[[Zermelo–Fraenkel set theory - Wikipedia]([Zermelo–Fraenkel set theory - Wikipedia]([Zermelo–Fraenkel set theory - Wikipedia](https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory))) Zermelo–Fraenkel set theory - Wikipedia] ===Mathematics -> Foundations -> Type theory=== ===Mathematics -> Foundations -> Category theory=== ===Mathematics -> Foundations -> Mathematical logic=== Mathematical logic is the study of formal logic within mathematics. [[Mathematical logic - Wikipedia](https://en.wikipedia.org/wiki/Mathematical_logic) Mathematical logic - Wikipedia] [[Mathematics - Wikipedia]([Mathematics - Wikipedia](https://en.wikipedia.org/wiki/Mathematics)#Mathematical_logic_and_set_theory) Mathematics: Mathematical logic and set theory - Wikipedia] ===Mathematics -> Foundations -> Paradoxes=== ===Mathematics -> Foundations -> Other=== ===Mathematics -> Disciplines -> Number theory=== The study of the numbers, integers and arithmetic functions. [[Mathematics - Wikipedia]([Mathematics - Wikipedia](https://en.wikipedia.org/wiki/Mathematics)#Number_theory) Mathematics: Number theory - Wikipedia] [[Number theory - Wikipedia](https://en.wikipedia.org/wiki/Number_theory) Number theory - Wikipedia] ===Mathematics -> Disciplines -> Geometry=== Geometry studies properties of space such as the distance, shape, size, and relative position of figures. [[Mathematics - Wikipedia]([Mathematics - Wikipedia](https://en.wikipedia.org/wiki/Mathematics)#Geometry) Mathematics: Geometry - Wikipedia] [[Geometry - Wikipedia](https://en.wikipedia.org/wiki/Geometry) Geometry - Wikipedia] ===Mathematics -> Disciplines -> Algebra=== Algebra is the art of manipulating equations and formulas, the study of variables and the rules for manipulating these variables in formulas. [[Mathematics - Wikipedia]([Mathematics - Wikipedia](https://en.wikipedia.org/wiki/Mathematics)#Algebra) athematics: Algebra - Wikipedia] [[Algebra - Wikipedia]([Algebra - Wikipedia](https://en.wikipedia.org/wiki/Algebra)) Algebra - Wikipedia] ===Mathematics -> Disciplines -> Calculus and analysis=== The study of the relationship of variables that depend on each other. Calculus is the mathematical study of continuous change. Analysis is advanced calculus, dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. [[Mathematics - Wikipedia](https://en.wikipedia.org/wiki/Mathematics) Mathematics - Wikipedia]#Calculus_and_analysis [[Calculus - Wikipedia](https://en.wikipedia.org/wiki/Calculus) Calculus - Wikipedia] ===Mathematics -> Disciplines -> Discrete mathematics=== The study of individual, countable mathematical objects. ===Mathematics -> Disciplines -> Statistics=== The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially probability theory. ===Mathematics -> Disciplines -> Other=== ===Science=== Science to me are mostly models that predict empirical data, making it mostly applied mathematics. Some models in psychology and sociology can act as guiding models forming future instead of predicting it instead. ===Science -> Mathematics=== Applied mathematics lives inside some mathematical foundations, classical or constructivistic. Let's use mostly classical that I mentioned already, in which most of mathematical science is done. Things in applied mathematics mostly live inside some space and time and one can study their evolution and complex interaction. ===Science -> Physics=== Physics is a field studying matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. Let's build the mathematical machinery to understand smallest fundamental particles first. Best book on physics from classical mechanics to standard model quantum field theory from mathematically rigorous perspective: [[Quantum Field Theory: A Tourist Guide for Mathematicians - G. B. Folland - Knihy Google]([Quantum Field Theory: A Tourist Guide for Mathematicians - G. B. Folland - Knihy Google](https://books.google.cz/books/about/Quantum_Field_Theory.html?id=KWMAoQEACAAJ)) Quantum Field Theory: A Tourist Guide for Mathematicians by G. B. Folland] ===Science -> Physics -> Mathematical foundations=== ===Science -> Physics -> Mathematical foundations -> Linear Algebra=== [[Linear algebra - Wikipedia]([Linear algebra - Wikipedia](https://en.wikipedia.org/wiki/Linear_algebra)) Linear algebra - Wikipedia] ===Science -> Physics -> Mathematical foundations -> Analysis=== Mathematics for the rate of change with derivatives and differential equations. [[Mathematical analysis - Wikipedia]([Mathematical analysis - Wikipedia](https://en.wikipedia.org/wiki/Mathematical_analysis)) Mathematical analysis - Wikipedia] ===Science -> Physics -> Mathematical foundations -> Symplectic geometry=== [[Quanta Magazine](https://www.quantamagazine.org/the-fight-to-fix-symplectic-geometry-20170209/) A Fight to Fix Geometry’s Foundations] Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. Symplectic geometry is a branch of differential geometry and differential topology. [[Symplectic geometry - Wikipedia](https://en.wikipedia.org/wiki/Symplectic_geometry) Symplectic geometry wiki] ===Science -> Physics -> Mathematical foundations -> Other=== ===Science -> Physics -> Classical -> Systems theory=== Systems theory studies arbitrary systems. Collection of interacting particles? Fluids? People? Interacting corporations? Architecture of a computer, or of a company? All works. Most of physics in inside this frame, with added relativity, quantum uncertainity and so on, or maybe some hyperexotic models of physics don't build on this foundation at all. [Systems science - Wikipedia]([Systems science - Wikipedia]([Systems science - Wikipedia](https://en.wikipedia.org/wiki/Systems_science))) [Systems theory - Wikipedia]([Systems theory - Wikipedia](https://en.wikipedia.org/wiki/Systems_theory)) ===Science -> Physics -> Classical -> Systems theory -> Dynamical complex continuous systems theory=== Complex systems are those having many interacting components. Dynamical systems study their behavior in time. Continuous systems are modelled by continuous time using differential equations, instead of difference equations. [Dynamical systems theory - Wikipedia]([Dynamical systems theory - Wikipedia](https://en.wikipedia.org/wiki/Dynamical_systems_theory)) ===Science -> Physics -> Classical -> Systems theory -> Other=== ===Science -> Physics -> Classical -> Classical mechanics=== ===Science -> Physics -> Classical -> Classical mechanics -> Intuitive description=== ===Science -> Physics -> Classical -> Classical mechanics -> Mathematical description=== A special case of dynamical continuous systems theory where equations of motion are constrained to be Euler–Lagrange equations of a least action principle. ===Science -> Physics -> Classical -> Classical mechanics -> Formulations=== [[Lagrangian and Hamiltonian Mechanics in Under 20 Minutes: Physics Mini Lesson - YouTube]([Lagrangian and Hamiltonian Mechanics in Under 20 Minutes: Physics Mini Lesson - YouTube]([Lagrangian and Hamiltonian Mechanics in Under 20 Minutes: Physics Mini Lesson - YouTube]([Lagrangian and Hamiltonian Mechanics in Under 20 Minutes: Physics Mini Lesson - YouTube](https://www.youtube.com/watch?v=0DHNGtsmmH8)))) Lagrangian and Hamiltonian Mechanics in Under 20 Minutes: Physics Mini Lesson] ===Science -> Physics -> Classical -> Classical mechanics -> Formulations -> Newtonian mechanics=== ===Science -> Physics -> Classical -> Classical mechanics -> Formulations -> Newtonian mechanics -> Concepts -> Newton's law of universal gravitation=== ===Science -> Physics -> Classical -> Classical mechanics -> Formulations -> Newtonian mechanics -> Subfields -> Ḱinematics=== ===Science -> Physics -> Classical -> Classical mechanics -> Formulations -> Analytical mechanics=== ===Science -> Physics -> Classical -> Classical mechanics -> Formulations -> Analytical mechanics -> Lagrangian mechanics=== ===Science -> Physics -> Classical -> Classical mechanics -> Formulations -> Analytical mechanics -> Hamiltonian mechanics=== ===Science -> Physics -> Classical -> Classical mechanics -> Subdisciplines -> Harmonic analysis=== ===Science -> Physics -> Classical -> Statistical mechanics=== [[Statistical Mechanics | Entropy and Temperature - YouTube]([Statistical Mechanics | Entropy and Temperature - YouTube](https://www.youtube.com/watch?v=8v0a2VPKTro)) Manim Statistical Mechanics | Entropy and Temperature] ===Science -> Physics -> Classical -> Statistical mechanics -> Thermodynamics=== ===Science -> Physics -> Classical -> Statistical mechanics -> Thermodynamics -> Nonequilibrium thermodynamics=== ===Science -> Physics -> Classical -> Statistical mechanics -> Ising model === ===Science -> Physics -> Classical -> Information theory=== ===Science -> Physics -> Classical -> Classical field theory=== Instead of discrete particles moving around, its a big continuum, like in electromagnetism and fluid mechanics. [Classical field theory - Wikipedia]([Classical field theory - Wikipedia]([Classical field theory - Wikipedia](https://en.wikipedia.org/wiki/Classical_field_theory))) [Field (physics) - Wikipedia](https://en.wikipedia.org/wiki/Field_(physics)) ===Science -> Physics -> Classical -> Classical field theory -> Subdisciplines -> Electromagnetism=== Electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. [Electromagnetism - Wikipedia](https://en.wikipedia.org/wiki/Electromagnetism) ===Science -> Physics -> Classical -> Classical field theory -> Subdisciplines -> Continuum mechanics=== ===Science -> Physics -> Classical -> Classical field theory -> Subdisciplines -> Continuum mechanics -> Fluid mechanics=== ===Science -> Physics -> Classical -> Classical field theory -> Subdisciplines -> Continuum mechanics -> Newtonian fluids=== ===Science -> Physics -> Classical -> Classical field theory -> Subdisciplines -> Continuum mechanics -> Non-newtonian fluids=== ===Science -> Physics -> Classical -> Other=== ===Science -> Physics -> Relativistic -> Special relativity=== Theory of the relationship between space and time. Based on just two postulates: - The laws of physics are invariant (identical) in all inertial frames of reference (that is, frames of reference with no acceleration). - The speed of light in vacuum is the same for all observers, regardless of the motion of light source or observer. ===Science -> Physics -> Relativistic -> Special relativity -> Concepts -> Time dillation=== [[Special Relativity: This Is Why You Misunderstand It - YouTube]([Special Relativity: This Is Why You Misunderstand It - YouTube](https://www.youtube.com/watch?v=ZdrZf4lQTSg)) Special Relativity: This Is Why You Misunderstand It] ===Science -> Physics -> Relativistic -> General relativity=== ===Science -> Physics -> Quantum=== ===Science -> Physics -> Quantum -> Quantum mechanics=== Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle). [Quantum mechanics - Wikipedia]([Quantum - Wikipedia](https://en.wikipedia.org/wiki/Quantum)_mechanics) [[What is the Schrödinger Equation? A basic introduction to Quantum Mechanics - YouTube]([What is the Schrödinger Equation? A basic introduction to Quantum Mechanics - YouTube]([What is the Schrödinger Equation? A basic introduction to Quantum Mechanics - YouTube]([What is the Schrödinger Equation? A basic introduction to Quantum Mechanics - YouTube]([What is the Schrödinger Equation? A basic introduction to Quantum Mechanics - YouTube]([What is the Schrödinger Equation? A basic introduction to Quantum Mechanics - YouTube]([What is the Schrödinger Equation? A basic introduction to Quantum Mechanics - YouTube](https://www.youtube.com/watch?v=2WPA1L9uJqo))))))) What is the Schrödinger Equation? A basic introduction to Quantum Mechanics] [[The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics - YouTube]([The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics - YouTube]([The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics - YouTube]([The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics - YouTube]([The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics - YouTube](https://www.youtube.com/watch?v=-Y0XL-K0jy0))))) The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics] ===Science -> Physics -> Quantum -> Quantum mechanics -> Concepts -> Schrödinger equation=== ===Science -> Physics -> Quantum -> Quantum mechanics -> Concepts -> Uncertainty principle=== ===Science -> Physics -> Quantum -> Quantum mechanics -> Concepts -> Wave particle duality=== ===Science -> Physics -> Quantum -> Quantum mechanics -> Formulations -> Categorical quantum mechanics=== ===Science -> Physics -> Unity=== ===Science -> Physics -> Unity -> Quantum statistical mechanics=== [Quantum statistical mechanics - Wikipedia]([Quantum statistical mechanics - Wikipedia]([Quantum - Wikipedia](https://en.wikipedia.org/wiki/Quantum)_statistical_mechanics)) ===Science -> Physics -> Unity -> Quantum information theory=== [Quantum information - Wikipedia]([Quantum - Wikipedia](https://en.wikipedia.org/wiki/Quantum)_information) ===Science -> Physics -> Unity -> Relativistic field theory=== A relativistic field theory is a classical field theory that complies with the basic rules of special relativity. [Relativistic Field Theory | SpringerLink](https://link.springer.com/chapter/10.1007/978-3-319-06581-6_5) ===Science -> Physics -> Unity -> Relativistic quantum mechanics=== Relativistic quantum mechanics is quantum mechanics applied with special relativity. [Relativistic quantum mechanics - Wikipedia]([Relativistic quantum mechanics - Wikipedia](https://en.wikipedia.org/wiki/Relativistic_quantum_mechanics)) ===Science -> Physics -> Unity -> Relativistic quantum mechanics -> Quantum field theory=== Quantum field theory is relativistic quantum mechanics in which elementary particles are interpreted as field quanta. Quantum field theory combines classical field theory, special relativity, and quantum mechanics together, but without gravity, which comes in general relativity that's not included. [[Quantum field theory - Wikipedia]([Quantum - Wikipedia](https://en.wikipedia.org/wiki/Quantum)_field_theory) Quantum field theory] ===Science -> Physics -> Unity -> Relativistic quantum mechanics -> Quantum field theory -> Gauge theory=== Gauge theories are general clas of quantum field theories used for the description of elementary particles and their interactions using group theory. A type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations according to certain smooth families of operations (Lie groups). Formally, the Lagrangian is invariant. In a gauge theory there is a group of transformations of the field variables (gauge transformations) that leaves the basic physics of the quantum field unchanged. This condition, called gauge invariance, gives the theory a certain symmetry, which governs its equations. In short, the structure of the group of gauge transformations in a particular gauge theory entails general restrictions on the way in which the field described by that theory can interact with other fields and elementary particles. [[Gauge theories - Scholarpedia](http://www.scholarpedia.org/article/Gauge_theories) Gauge theories] [[Gauge theory - Wikipedia](https://en.wikipedia.org/wiki/Gauge_theory) Gauge theory Wiki] ===Science -> Physics -> Unity -> Relativistic quantum mechanics -> Quantum field theory -> Gauge theory -> Standard model=== The current most empirically proven model is standard model, which is a type of quantum field theory with all the measured data about particles added. ===Science -> Physics -> Unity -> Relativistic quantum mechanics -> Quantum field theory -> Axiomatic Quantum field theory=== ===Science -> Physics -> Unity -> Relativistic quantum mechanics -> Quantum field theory -> Quantum field theory for Mathematicians=== Best book on physics from classical mechanics to standard model quantum field theory from mathematically rigorous perspective: [[Quantum Field Theory: A Tourist Guide for Mathematicians - G. B. Folland - Knihy Google]([Quantum Field Theory: A Tourist Guide for Mathematicians - G. B. Folland - Knihy Google](https://books.google.cz/books/about/Quantum_Field_Theory.html?id=KWMAoQEACAAJ)) Quantum Field Theory: A Tourist Guide for Mathematicians by G. B. Folland] Complex mathematics of quantum field theory: [[Quantum Field Theory for Mathematicians - Robin Ticciati - Knihy Google](https://books.google.cz/books/about/Quantum_Field_Theory_for_Mathematicians.html?id=l-ruCWBpK8AC) Quantum Field Theory for Mathematicians by Robin Ticciati] ===Science -> Physics -> Unity Divide unity into quantum gravity solutions, unifying fundamental forces, classical and GR emerging from QM (quantum darwinism, Sean Carrol), physics concepts penetrating all subdisciplines: no hiding theorem, Black hole inf paradox and solutions to it ===Science -> Physics -> Unity -> Quantum darwinism=== ===Science -> Physics -> Unity -> Spacetime from entaglement by Sean Carrol=== ===Science -> Physics -> Unity -> Loop quantum gravity=== ===Science -> Physics -> Unity -> Supersymmetry=== ===Science -> Physics -> Unity -> String theory=== ===Science -> Physics -> Unity -> Holographic principle, spacetime as error correcting code from entaglement=== ===Science -> Physics -> Unity -> Asymptotic gravity=== ===Science -> Physics -> Unity -> Woflram physics project: Hypergraphs === ===Science -> Physics -> Unity -> Cellular Automaton Interpretation of Quantum Mechanics=== ===Science -> Physics -> Unity -> Amplituhedron === ===Science -> Physics -> Unity -> Other=== ===Science -> Physics -> Fields -> Cosmology=== [Cosmology - Wikipedia](https://en.wikipedia.org/wiki/Cosmology) [Cosmology - Wikipedia](https://en.wikipedia.org/wiki/Cosmology)#Historical_cosmologies [Physical cosmology - Wikipedia](https://en.wikipedia.org/wiki/Physical_cosmology) ===Science -> Physics -> Fields -> Cosmology -> Astrophysics=== ===Science -> Emergence=== General math of emergence of higher scales and other fields from physics. [Emergence - Wikipedia](https://en.wikipedia.org/wiki/Emergence) [Emergence - Wikipedia](https://en.wikipedia.org/wiki/Emergence)#In_science ===Science -> Emergence -> Effective Field Theory=== ===Science -> Emergence -> Renormalization Group=== ===Science -> Emergence -> Pointcare Map=== ===Science -> Emergence -> Petrubation theory=== ===Science -> Systems science=== ===Science -> Systems science -> Systems theory=== ===Science -> Systems science -> Dynamical systems theory=== ===Science -> Systems science -> Nonlinear systems theory=== ===Science -> Systems science -> Complex systems theory=== ===Science -> Systems science -> Chaos theory=== ===Science -> Systems science -> Cybernetics=== ===Science -> Systems science -> Multi agent systems theory=== [Multi-agent system - Wikipedia](https://en.wikipedia.org/wiki/Multi-agent_system) ===Science -> Systems science -> Network theory=== ===Science -> Systems science -> Game theory===