The Bertrand Paradox:
A question that isn’t sufficiently well-defined can result in two or more different answers that can all be correct
Is Mathematics Unreasonably Effective?
Why the argument that conventional mathematics is amazingly effective for science is completely wrong
A failure to understand:
An example of how to completely misunderstand Cantor’s Diagonal proof
Wang’s Paradox (The Sorites paradox):
If you keep removing grains of sand from a heap of sand, when does the heap stop being a heap?
What does it mean to “select a real number at random”?
A duplicitous argument:
An example of how a mathematician refuses to play fair in an argument when his claims are challenged
Man versus Machine:
Roger Penrose claims that Gödel’s incompleteness proof indicates that human brains must be using quantum processes that no machine could replicate
The Courant & Robbins Contradiction:
A contradiction in a proof that provides a demonstration of the inherent contradictions that typically result from illogical assumptions about the infinite
Turing’s Uncomputable Number:
An error in Turing’s claim that he has defined an ‘uncomputable number’
Gödel on Church’s Paradox:
A paradox that is reliant on the confusion of different levels of language
The Balls in the Urn Paradox (The Ross-Littlewood paradox):
How woolly thinking about infinity can lead to contradictions
Fake News and Fake Mathematics:
How some parts of mathematics have been fabricated without any supporting logical basis
How to tell if someone is a crackpot:
An examination of the claims of the crackpot John Gabriel
Sennimalai Kalimuthu - Crackpot or Joker?:
An examination of a claimed “proof ” by Sennimalai Kalimuthu
Curry’s Paradox (Lob’s paradox):
A paradox that relies on an inconsistent system for its creation
Must a proof be correct simply because someone claims that it has been checked by a computer program?
Why do people believe weird things?
Why do intelligent people continue to defend beliefs that have no logical basis?
Chaitin’s Omega number:
The inherent error in Chaitin’s claims about his ‘Omega number’
The Consistency of Arithmetic:
An erroneous proof of consistency by Storrs McCall
The Law of the Excluded Middle:
Is it being applied within the system or outside of the system?