Introduction:
Fullerene is a unique form of carbon consisting of hollow cage-like structures, with the most common form being C60. It was first discovered in 1985 and has since become a topic of great interest due to its unusual physical and chemical properties. However, the formation enthalpy of fullerene is highly positive, raising questions about its stability and existence.

Formation Enthalpy:
The formation enthalpy of a compound is the enthalpy change when one mole of the compound is formed from its constituent elements in their standard states. For fullerene, the formation enthalpy is highly positive, indicating that it requires a large input of energy to form. This suggests that fullerene should be highly unstable and unlikely to exist under normal conditions.

Experimental Evidence:
Despite the high positive formation enthalpy, fullerene has been experimentally synthesized and its existence has been confirmed. Several lines of evidence support the existence of fullerene:

1. Synthesis: Fullerene has been successfully synthesized in the laboratory using various methods, including laser vaporization, electric arc, and chemical vapor deposition. These methods involve high-energy processes that provide the necessary energy to overcome the positive formation enthalpy barrier.

2. Structural Analysis: The structure of fullerene has been extensively studied using techniques like X-ray crystallography and electron microscopy. These studies have confirmed the presence of the hollow cage-like structure composed of carbon atoms.

3. Physical Properties: Fullerene exhibits unique physical properties such as high thermal and chemical stability, high electron mobility, and high tensile strength. These properties have been experimentally observed and are consistent with the existence of fullerene.

4. Spectroscopic Analysis: Spectroscopic techniques like infrared spectroscopy and nuclear magnetic resonance have been used to characterize fullerene and its derivatives. These analyses provide information about the molecular vibrations and chemical shifts, confirming the presence of fullerene molecules.

Conclusion:
Despite the highly positive formation enthalpy, the existence of fullerene has been experimentally confirmed through various synthesis methods and extensive characterization. The unique physical and chemical properties exhibited by fullerene further support its existence. While the positive formation enthalpy suggests that fullerene is thermodynamically unstable, the kinetic factors involved in its synthesis and the resulting stability of the molecule contribute to its existence.