Editing Theoretical computer science (section)

== History ==
{{Main|History of computer science}}

While logical inference and mathematical proof had existed previously, in 1931 [[Kurt Gödel]] proved with his [[incompleteness theorem]] that there are fundamental limitations on what statements could be proved or disproved.

[[Information theory]] was added to the field with [[A Mathematical Theory of Communication|a 1948 mathematical theory of communication]] by [[Claude Shannon]]. In the same decade, [[Donald Hebb]] introduced a mathematical model of [[Hebbian learning|learning]] in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of [[neural network]]s and [[parallel distributed processing]] were established. In 1971, [[Stephen Cook]] and, working [[Multiple discovery|independently]], [[Leonid Levin]], proved that there exist practically relevant problems that are [[NP-complete]] – a landmark result in [[computational complexity theory]].<ref>{{cite book |doi=10.1145/800157.805047 |chapter=The complexity of theorem-proving procedures |title=Proceedings of the third annual ACM symposium on Theory of computing - STOC '71 |date=1971 |last1=Cook |first1=Stephen A. |pages=151–158 |isbn=978-1-4503-7464-4 }}</ref>

Modern theoretical computer science research is based on these basic developments, but includes many other mathematical and interdisciplinary problems that have been posed, as shown below:

{| style="border:1px solid #ddd; text-align:center;  margin: 0 auto;" cellspacing="15"
| <math> P \rightarrow Q \,</math>
| [[File:DFAexample.svg|96px]]
| [[File:Elliptic curve simple.svg|96px]]
| [[File:6n-graf.svg|96px]]
| [[File:Wang tiles.svg|96px]]
| '''P = NP''' ?
|-
| [[Mathematical logic]]
| [[Automata theory]]
| [[Number theory]]
| [[Graph theory]]
| [[Computability theory]]
| [[Computational complexity theory]]
|-
| '''GNITIRW-TERCES'''
| <math>\Gamma\vdash x: \text{Int}</math>
| [[File:Commutative diagram for morphism.svg|96px]]
| [[File:SimplexRangeSearching.svg|96px]]
| [[File:TSP Deutschland 3.png|96px]]
| [[File:Blochsphere.svg|96px]]
|-
| [[Cryptography]]
| [[Type theory]]
| [[Category theory]]
| [[Computational geometry]]
| [[Combinatorial optimization]]
| [[Quantum computer|Quantum computing theory]]
|}