Mathematical Ambiguity

This blog post is a placeholder for organizing links to interesting resources related to mathematical ambiguity discussions:

• https://en.wikipedia.org/wiki/Order_of_operations 
• https://dlmf.nist.gov/
  
• https://people.math.harvard.edu/~knill/pedagogy/ambiguity/
• https://people.math.harvard.edu/~knill/pedagogy/ambiguity/ambiguity.pdf
  
• https://scienceblogs.com/evolutionblog/2013/03/15/the-horror-of-pemdas
  
• https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html 
  

Pi calculated to 62.8 trillion decimal places

 Competence Centre for Data Analysis, Visualisation and Simulation (DAViS)

https://www.fhgr.ch/en/specialist-areas/applied-future-technologies/davis-centre/pi-challenge/#c16197

• "The challenge for this record attempt is taken up by project leader Thomas Keller and by the head of DAViS, Prof. Dr Heiko Rölke."
• "DAViS as part of the University of Applied Sciences of the Grisons is consolidating expertise in the area of high-performance computing (HPC) and HPC infrastructure for a mandate of the canton of Grisons."
•  2021-08-14: "This Saturday morning at 9:30 am, our High Performance Computer successfully completed its calculation to 62'831'853'071'750 decimal places, hence an additional 12.8 trillion decimal digits of Pi have been discovered."

Babylonians Used Applied Geometry 1,000 Years Before Pythagoras

 

• https://www.smithsonianmag.com/smart-news/ancient-tablet-shows-babylonians-used-pythagorean-geometry-1000-years-pythagoras-180978376/
• https://www.sciencealert.com/this-3-700-year-old-tablet-shows-the-oldest-known-example-of-applied-geometry 
  

How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.

•  How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer.
• https://www.quantamagazine.org/how-many-numbers-exist-infinity-proof-moves-math-closer-to-an-answer-20210715/
• Martin’s Maximum++ implies Woodin’s axiom (∗) 
• https://annals.math.princeton.edu/2021/193-3/p03 
• https://en.wikipedia.org/wiki/Continuum_hypothesis
  

The Mathematics Handbook, compiled by Alexander Spartalis

"The Mathematics Handbook", v4.1, June 2nd, 2019. 

(formerly known as the "All In One Mathematics Cheat Sheet")

Alexander's web site for the book is here:  

• http://mathscheats.weebly.com/ 

You can find the full PDF here

• https://drive.google.com/file/d/1MM2Hu5qlptkg8dNLM9QibeXHErLz73Qy/view
• Now, 640 pages 

The Antikythera Mechanism

source: https://en.wikipedia.org/wiki/Antikythera_mechanism

• https://en.wikipedia.org/wiki/Antikythera_mechanism
• https://bigthink.com/robby-berman/an-ancient-device-too-advanced-to-be-real-gives-up-its-secrets-at-last

Octonions

Physicists puzzled by strange numbers that could explain reality
https://bigthink.com/surprising-science/physics-mystery-octonions

The Peculiar Math That Could Underlie the Laws of Nature

https://www.quantamagazine.org/the-octonion-math-that-could-underpin-physics-20180720/