Chemistry is fun. Too hard for precise physics (pre quantum computing, see also quantum chemistry), but not too hard for some maths like social sciences.

And it underpins biology.

Theory that atoms exist, i.e. matter is not continuous.

Much before atoms were thought to be "experimentally real", chemists from the 19th century already used "conceptual atoms" as units for the proportions observed in macroscopic chemical reactions, e.g. $2H_2+O_2\leftrightarrow H_{2}O$. The thing is, there was still the possibility that those proportions were made up of something continuous that for some reason could only combine in the given proportions, so the atoms could only be strictly consider calculatory devices pending further evidence.

Subtle is the Lord by Abraham Pais (1982) chapter 5 "The reality of molecules" has some good mentions. Notably, physicists generally came to believe in atoms earlier than chemists, because the phenomena they were most interested in, e.g. pressure in the ideal gas law, and then Maxwell-Boltzmann statistics just scream atoms more loudly than chemical reactions, as they saw that these phenomena could be explained to some degree by traditional mechanics of little balls.

Confusion around the probabilistic nature of the second law of thermodynamics was also used as a physical counterargument by some. Pais mentions that Wilhelm Ostwald notably argued that the time reversibility of classical mechanics + the second law being a fundamental law of physics (and not just probabilistic, which is the correct hypothesis as we now understand) must imply that atoms are not classic billiard balls, otherwise the second law could be broken.

Pais also mentions that a big "chemical" breakthrough was isomers suggest that atoms exist.

Very direct evidence evidence:

Less direct evidence:

Subtle is the Lord by Abraham Pais (1982) page 40 mentions several methods that Einstein used to "prove" that atoms were real. Perhaps the greatest argument of all is that several unrelated methods give the same estimates of atom size/mass:

Subtle is the Lord by Abraham Pais (1982) mentions that this has a good summary of the atomic theory evidence that was present at the time, and which had become basically indisputable at or soon after that date.

On Wikimedia Commons since it is now public domain in most countries: commons.wikimedia.org/w/index.php?title=File:Perrin,_Jean_-_Les_Atomes,_F%C3%A9lix_Alcan,_1913.djvu

An English translation from 1916 by English chemist Dalziel Llewellyn Hammick on the Internet Archive, also on the public domain: archive.org/details/atoms00hammgoog

Subtle is the Lord by Abraham Pais (1982) page 85:so it is quite cool to see that organic chemistry is one of the things that pushed atomic theory forward. Because when you start to observe that isomers has different characteristics, despite identical proportions of atoms, this is really hard to explain without talking about the relative positions of the atoms within molecules!

TODO: is there anything even more precise that points to atoms in stereoisomers besides just the "two isomers with different properties" thing?

Was the first model to explain the Balmer series, notably linking atomic spectra to the Planck constant and therefore to other initial quantum mechanical observations.

This was one of the first major models that just said:

It still treats electrons as little points spinning around the nucleus, but it makes the non-classical postulate that only certain angular momentums (and therefore energies) are allowed.

Bibliography:

Bagic jump between orbitals in the Bohr model. Analogous to the later wave function collapse in the Schrödinger equation.

Causality and quantum jumps are incompatible.

Refinement of the Bohr model that starts to take quantum angular momentum into account in order to explain missing lines that would have been otherwise observed TODO specific example of such line.

They are not observe because they would violate the conservation of angular momentum.

Introduces the azimuthal quantum number and magnetic quantum number.

TODO confirm year and paper, Wikipedia points to: zenodo.org/record/1424309#.yotqe3xmjhe

This technique is crazy! It allows to both:You actually see discrete peaks at different minute counts on the other end.

It is based on how much the gas interacts with the column.

Detection is usually done burning the sample to ionize it when it comes out, and then you measure the current produced.

The procedure remind you a bit of gel electrophoresis, except that it is in gaseous phase.

The name makes absolutely no sense in modern terms, as nor colors nor light are used directly in the measurements. It is purely historical.

Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!

The private key is made of two randomly generated prime numbers: $p$ and $q$. How such large primes are found: how large primes are found for RSA.

The public key is made of:

Given a plaintext message m, the encrypted ciphertext version is:This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.

The inverse operation of finding the private m from the public c, e and $n$ is however believed to be a hard problem without knowing the factors of n.

However, if we know the private p and q, we can solve the problem. As follows.

First we calculate the modular multiplicative inverse. TODO continue.

Bibliography:

TODO why it is optimal: physics.stackexchange.com/questions/149214/why-is-the-carnot-engine-the-most-efficient