Depends on what you mean by "discover". Around 450 BC, Democritus proposed his idea that matter was not infinitely divisible, but made of chunks called "atoms", which each had distinct properties that contributed to the properties of the whole material. This is pretty similar to the true state of affairs, but this was pretty much guesswork on his part. The Greeks never performed any kind of experiments that could confirm the existence of particles.
People didn't really start observing particles like electrons until the latter half of the 19th century, although they had a rough idea that they had to exist prior to that. Protons and neutrons weren't observed directly until the 20th century.
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The Greeks did not discover particles in the modern scientific sense. While ancient Greek philosophers such as Democritus proposed the idea of atoms as indivisible particles, it was not until the development of modern atomic theory in the 19th century that a more rigorous understanding of particles emerged.
James Chadwick used a series of experiments involving alpha particles and beryllium to discover neutrons in 1932. By observing the scattering of these particles, he was able to infer the existence of neutrons, which are electrically neutral particles found in the nucleus of atoms.
J.J. Thompson discovered the electron in 1897 through his experiments with cathode rays. He observed that cathode rays were negatively charged particles that were much smaller than atoms. This discovery led to the development of the plum pudding model of the atom.
Subatomic particles were discovered through experiments involving the interaction of matter with various forms of radiation, such as beta particles, gamma rays, and alpha particles. Scientists like J.J. Thomson, Ernest Rutherford, and James Chadwick played integral roles in the discovery of electrons, protons, and neutrons, respectively. Their contributions to the field of atomic and nuclear physics helped unravel the nature of subatomic particles and their properties.
Gell-Mann and Zweig used the concept of strangeness to classify particles, which eventually led to the development of the quark model. The idea of quarks emerged as a theoretical explanation to provide a deeper understanding of the classification of subatomic particles.
Thomson discovered the electron. By conducting experiments with cathode rays, he was able to determine the properties of these particles, which led to the discovery of the electron as a fundamental constituent of atoms.