Hein's Thoughts

I walked into a store (a pizza parlor) for the first time in two months yesterday.  I wore two masks (surgical and n95), gloves, and goggles.  There were about 3 people (employees) in the store.   I spent two minutes in the store picking up the pizza, used hand sanitizer in the car, and sterilized the box in the car.  In my county there were about 20 new cases last week out of 60,000 people. Why am I so careful?  My son was on the lung transplant list and has serious lung issues.  My parents are in their 80s. The clerk at the store wore a mask.  The sign on the door said that masks were required.  I don't know if they were permitting people to dine in. If you wear a mask and do social distancing, you certainly slow down the spread of the illness.  Slowing down the spread of COVID19 prevents hospitals from becoming overwhelmed.  It also helps save lives because we are learning more and more about the virus, improving treatments, and...

I liked "Mathematical Thought from Ancient to Modern Times" by Kline. " The History and Concept of Mathematical Proof " by Krantz (formerly from Penn State!) looks interesting. " Proof: A Brief Historical Survey " looks cool. "A History of Mathematical Proof: Ancient Greece to the Computer Age " is more formal with no pictures and diagrams, but it's written for non-mathematicians. " The History of Mathematical Proof in Ancient Traditions " by Chemla is AN ENTIRE BOOK devoted to the history of proofs in many cultures. I love "proofs without words". (See e.g.  Wikipedia ,  MAA ,  Sangaku ) The aptly titled article " Aristotle and Mathematics " is more about logic and proof than it is about mathematics.

So much of our thoughts are wasted because they are not committed to writing in an understandable way.  A large part of the reason why is that it takes effort to organize our thoughts to the point where someone else can understand those thoughts.  And then there is publishing.  It takes some effort to publish our thoughts.  Some of us may fear criticism for sharing our thoughts. If I die a month from now, many of my most treasured thoughts will be lost.  I have written a lot of them down in my yellow note books, about 300 of them, but most of the thoughts were not written in a way that others would understand them.  Most of what I've written in those notebooks, even I would not be able to decipher. I love the idea of investment.  How long do you need to invest in order to live off your investments? T = 1/r ln( 1/alpha) if you save alpha dollars for every dollar you receive and you have a fixed interest rate of r times your investment.   ...