Monday Morning Math: Pythagoras

This week’s mathematician is someone you have probably heard about, although it turns out very little is known for certain. 

The mathematician is Pythagoras.  

From Thomas Stanley, (1655), The history of philosophy: containing the lives, opinions, actions and Discourses of the Philosophers of every Sect, illustrated with effigies of divers of them.

Pythagoras was probably born in Greece, on the island of Samos, over 2500 years ago (570 BCE, plus or minus a few decades).  His mother was from that island, and his father Mnesarchus was a merchant.  Pythagoras would travel with him sometimes when he was a child, and when he was an adult he studied mathematics with Thales, another now-famous mathematician.   

After many years (decades) of study, Pythagoras formed a group known as the Pythagoreans, who followed a strict vegan diet and believed that everything was essentially a number.  There was an inner circle of mathematicians and an outer circle, and there is some indication that the groups were equally welcoming to women and men. It is not possible to distinguish who proved any one result (because secrecy was the name of the game rather than publishing), but there were important results from this group related to music and geometry.  

Two of the most significant results attributed to Pythagoras are the Pythagorean Theorem (written in geometric terms that a square on the hypotenuse of a right triangle has the same area as the sum of squares on each of the two legs) and that the square root of 2 is irrational (written in geometric terms that the side and the diagonal of a square are incommensurable, meaning there’s no teeny tiny amount that fits into both an integer number of times.  There are stories that someone figured this out and was killed, either for figuring this out or for telling people outside the Pythagoreans, but like the rest of what I’ve written this was a story – everything we supposedly know about Pythagoras comes from reports well after his death, so at best this is educated guesswork.

Etching on the wall of Peckham Hall, our math and science building. Not seen is the QED in the lower right corner, as it was also in darkness when I took the photo just now

Finally, the video below, from BBC learning, is under 5 minutes and fun to watch, though it does start off with an excited “Pythagoras!” that will get the attention of anyone around you.

Other sources:

• https://www.famousscientists.org/pythagoras/
• https://mathshistory.st-andrews.ac.uk/Biographies/Pythagoras/

Monday Morning Math: 24

Instead of a mathematician today, we’ll look at the number 24.  (Thanks to Kevin Laley for the suggestion to revisit  Adam Spencer’s Book of Numbers: A bizarre and hilarious journey from 1 to 100!  Wolfram Alpha was also a nice resource.)

• 24 =4! 
• 24 can be written as , which is the same thing as  and also 
• 24 is the smallest number that can be written as a sum of 2 primes in three different ways.  (Can you find them?)
• It is possible to draw a regular icositetragon (that’s a 24-gon and yes I had to look it up) using a straightedge and compass.  I don’t think it would be too hard, either – I’d start with a regular hexagon, which you can draw using equilateral triangles, and which happens to be part of the homework assignment for the Geometry students this past weekend.
• There are 24 hours in a day.  This apparently comes to the United States from a path starting with Egypt (via Babylon, where the hour was then divided into 60 minutes) although China also had 24 hours in a day. 
• There are 24 letters in the Greek alphabet, alpha to omega.  Omicron is the 15th letter, in case you were wondering.
• Pure gold is 24 karat.   If you want to make fancy desserts like on The Great British Baking Show then you want  your gold to be 22-24 karats.

Monday Morning Math: Elbert Frank Cox

Our Monday morning mathematician is Elbert Frank Cox, the first African-American to receive a PhD in Mathematics.

Elbert Frank Cox, yearbook picture from Indiana University

Elbert Frank Cox was born on December 5, 1895, in Evansville, Indiana.  He was adept in music as well as mathematics and was offered a scholarship to the Prague Conservatory of Music to play violin, but he chose to attend Indiana University to study mathematics; he earned an A in every math class.  He served in France during World War I, then returned to the US and taught (following in the footsteps of his own father, who was teacher and principal of the Third Avenue School).

Cox joined the graduate program at Cornell University, and in 1925 earned his PhD in mathematics: his thesis was entitled “The Polynomial Solutions of the Difference Equation aF(x+1) + bF(x) = Phi(x)”  He taught at West Virginia State College for four years before taking a position at Howard University.  Talitha Washington writes, “In those days many Black scholars migrated to Howard University. In 1929 Cox joined the faculty, and by 1943, Howard University employed five of the eight Black math Ph.D.’s.”  

During the thirty-seven years that Cox was at Howard University he published another paper, directed Masters’ Students (more than any other faculty), and served as department Chair.  Harris notes,

Although the professional societies had African-American members, it was difficult and unpleasant for them to attend meetings, especially as they were frequently not permitted to attend social events or to lodge at the hotels and convention centers where the meetings were held, [James Donaldson] wrote [in A Century of Mathematics in America by the AMS]. Cox allowed his membership in the AMS to lapse shortly after becoming the organization’s first African-American member in 1925, and did not renew it again until 1948. However, he held a membership in Beta Kappa Chi, a black scientific fraternity, which allowed him to maintain contact with the scientific community.

Elbert Cox married Belulah Kaufman (while he was teaching in West Virginia) and they had four children.  Cox passed away in 1969, three years after retiring from Howard University, but his name lives on through honors such as the Elbert F. Cox Scholarship Fund at Howard University and the Cox-Talbot Address, an annual lecture of the National Association of Mathematicians.

Sources: 

• “Elbert Frank Cox” by Johnny L. Houston of the National Association of Mathematicians, reposted by the Mathematical Association of America
• “Evansville Honors the First Black Ph.D. in Mathematics and His Family” by Talitha M. Washington, Notices of the American Mathematician Society
• “Math Department Honors CU pioneer Elbert Cox, first black math Ph.D.” by  Lissa Harris
• The Mathematics Genealogy Website
• Wikipedia