Difference between revisions of "Session:Faith in mathematics (Wondrous Mathematics)"

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{{Session
 
{{Session
 
|Is for kids=No
 
|Is for kids=No
|Has description=Since Gödel's celebrated work we know: The rules of mathematics are incomplete. There are true statements for which we have proof that they don't have a proof and there are statements for which we can arbitrarily decide whether they are true or not.
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|Has description=Since Gödel's celebrated work we know: The rules of mathematics are incomplete. There are true statements for which we have proof that they don't have a proof and there are statements for which we can arbitrarily decide whether they are true or not. Learn more about this curious state of affairs in the session!
 
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This talk will give a gentle introduction to one of the cornerstone insights of mathematical logic: Gödel's unsettling incompleteness theorem, which states:
 
This talk will give a gentle introduction to one of the cornerstone insights of mathematical logic: Gödel's unsettling incompleteness theorem, which states:
  
1. There are statements which we know are true but for which we have proof that they will never have proof.
+
# There are statements which we know are true but for which we have proof that they will never have proof.
 
+
# There are statements for which we can arbitrarily decide whether they should be true or not.
2. There are statements for which we can arbitrarily decide whether they should be true or not.
 
  
 
These results wouldn't be surprising if they referred to statements about the real world. But they refer to purely mathematical statements, which are commonly thought to be genuinely objective. In the talk we'll learn that the naive understanding of logic as taught in schools is not tenable: There is a (well-understood) place for faith in mathematics.
 
These results wouldn't be surprising if they referred to statements about the real world. But they refer to purely mathematical statements, which are commonly thought to be genuinely objective. In the talk we'll learn that the naive understanding of logic as taught in schools is not tenable: There is a (well-understood) place for faith in mathematics.
  
 
The talk is aimed at people who enjoy mathematical thinking, but absolutely no prerequisites in formal logic are needed.
 
The talk is aimed at people who enjoy mathematical thinking, but absolutely no prerequisites in formal logic are needed.
 +
 +
PS: True statements which are not provable – isn't this a paradox? How do we know that those statements are true if not by a proof? The talk will demystify this apparent paradox!
 +
 +
Questions are very much welcome! Drop by at the Curry Club Assembly (in the main hall where most of the assemblies are located, near Gate 2.3 and the virtual reality booth).
 +
 +
* '''[https://rawgit.com/iblech/mathezirkel-kurs/master/superturingmaschinen/faith-in-mathematics.pdf Slides]'''
 +
* [http://math.andrej.com/2008/02/02/the-hydra-game/ Hercula vs. Hydra]
 +
* [https://en.wikipedia.org/wiki/Busy_beaver The Busy Beaver function]
 +
* [https://www.youtube.com/watch?v=sUqwFbbwHQo Talk about super Turing machines] (in German)
 +
* [https://en.wikipedia.org/wiki/Chaitin%27s_constant Chaitin's constant]
 +
* [https://en.wikipedia.org/wiki/List_of_large_cardinal_properties List of large cardinal axioms]

Latest revision as of 19:23, 29 December 2017

Description Since Gödel's celebrated work we know: The rules of mathematics are incomplete. There are true statements for which we have proof that they don't have a proof and there are statements for which we can arbitrarily decide whether they are true or not. Learn more about this curious state of affairs in the session!
Website(s)
Type Talk
Kids session No
Keyword(s) art
Processing assembly Assembly:Curry Club Augsburg
Person organizing User:IngoBlechschmidt
Language en - English
en - English
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Starts at 2017/12/29 11:30
Ends at 2017/12/29 12:30
Duration 60 minutes
Location Room:Lecture room 12

This talk will give a gentle introduction to one of the cornerstone insights of mathematical logic: Gödel's unsettling incompleteness theorem, which states:

  1. There are statements which we know are true but for which we have proof that they will never have proof.
  2. There are statements for which we can arbitrarily decide whether they should be true or not.

These results wouldn't be surprising if they referred to statements about the real world. But they refer to purely mathematical statements, which are commonly thought to be genuinely objective. In the talk we'll learn that the naive understanding of logic as taught in schools is not tenable: There is a (well-understood) place for faith in mathematics.

The talk is aimed at people who enjoy mathematical thinking, but absolutely no prerequisites in formal logic are needed.

PS: True statements which are not provable – isn't this a paradox? How do we know that those statements are true if not by a proof? The talk will demystify this apparent paradox!

Questions are very much welcome! Drop by at the Curry Club Assembly (in the main hall where most of the assemblies are located, near Gate 2.3 and the virtual reality booth).