This question refers to several topics we would need to address. First, we need to define what is understood under the name of 'antibiotics' and whether they could have been actually discovered. Second, the general history of the development of the antibiotics. Third, the role of Sir Alexander Fleming in said process against the backdrop of the two previous issues.

The antibiotics are a class of antibacterial agents that are used to treat the bacterial infections by inhibition of the microbial growth and killing the bacteria. They can be produced from naturally occurring organisms, such as various molds or synthesized artificially. Although used intuitively for centuries (and possibly millennia), the modern research of the antibiotics was possible only after the discovery of microbial pathogens.

It should be noted that the first antibiotics described in length and introduced to the medical practice were invented rather than discovered, as they were synthetic substances rather than naturally existing organisms. It is generally accepted that the field of antibiotics development has been pioneered by Paul Ehrlich, German scientist who noticed that some dyes tend to stain certain tissues or cells and came to a conclusion that it should be possible to isolate or create substances that would bind to e.g bacteria, killing them in the process while posing little to no harm to the host. Ehrlich experiments that started in late 1880s and were later conducted with the cooperation with Alfred Bertheim and Sahachiro Hata led to the introduction of the first synthetic antibacterial agent, arsphenamine, created in 1907 and since 1910 marketed as Salvarsan and prescribed as a treatment for syphilis (caused by an infection with a bacterium Trepanoma pallidum). These were followed by sulphonamides in 1930s. It is worth noting that Protonsil, the first drug of this type was introduced only in 1935, even though the first sulfonamide was created roughly concurrently with salvarsan, having been first made by Austrian chemist Paul Gelmo in 1908.

The discovery of the penicillin is largely attributed to Sir Alexander Fleming, but as in many cases of the scientific discovery and invention, he wasn't the first to observe the relevant phenomenon and describe them, but was the first to do it in necessary detail using available knowledge that has been build in the meantime. Fleming's discovery was, in fact, preceded by more than half of century, courtesy of his compatriot, Sir John Scott Burdon-Sanderson, who observed in 1871 that the culture contaminated by a mold shows no bacterial growth. Three years later, another British physician, Sir William Roberts noticed that Penicillium mold (in this case Penicillium glaucum) are generally never contaminated by bacteria. He discussed it with his French colleague, Louis Pasteur, who conducted experiments with Jules Joubert in 1877 confirming that Bacillus antracis (anthrax) does not grow in the presence of a Penicillium notatum mold. Some time later, another French scholar, Ernest Duchesne, experimented on the bacteria and noticed that Penicillium glaucum indeed kills many pathogens and weakens others to the point of attenuation (Duchesne confirmed that by injecting guinea pigs with the bacteria treated by the mold and the animals not only survived but also developed immunity). He summarized his experiments in a thesis that went largely unnoticed, possibly due to young age of the author (Duchesne was only 23 at the time). Given that this was a first scientific paper that proposed therapeutic usage of molds due to their anti-bacterial properties, it could have been dismissed or overlooked by scholars (including Pasteur himself) unwilling to believe that a young, unknown student was able to make such a breakthrough in medicine. Two years before Duchesne's thesis, Italian biologist Vincenzo Tiberia also used penicillin injections on animals infected with bacteria, but the results of his work was considered inconclusive. Then, shortly before Fleming, in 1920, two Belgian biologists, Andre Gratia and Sara Dath observed that the contamination of a Streptococcus aureus with penicillin mold inhibits the bacterial growth. Scientific article presenting their findings garnered some interests, so did the 1923 one written by Clodomiro Twight, Costa Rican scientist working at Pasteur Institute in Paris, but both did not result in any breakthrough. It is worth noting that Fleming's discovery met with similar reaction, in large part due to poor translation to a practical application caused by technical constraints in production of penicillin. This was continued until early 1940s, when Ernst Chain, Norman Heatley and Edward Abraham managed to purify the antibiotic and devise a method of mass production in 1940. But it was not until the Fleming's acquaintance was admitted to a hospital with a diagnosis of severe meningitis, showing no improvement during the sulfonamides therapy. Fleming decided to administer penicillin, resulting in rapid recovery. This demonstration of the drug efficacy finally persuaded the government to green-light the introduction of penicillin as a mass-produced antibiotic, with the large-scale production in mid-1943, initially for the Allied soldiers.

Thus, Sir Alexander Fleming was not the first to observe the bactericidal effects of the Penicillium mold or made conjectures about its medical usage. His observations and experiments went largery unnoticed, much like those of his predecessors. But he is today considered a 'creator' of penicillin, because he discovered a particular type of penicillin that will later be used to create popular antibiotic (benzylpenicillin, penicillin G or Penicillin II) it were his associates who finally made a purified drug suitable for mass production and it was Fleming himself who was instrumental in persuading the authorities to introduce it as an efficient antibacterial drug. He also followed up with the research on the antibiotic resistance in the early 1940s, strengthening his link to the development of the antibiotics.

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Aminov, R.I., A Brief History of the Antibiotic Era: Lessons Learned and Challenges for the Future, in: Frontiers in Microbiology, 2010, 1:134.