This post is about two popular-mathematics books the I recently read:

### MY BRAIN IS OPEN: The Mathematical Journeys of Paul Erdős / Bruce Schechter

On one occasion, Erdős met a mathematician and asked him where he was from. “Vancouver,” the mathematician replied. “Oh, then you must know my good friend Elliot Mendelson”, Erdős said. The reply was “I AM your good friend Elliot Mendelson.”

Several years ago I read another biography of Erdős by Paul Hoffman, which was nice, though focused mainly on Erdős’s eccentricities. I think that Schechter’s biography would appeal more to mathematicians, since it consists of a lower dose of eccentricities and of a higher dose of details about the mathematical world. For example, it was very interesting to read about how a Hungarian mathematics journal for high school students helped in the nurturing of many great mathematicians, and about the events that led to the elementary proof for the prime number theorem by Selberg and Erdős. I definitely recommend this book.

For those who are looking for an even lower dose of eccentricities and more details about the mathematical world, I recommend the piece “In and Out of Hungary, Paul Erdös, His Friends, and Times” by László Babai. It can be found in volume 2 of Combinatorics, Paul Erdös is eighty, and it contains many details about the Hungarian mathematical world (and about 20-th century Hungarian history in general).

### Mathematical Cranks / Underwood Dudley

Represent heaven, the home of God, as a vector space of infinite dimension over some field known to god but unknown to us, in which the activities of God are quantifiable. Lengths will be measured (Revelation chapter 21 verse 15) in the usual way, as the square roots of the inner self-products of vectors (assuming heaven to be euclidean).

According to Wikipedia, a “Crank” is a pejorative term used for a person who holds an unshakable belief that most of his or her contemporaries consider to be false… The term crank is often applied to persons who contradict rigorously proven mathematical theorems, such as the impossibility of squaring the circle by ruler and compass. In Tel Aviv University we used to have an interesting crank about three years ago. Almost every day he would arrive early in the morning to the mathematics/computer science building and stay until the early evening. He would randomly approach people, ask them if they are computer science students, and then tell them that he had proved that P=NP. After a couple of minutes of conversation, one would reveal that his knowledge in computer science is rather limited and he mainly repeats several phrases over and over (though some of the first year students took him more seriously). He stated that he solved the problem by finding an algorithm for the “monkey embedding” problem. When asked if he is going to claim the million dollar millennium award for the problem, he would answer that first he is filing for a lawsuit against Tel Aviv university for teaching false material. Oh, and he would also constantly ask if you know where Noga Alon is…

Underwood Dudley’s book describes a variety of such stories, many of which I found interesting. In addition to the usual circle squarers and angle triserctors, you can find in the book the above prayer, an explanation of how the government uses linear programming to control the people, and more. The last couple of decades introduced various new types of crankery due to the internet (such as the wonderful Professor Edgar Escultura, which have led to many fascinating debates). Thus, it is unfortunate that the book was written in the early 90’s, which already makes it somewhat outdated.