Understanding Mathematical Formalism: A Comprehensive Audio Guide 🎧

This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Mathematical_logic 00:01:52 1 Subfields and scope 00:03:28 2 History 00:04:28 2.1 Early history 00:04:59 2.2 19th century 00:06:29 2.2.1 Foundational theories 00:10:30 2.3 20th century 00:11:35 2.3.1 Set theory and paradoxes 00:14:08 2.3.2 Symbolic logic 00:16:32 2.3.3 Beginnings of the other branches 00:18:29 3 Formal logical systems 00:19:17 3.1 First-order logic 00:22:37 3.2 Other classical logics 00:25:30 3.3 Nonclassical and modal logic 00:26:41 3.4 Algebraic logic 00:27:19 4 Set theory 00:31:13 5 Model theory 00:33:10 6 Recursion theory 00:34:43 6.1 Algorithmically unsolvable problems 00:36:15 7 Proof theory and constructive mathematics 00:37:58 8 Applications 00:39:28 9 Connections with computer science 00:40:56 10 Foundations of mathematics 00:45:29 11 See also Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: - increases imagination and understanding - improves your listening skills - improves your own spoken accent - learn while on the move - reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services/invoke/uid/0000001a130b3f91 Other Wikipedia audio articles at: https://www.youtube.com/results?search_query=wikipedia+tts Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.9951108371533246 Voice name: en-US-Wavenet-C "I cannot teach anybody anything, I can only make them think." - Socrates SUMMARY ======= Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those. Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.