390 Quick Answers 29 April


All have draft feedback now, and a more updated current average.  I have included all reactions up to today (there are only 2 left), and dropped a zero for those who have one.  I have _not_ made any drops for those without zeroes, because I don't know if they will be the lowest. 

Think of exam topics.  Reminder:  look back at the questions on the last exam for creative ideas for the final.  Reminder:  you need 2x6 or 3x4 for _both_ post 1600 and across all history.  That is 4, 5, or 6 questions. 

For the reactions due by Sunday, you are also writing 5 course reactions (in the place of reading reactions, because you will have *finished the book!* by then).  These are reactions to what you learned in the course.  Big picture thoughts on history of mathematics.  Maybe large takeaways.  

As one of your lecture reactions for either day (better for the first one) you may make a request for what you want me to talk about on Monday.  I’m not promising that I can pull together anything, but I’ll try what I can.  It will be an interesting day, surely.  

And, if anyone wants to email reactions after Monday … I promise to be happy for the feedback, and I will reply and respond for as long as you like.  Truth:  I enjoy reading your writing, and I will miss it. 

Our final is 3:30-6p here 2 weeks from now.  It will be a very familiar day and time.  I have fixed the software so that it will be impossible to submit past 6p.  Know that now. 

Reminder to all:  we’re in the 20th century.  Nothing that is being discussed now is obvious.  One of the big themes this time is trying understand the foundations deeply.  Each time the answer is “it’s more complicated than you expect.” 

More individual than group comments this time, should serve well for catching up the bit that we're behind. 


Lecture Reactions

What does it mean to be a model for hyperbolic geometry?  Not as much of a physical object that is touchable (although those models are great pedagogically), but a mathematically described object.  We know that hyperbolic geometry is consistent because it applies to the hyperbolic plane which can be described mathematically.  Non-Euclidean geometry proves that the fifth postulate is independent of the others.  It does not disprove anything. 

The 4-colour theorem was first proven in 1976 by Appel and Haken.  It has been reproven a few times since then by other computers.  There is no printed proof. 

Perelman declined all notoriety from his discoveries and has since been mostly a recluse.   "I'm not interested in money or fame, I don't want to be on display like an animal in a zoo. I'm not a hero of mathematics. I'm not even that successful; that is why I don't want to have everybody looking at me.”



Reading Reactions

The size of the natural numbers is denoted by Aleph_0.  I will write this.  This is not the symbol for the cardinality of an arbitrary set, but it is the particular cardinality of the naturals.  The question of the continuum hypothesis is if there is a set of size larger than the naturals and smaller than the reals.  The answer is “could be” - both ways are consistent with mathematics. 

We do still have international mathematics olympiads.