Reminders - SOFIs, exam a week from Tuesday in Milne 105 - bring computers.  

"On the final, are we allowed cover topics that we addressed in our papers?"  Yes, but try to avoid merely summarising your paper.  I expect your paper will be more narrow than any questions on the exam - if some examples are from your paper, incude some that are not.  


Thank you all for this semester.  Thank you especially to the over a third of the class that received full credit for reading reactions.  I hope you've each learned at least someting along the way that you're glad to know.  And I am most grateful for all the kind messages included in these reading reactions.  I deeply believe we've done something exceptional here and I'm very pleased to see some resonance from you.  I faught hard to teach this class, and I'm glad I did, and I'm glad that some of you are glad I did.  I presume sometime I will again, but I don't know when that will be.  Whenever it is, no time will be as special as the first. 


Quick Answers §11.4.3-end

Rejewski's codebreaking work was naturally secret, so wasn't published.   Engima merely made codes. 

"I did my 348 project/presentation on CAPTCHAs. Alan Turing's "Turing Test" is a major part of breaking CAPTCHAs. With his "Bombe" machine for engima decryption he broke the U-Boat Enigma, essentially saving the battle of the Atlantic. http://www.turing.org.uk/turing/ "

"If I'm remembering correctly, Turing has a tragic story, doesn't he?"  Yes.  As you may notice, I'm trying to stick to the mathematics.  Should be easy to find lots of details about the other side - see end here. 

How do you pronounce Einsatzgruppen?

Goldbach's conjecture remains unproven.

The *only* place on-line I found a result for "Tauberian Integral" is referencing back to our book.  I guess it's not so famous. 

"is Admiral Isoroku Yamamoto a Japenese citizen?  When Suzuki says he was the architect of Pearl Harbor, does he mean he designed its layout and structures or he was in charge of the Japanese raid on it?"  Yes.  The latter.  

Black Mtn College (where Dehn taught) did not award degrees, or have grades, or really have formal courses.  It was very open and informal, but also apparently quite successful for its brief (24 year) history.  Here's some history.  

"Is it common for mathematicians to name their books "On ____" ? For example, "On Spirals" and and Turing's "On Compatible Numbers" ?"  Yes, in fact, it is quite.  The image for the new PRISM shirts is from _On Knots_. 

Strangely many people still want this not to be mathematics history and to be current events.  It's just not.  I say one last time - the ending was inevitable.  Chapter 11 was nearly impossible for Suzuki to write, and I think with my additions, we've done some to learning about 20th century mathematics, but it's immensely big and difficult to do.  It's almost as if you don't believe when I try to tell you how much is actually out there.  There is a vast amount of mathematics done in the late 20th century.  No, more than that. 

"It really feels nice to finally finish an entire book for a math course.  In other classes it always seems like we were skipping various sections and often times entire chapters, and I don't believe I've ever used a math textbook from cover to cover like this before."  -- I totally agree.  We didn't skip a single word (at least I didn't and you were encouraged to not).  Congratulations. 

"I learned a lot in this course, and can't believe we only got up to about 1950!"  Thank you for the first part.  For the second (hm, maybe this means "there's so much even without the massive amount after 1950", in any case) - let's compare - at Fredonia - Archimedes, me before - Galois?  I tell you, it is unprecedented and big deal that we got as far as we did.  A BIG DEAL.  Here's another perspective - before this I have taken 2 history classes (at Cornell) co-taught two (at Indiana University) and taught two (at UNLV).  And we have *never* gone past 1850 in any of them.  This last 100 years we've done has not been easy for Suzuki or me, and we've only given you a glimpse, but we've tried hard to do so.  For all of you who want more recent, here's a place to start.  You can work your way backwards from there using the links on the bottom.  Notice the vast numbers.  Also notice that there's unlikely to be a coherent story to this.  Especially notice the numbers for 1900-1904 and the like.  (Later ones aren't as there because they, similarly, recognise that this isn't history at this point).  Finally on this point - how many of you attended Aaron Luttman's talk about mathematics in your lifetime? 

One can pursue a course or degree program of financial mathematics.  Our actuary experts know more about this. 

An interesting epilogue question - does Suzuki plan to write a sequel?  I would say surely not. 

This book is copyright 2009, about as new as it gets.  There's nothing more modern out there like it.  There's a book that goes more in depth up to the time of Euler - by Calinger - in the library. 

NSA definitely still exists - you may definitely go seek employment from them (and I have many friends who work there).  I have spoken of them before, and they definitely do employ more mathematicians than anyone else in the world. 


Past: 

Math. Tables Project - Gertrude Blanch - large numbers of human computers

Fractals are objects with non-integer dimensions.  We saw three of them - Cantor set, Sierpinski triangle, and Menger sponge.

The links about Hilbert's problems from the day I was gone include which are still unsolved.