Mathematical Curios

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?

Random selection:

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

Kalimuthu Sennimalai - Crackpot or Joker?:

An examination of a claimed “proof ” by Kalimuthu Sennimalai

Curry’s Paradox (Lob’s paradox):

A paradox that relies on an inconsistent system for its creation

Computer Proofs:

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?