IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-64217-3_3.html
   My bibliography  Save this book chapter

Gödel’s Incompleteness Theorems

In: Introduction to Incompleteness

Author

Listed:
  • Serafim Batzoglou

    (Seer Inc.)

Abstract

Gödel’s first incompleteness theorem holds a special place in the history of mathematics. In a popular list of the “top 100” theorems of all time, it ranks 6 th $${ }^{th}$$ , following the irrationality of 2 $$\sqrt {2}$$ , Gauss’s fundamental theorem of algebra, the countability of the rationals, the Pythagorean theorem, and the prime number theorem. And for good reason: for those expecting a foundation of mathematics on a defined collection of axioms from which all theorems are derived, the result must have been as startling as the discovery of 2 $$\sqrt {2}$$ by the Pythagoreans, who believed that all numbers are rational.

Suggested Citation

  • Serafim Batzoglou, 2024. "Gödel’s Incompleteness Theorems," Springer Books, in: Introduction to Incompleteness, chapter 0, pages 35-54, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-64217-3_3
    DOI: 10.1007/978-3-031-64217-3_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-031-64217-3_3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.