Mathematical logic | Mathematical proofs | Mathematical terminology
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures. The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language. (Wikipedia).
Advice on learning mathematical proofs -- How to do Mathematical Proofs (PART 10)
Advice on learning mathematical proofs -- This is the final video on a series of videos on: How to do mathematical proofs. The course is structured in such a way to make the transition from applied-style problems in mathematics (sometimes referred to as engineering mathematics) to pure mat
From playlist How to do Mathematical Proofs
Introduction to Direct Proofs: If n is even, then n squared is even
This video introduces the mathematical proof method of direct proof provides an example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Mathematical Notations -- How to do mathematical proofs (PART 2)
This video contains the preliminary mathematical notation that will be used in the course. This is preliminary video (part 0) on a series of videos: How to do mathematical proofs. The course is structured in such a way to make the transition from applied-style problems in mathematics (som
From playlist How to do Mathematical Proofs
Examples of Proof by Contradiction -- How to do Mathematical Proofs (PART 7)
This is the fifth video on a series of videos on: How to do mathematical proofs. The course is structured in such a way to make the transition from applied-style problems in mathematics (sometimes referred to as engineering mathematics) to pure mathematics much smoother. The course will
From playlist How to do Mathematical Proofs
Introduction to Common Mathematical Proof Methods
This video introduces the common methods of mathematical proofs and provides a basic example of a direct proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
How to do mathematical proofs -- Introduction to Mathematical Proofs (PART 1)
This is the introductory video on a series of videos: How to do mathematical proofs. The course is structured in such a way to make the transition from applied-style problems in mathematics (sometimes referred to as engineering mathematics) to pure mathematics much smoother. The course w
From playlist How to do Mathematical Proofs
Geometry: Ch 5 - Proofs in Geometry (5 of 58) How to Proof Proofs
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is and how to proof proofs in geometry. Next video in this series can be seen at: https://youtu.be/xuWliQ6CHpw
From playlist GEOMETRY 5 - PROOFS IN GEOMETRY
Basic Methods of Proof -- How to do mathematical proofs (PART 5)
This is the third video on a series of videos on: How to do mathematical proofs. The course is structured in such a way to make the transition from applied-style problems in mathematics (sometimes referred to as engineering mathematics) to pure mathematics much smoother. In this video, w
From playlist How to do Mathematical Proofs
Learning to write an algebraic proof
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Talkrunde: Formalisierung der Mathematik - Wann führen Computer die Beweise?
Im Rahmen der 5. Bonner Mathenacht am 29.04.2022,, organisiert vom Hausdorff Center for Mathematics, fand eine Talkrunde zum Thema "Formalisierung der Mathematik - Wann führen Computer die Beweise?" statt. Teilnehmer*innen waren: Prof. Dr. Erika Abraham (RWTH Aachen), Prof. Dr. Peter Koep
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8ECM Invited Lecture: Andrej Bauer
From playlist 8ECM Invited Lectures
Patrick Massot - Why Explain Mathematics to Computers?
A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk, I'll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be us
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Math Talk! Dr. Andrej Bauer on proof assistants, constructive mathematics, philosophy, and more.
In this wonderful discussion with Dr. Andrej Bauer we discuss a whole host of topics centering around constructive mathematics, and proof assistants. Support Ukraine through Shtab Dobra: Instagram: https://www.instagram.com/shtab.dobra/ Facebook: https://www.facebook.com/shtab.dobra PayPa
From playlist Math Talk!
A conversation between Mario Carneiro, Norman Megill and Stephen Wolfram
Stephen Wolfram plays the role of Salonnière in this new, on-going series of intellectual explorations with special guests. Watch all of the conversations here: https://wolfr.am/youtube-sw-conversations Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this
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Séminaire Bourbaki - 21/06/2014 - 3/4 - Thomas C. HALES
Developments in formal proofs A for mal proof is a proof that can be read and verified by computer, directly from the fundamental rules of logic and the foundational axioms of mathematics. The technology behind for mal proofs has been under development for decades and grew out of efforts i
From playlist Bourbaki - 21 juin 2014
IMS Public Lecture - Can Every Mathematical Problem Be Solved?
Menachem Magidor, The Hebrew University of Jerusalem, Israel
From playlist Public Lectures
In this video I talk about mathematics and proof writing. I start by answering a question I received from a viewer. He wants to know how a person knows that a proof is correct. I also discuss a book titled Foundations of Higher Mathematics. It was written by Fletcher and Patty. Do you have
From playlist Inspiration and Advice
How to write an algebraic proof
👉 Learn how to write an algebraic proof. Algebraic proofs are used to help students understand how to write formal proofs where we have a statement and a reason. In the case of an algebraic proof the statement will be the operations used to solve an algebraic equation and the reason will
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Andrej Bauer - Formalizing invisible mathematics - IPAM at UCLA
Recorded 13 February 2023. Andrej Bauer of the University of Ljubljana presents "Formalizing invisible mathematics" at IPAM's Machine Assisted Proofs Workshop. Abstract: It has often been said that all of mathematics can in principle be formalized in a suitably chosen foundation, such as f
From playlist 2023 Machine Assisted Proofs Workshop