The atomic hypothesis, also referred to as 'the atomic theory', basically states that all matter is made of indivisible, indestructible particles. This is a cornerstone of modern sciences. The distinguished scientist and Nobel Laureate Richard Feynman wrote, in 1963:
- "If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms--little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see there is an enormous amount of information about the world, if just a little imagination and thinking are applied." 
- "... there is a portion of every thing, i.e. of every elemental stuff, in every thing...[but] each is and was most manifestly those things of which there is most in it."
Anaxagoras, like Empedocles, did not think that matter came into being and went out of being, in other words, matter was indestructible and was changeable in form but not substance and those changes had to do with combinations of matter:
- "The Greeks are wrong to accept coming to be and perishing, for no thing comes to be, nor does it perish, but they are mixed together from things that are and they are separated apart. And so they would be correct to call coming to be being mixed together, and perishing being separated apart."
Democritus, evidently working from earlier works by Leucippus and influenced by Anaxagoras (who was still alive when Democritus tried to see him), proposed it in the 5th century BC, it was later picked up and discussed by Epicurus in the late 4th to early 3rd century BC, but it was just an idea that was never developed or really accepted. Aristotle rejected the idea since he thought it was necessarily associated with a void which he also rejected. Pierre Gassendi in the late 16th and early 17th century AD wrote criticising Aristotle and is widely acknowledge as the one who revived the idea. He described his approach to this idea in a book he published in 1649 AD. He was of the opinion that the properties of atoms depended on their shape. He also thought that they might join together and form molecules. In addition he proposed that atoms moved in a void with nothing between them. Robert Boyle and Isaac Newton were later to continue to develop the concept.
Dalton’s atomic hypothesis
John Dalton, frequently referred to as the father of modern chemistry, introduced his atomic hypothesis in 1803 following the work of Lavoisier’s quantitative measurements in the 1780s which provided the means to accurately measure chemical compounds and Proust’s Law of Constant Composition (also known as the Law of Definite Proportions) in 1799. Dalton had studied gases and noted the weight ratios of nitrogen, oxygen and carbon and proposed the Law of Simple Multiple Proportions (later confirmed by chemist Jöns Jacob Berzelius). Dalton’s hypothesis differed from earlier versions in that he was able to advance accurate weight measurements to support his hypothesis. This is very significant because he was not making a philosophical statements that atoms existed because they are required or obvious but that there was in fact real scientific evidence, that is to say, experimental evidence to provide support for the hypothesis.
Elements themselves are pure because all the atoms of an element are identical and that they have the same mass. Elements differ from each other because their atoms are different and they have different masses.
- the ultimate particles of all homogeneous bodies are perfectly alike in weight, figure, &c. In other words, every particle of water is like every other particle of water; every particle of hydrogen is like every other particle of hydrogen, &c.
Compounds on the other hand are made of different elements, are pure substances that can not be separated by phase changes and have consistent, that is to say, constant compositions with fixed ratios of elements which can in turn be weighed.
Dalton also proposed that chemical reactions of elements and compounds involve the rearrangement of combinations. 
- Richard Feynman (1963). Six Easy Pieces: Fundamentals of Physics Explained Penguin Books ISBN-10: 0140276661
- quoted in Anaxagoras of Clazomenae J J O'Connor and E F Robertson (1999) University of St. Andrews, Scotland
- quoted in Anaxagoras S. Marc Cohen (2002). University of Washington, Seattle, WA
- Democritus Ancient Greek Scientists (2001). Thessaloniki Museum of Technology; Democritus Sylvia Berryman (2004). Stanford Encyclopedia of Philosophy; John Gribbin (2002), Science, a History. Penguin Press; Macrocosmos: From Leucippus to Yukawa Hans Haubold, A. M. Mathai,(1998) Encyclopedia of Applied Physics, Vol. 23 (Page 47 - 81), 1998 WILEY-VCH Verlag GmbH, ISBN: 3-527-29476-7; Atomism S. Marc Cohen (2002). University of Washington, Seattle Washington
- He made his initial announcement on the relative weights of the atoms on October 21st, 1803, at the Manchester Literary and Philosophical Society. Dalton had evidently derived his lexicon from ancient Sanskrit works of Kanda describing discontinuous matter, the Greek philosopher Democritus who proposed water as empty space with smooth balls he called atoms gliding over each other and an idea proposed by Issac Newton that God had made matter in solid, impenetrable moveable particles.
- To give one a scope of the scale, if the atoms in an apple were magnified to the size of the apple, the apple would be magnified to the size of the earth. Richard Feynman, Robert Leighton, Matthew Sands (1963), Lectures on Physics, Vol 1, chapter one, "Atoms in Motion". Addison-Wesley Pub.Co.: Menlo Park, CA
-  excerpt from Dalton's 1808 A New System of Chemical Philosophy
- Dalton’s Atomic Theory Eden Francis, (2002) Clackamas Community College. Oregon City, OR; John Dalton John Blamire, (2002) City University, New York; On the Constitution of Bodies Chapter II and On Chemical Synthesis Chapter III John Dalton (1808) excerpts from A New System of Chemical Philosophy.