Browse Definitions :
Definition

Incompleteness Theorem

The Incompleteness Theorem is a pair of logical proofs that revolutionized mathematics. The first result was published by Kurt Gödel (1906-1978) in 1931 when he was 24 years old.

The First Incompleteness Theorem states that any contradiction-free rendition of number theory (a branch of mathematics dealing with the nature and behavior of numbers and number systems) contains propositions that cannot be proven either true or false on the basis of its own postulates. The Second Incompleteness Theorem states that if a theory of numbers is contradiction-free, then this fact cannot be proven with common reasoning methods.

Some mathematicians found Gödel's proofs disturbing when they were published. Today, serious students of mathematical logic find them fascinating. Some people have seized upon Gödel's results and attempted to apply them to nature in general, to social science, and even to theology. Many of these extensions of Gödel's results are inappropriate; a few are, by scientific standards, ridiculous.

Kurt Gödel was born in the Czech Republic and grew up in Austria (which was the Austro-Hungarian Empire in Gödel's early childhood). His primary language was German. Although he is most famous for his contribution to mathematical logic, he also did much work in set theory . He was a friend of Albert Einstein during the time they were both at the Institute for Advanced Study at Princeton University

This was last updated in September 2005

Continue Reading About Incompleteness Theorem

Start the conversation

Send me notifications when other members comment.

Please create a username to comment.

-ADS BY GOOGLE

File Extensions and File Formats

SearchCompliance

  • PCI DSS (Payment Card Industry Data Security Standard)

    The Payment Card Industry Data Security Standard (PCI DSS) is a widely accepted set of policies and procedures intended to ...

  • risk management

    Risk management is the process of identifying, assessing and controlling threats to an organization's capital and earnings.

  • compliance framework

    A compliance framework is a structured set of guidelines that details an organization's processes for maintaining accordance with...

SearchSecurity

  • Trojan horse (computing)

    In computing, a Trojan horse is a program downloaded and installed on a computer that appears harmless, but is, in fact, ...

  • identity theft

    Identity theft, also known as identity fraud, is a crime in which an imposter obtains key pieces of personally identifiable ...

  • DNS over HTTPS (DoH)

    DNS over HTTPS (DoH) is a relatively new protocol that encrypts domain name system traffic by passing DNS queries through a ...

SearchHealthIT

  • telemedicine (telehealth)

    Telemedicine is the remote delivery of healthcare services, such as health assessments or consultations, over the ...

  • Project Nightingale

    Project Nightingale is a controversial partnership between Google and Ascension, the second largest health system in the United ...

  • medical practice management (MPM) software

    Medical practice management (MPM) software is a collection of computerized services used by healthcare professionals and ...

SearchDisasterRecovery

SearchStorage

  • M.2 SSD

    An M.2 SSD is a solid-state drive (SSD) that conforms to a computer industry specification and is used in internally mounted ...

  • kilobyte (KB or Kbyte)

    A kilobyte (KB or Kbyte) is a unit of measurement for computer memory or data storage used by mathematics and computer science ...

  • virtual memory

    Virtual memory is a memory management capability of an operating system (OS) that uses hardware and software to allow a computer ...

Close