**Core Concept**
The smallpox vaccine is a pioneering example of immunization against a viral disease. It involves the use of a mild, related virus (cowpox) to elicit an immune response against the more virulent smallpox virus, taking advantage of the phenomenon of immunological cross-reactivity.

**Why the Correct Answer is Right**
Edward Jenner, an English physician, developed the smallpox vaccine in 1796 by administering cowpox material to James Phipps, the son of Jenner's gardener. This groundbreaking experiment led to the creation of the first vaccine, which was instrumental in the global eradication of smallpox in 1980. The mechanism involves the stimulation of humoral immunity, where the immune system produces antibodies against the smallpox virus due to its similarity to cowpox.

**Why Each Wrong Option is Incorrect**
**Option A:** **Incorrect**, as Louis Pasteur made significant contributions to vaccination with the development of vaccines for anthrax and rabies, but he did not create the smallpox vaccine.
**Option B:** **Incorrect**, as Robert Koch was a renowned microbiologist who made significant contributions to the germ theory of disease, but he did not create the smallpox vaccine.
**Option C:** **Incorrect**, as Alexander Fleming discovered penicillin, revolutionizing the treatment of bacterial infections, but he did not create the smallpox vaccine.

**Clinical Pearl / High-Yield Fact**
The development of the smallpox vaccine highlights the importance of serendipity in medical research, as Jenner's observation of milkmaids being immune to smallpox led to the creation of the first vaccine.

**Correct Answer: C. Edward Jenner**