The ancient Greeks considered the question of the smallest bits of matter. They envisioned a process in which a bit of matter is cut in half and then one of the halves is cut in half. They asked whether this process could continue indefinitely or whether it must terminate. Democritus decided it must terminate. The name he gave to the smallest bit was "a"+"tom," "a" being Greek for not and "tom" for cut. Thus "atom" is Greek for not cutable.

The Greeks after Democritus did nothing further with the concept of "atoms." It was not until shortly after 1800 that atomic theory was developed by John Dalton. Dalton stated that material of each element is made up of tiny, identical and immutable particles which combine in small whole number ratios to form compounds. This formulation was based upon his own extensive chemical investigations supplemented by discoveries made other scientists of his time such Antoine Lavoisier's that mass is conserved in chemical reactions. Dalton's discoveries had to do with the existence of atoms but said nothing about the nature and structure of atoms.

It was the British scientist Lord Kelvin (William Thomson) who first proposed in1867 a structural model of an atom. Kelvin proposed that atoms are composed of interlinked vortex rings. (A "smoke ring" is a vortex ring.) This model was popular in Britain but not in Germany.

William Thomson was born in Belfast, Ireland and is commonly said to have been Scot-Irish, but ethnically he was neither Scot nor Irish. Instead, as his family name clearly indicates, he was the descendant the Angles of the Anglo-Saxon invasion who settled in the Lowlands of Scotland. In effect, ethnically he was Anglish.

The popularity in Britain of the vortex ring model of an atom only lasted until the discovery by the British scientist J.J. Thomson of the particle of electrical charge subsequently known as the electron. This led to the so-called plum pudding model of an atom; i.e., electrons were the negatively charged plums in pudding of positive charge.

The plum pudding model was quickly dispelled by the brilliant experiments of Ernest Rutherford in 1911. Rutherford had positive charged alpha particles impinge upon very thin gold foil. Most of the alpha particles passed through the foil unaltered in direction. A few were deflected. The small proportion of deflected particles indicated that most of a gold atom consisted of empty space. Some of the alpha particles were bounced backwards from the foil. This indicated that a gold atom consisted of a small compact positively charged kernel surrounded by its electrons. It was given the name nucleus, the Latin term for the kernel of a nut.

In 1913 Niels Bohr of Copenhagen proposed his solar system model of the and used it to very accurately explain the spectrum of hydrogen. It was found that the Bohr model could be used to explain the spectra of hydrogen-like atoms, ones with a single valence electron, but not the spectra of atoms with multiple valence electrons.

In Copenhagen rapid innovations were made in quantum theory in the 1920's by Werner Heisenberg. But these were superseded by the wave mechanics of Erwin Schrödinger of Vienna, Austria. Because Schrödinger's equation involved an unspecified variable, called arbitrarily the wave function, there were various interpretations of the nature of this variable. The Copenhagen School correctly interpreted the wave function being such that its squared magnitude is the probability density. But the Copenhagen School then made the unwarranted assertion that material particles cannot have a probability density function and therefore particles like electrons cannot have a material existence until they are subjected to measurement. This became the defining proposition of the Copenhagen Interpretation of quantum theory. Contrary to this proposition, the truth is that any particle in motion has a probability density function based upon the proportion of the time it spends in various intervals. This time-spent probability density function is inversely proportional to its speed; i.e.; the absolute value of its velocity.

An electron has a set of four quantum numbers. According to the Exclusion Principle proposed by Wolfgang Pauli in 1925 there can be only one electron with a particular set of quantum numbers. This proposition does not hold with just three quantum numbers. But in 1922 Ulenbach and Goudsmit had carried out experiments involving the injection of silver ions into a strongly spatially varying magnetic field. They found these ions were separated into equal beams.

Later Stern and Gerlach identified this separation as being due to particle spin, an intrinsic characteristic of charged particles. It turned out that this two-valued intrinsic characteristic for electrons was just what was needed to make Pauli's Exclusion Principle apply to the electrons of an atom.

In 1927 Heisenberg publish an article defining what subsequently became known as the Uncertainty Principle. Because the Uncertainty Principle says the location and the momentum, and hence velocity, cannot be simultaneously known to arbitrarily precision an electron cannot have a definite location and velocity and thus cannot have a material existence. This was thought to support the Copenhagen Interpretation of quantum theory. This was another unwarranted assertion of the Copenhagen Interpretation of quantum theory. The time-spent probability density distributions for material particles satisfy the Uncertainty Principle.

The Copenhagen Interpretation model of the atom is one of a long line of such models that were popular for a period but were ultimately rejected.

In 1932 James Chadwick discovered a neutral particle, subsequently called the neutron. This particle clarified a lot concerning atomic nuclei, but raised other questions. Having nuclei made up of neutrons and protons explained puzzlements concerning the atomic weights of elements. It predicted that there could be nuclei of the same element with differing atomic weights. It indicated that for the periodic table the elements should be arranged by their atomic numbers rather than their atomic weights. The puzzlement concerning neutrons that was found later is that outside of nuclei neutrons are unstable with a half-life of about 15 minutes. Within nuclei neutrons are generally stable.

The big puzzlement was how multple protons could held together in nuclei. It was conjectured that all nucleons are attracted to each other with a force that drops off with separation distance s faster than 1/s². Thus at a sufficiently short distance it would be stronger than the electrostatic repulsion between protons. At sufficiently large distances it would be weaker than the electrostatic repulsion between protons. This was accepted as the physical reality and this force between nucleons was called the strong force. But explaining is a weak criterion for the truth. The strong force model performs very poorly in explaining the binding energies of nuclei. See A testing of the conventional model. For an alternate explanation of what hold a nucleus together see Nucleus.

About 1949 Maria Goeppert Myer and Hans Jensen of Germany proposed a shell structure for protons and for neutrons that is identified by the number of stable isotopes and isotones. The filled shells have an unusually large number of stable nuclides. These numbers are called the nuclear magic numbers. There are also identifiable subshells. A slight modification of the Goeppert-Myer-Jensen formulation gives a set of three quantum numbers for each proton and for each neutron.

If a quantum number is included which identifies whether the nucleon is a proton or neutron then a set four quantum numbers would identify the nucleon and Pauli's Exclusion Principle would be satisfied.

In 1964 Murray Gell Mann of Cal Tech published a conjectural proposal that nucleons are composed of structures which he named quarks. Initially there were just two kinds of quarks, called Up quarks and Down quarks. As proposed by Gell Mann an Up quark has an electrostatic charge of 2/3 and the Down quark a charge of − 1/3. According to Gell Mann a proton is composed of two Up quarks and a Down quark. Its charge is thus 2(2/3)−1/3=1. The neutron is composed of two Down quarks and one Up quark. Its charge is thus 2(−1/3)+2/3=0.

Later it was found that the existence of some exotic particles could be explained by the existtence of a thrd quark. That quark was called the strangeness quark. Still later another quark was added and called the charm quark. And finally two more quarks were added and called initially truth and beauty but the physics community decided that these names were too facetious and changed their names to top and bottom.

No evidence of quarks was found in the results particle collisions. This has led to dubious explanations such as the force between quarks increasing with separation distance rather than decreasing, There are more plausible explanations such as given in A sensible model of quark confinement.