra, Kapila with Sankhya and Charaka with Ayurveda. The correct approach is to recall which sage is linked specifically with Nyaya and its logical method.

Step-by-Step Solution:
Step 1: Note that the Nyaya Sutra is the central text of the Nyaya school of philosophy. Step 2: Recall that this text is traditionally attributed to the sage Gautam, sometimes referred to as Akshapada Gautam. Step 3: Vyasa is associated with compiling the Vedas and with the Brahma Sutra of the Vedanta school. Step 4: Kapila is the legendary founder of the Sankhya school and is not the author of the Nyaya Sutra. Step 5: Charaka is linked to classical Ayurveda and the Charaka Samhita, not to Nyaya logic. Step 6: Therefore, among the given options, Gautam is the correct answer.

Verification / Alternative check:
Standard introductions to Indian philosophy consistently state that Nyaya philosophy is based on the Nyaya Sutra of Gautam. Textbooks for competitive exams, university syllabi and encyclopedias of religion and philosophy repeat this attribution. Checking any of these sources will confirm that Gautam is the traditional author linked with this text.

Why Other Options Are Wrong:
Vyasa: Central figure for Vedanta and the Brahma Sutra, but not for the Nyaya Sutra.
Kapila: Credited with the Sankhya system, which focuses on enumeration of principles, not with Nyaya logic texts.
Charaka: Key authority in ancient Indian medicine and the Charaka Samhita, unrelated to Nyaya philosophical logic.

Common Pitfalls:
Students sometimes confuse these sages because they all belong to the broad field of ancient Indian knowledge. Without a clear mapping between schools and texts, it is easy to mix up Nyaya, Sankhya and Vedanta. A helpful strategy is to remember one main pair for each system: Nyaya Sutra and Gautam, Sankhya philosophy and Kapila, Vedanta and Vyasa, Ayurveda and Charaka.

Final Answer:
The Nyaya Sutra is traditionally attributed to the sage Gautam.