If the Big Bang Theory is correct, then our whole life is just one big accident. The same is true for evolution and natural selection. It could even be argued that every man, woman, and child on Earth is the result of a happy coincidence of meeting their parents. And many of the most important inventions were made by mistake.
Penicillin
Dr. Fleming discovered penicillin by accident. In 1928, a scientist was researching an influenza virus and noticed that one of his petri dishes with a culture of bacteria was infected with a fungus. Fleming did not throw away the "spoiled" drug, but began to observe the development. Seeing the toxicity of the fungus to staphylococcus, the scientist was able to isolate the drug penicillin, which became a salvation for hundreds of thousands of people.
Dead Sea Scrolls
In 1947, two Bedouin shepherds stumbled upon a deep cave in the hillside. Here they found hermetically sealed vessels. The shepherds sold the papyrus blackened from time to time to a Jerusalem antiquarian - it turned out that they preserved the oldest copies of the Bible.
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X-ray
Wilhelm Konrad Roentgen was not considered a prominent figure in the world of physics in 1895. His discovery of a new type of radiation happened quite by accident and provoked a strong leap in the development of medicine. In 1901, Roentgen was awarded the world's first Nobel Prize in physics.
Pompeii
The eruption of Vesuvius buried the most beautiful Italian city alive. But mankind learned about this tragedy a thousand years later: in 1710, a simple peasant stumbled upon pieces of marble and sold them to a local doge. He ordered excavations at the specified location and found many more artifacts. In 1748, Joaquin de Roca Alcubierre discovered the trail that led him to what remained of the great city.
Beer
The ancient discovery of fermentation almost certainly happened by accident. No one knows exactly who invented the first beer, but the world's first bakers should have noticed the reaction of the damp grain. Moreover, some anthropologists and archaeologists even theorize that it was beer that first appeared, and only then people thought of making bread from grain.