Throwback Fact: The Mathematical Association of America

In a couple of weeks the Center of Math will be attending the Joint Mathematics Meeting (JMM) in Seattle. The American Mathematical Society (AMS) and the Mathematical Association of America (MAA) run this annual event, which is one of the largest mathematics meeting in the world. To get ready for our trip, the Center of Math wanted to write about the history of the MAA for this weeks Throwback Fact. And if your wondering why we aren’t talking about the AMS, it’s because we already did a Throwback Fact on them, which you can check out here. So keep reading to learn more about the MAA!

Current logo by the MAA. Visit their website here!

Throwback Fact: Thales of Miletus

Thales of Miletus was an ancient Greek mathematician, scientist, and philosopher who predated most well known Greek thinkers. Though his contributions and discoveries in physical sciences and philosophy were noteworthy, this is the Center of Math, and thus we are going to focus on his contributions to mathematics for this week's Throwback Fact.  So, keep reading to learn more!

Thales
Source: Wikipedia

Throwback Fact: The SAT

This Saturday marks the first SAT exam of the year, so to celebrate, the Center of Math is going to talk about the history of the SAT for this week's Throwback Fact. Keep reading to learn more about the SAT!

Throwback Fact: Three German Mathematicians

Happy Oktoberfest! With the annual festival taking place right now in Germany, the Center of Math wanted to celebrate by talking about three famous German mathematicians for this week's Throwback Fact.

Throwback Fact: The ACT

With the first ACT exam quickly approaching--this Saturday, in fact!--the Center of Math wanted to talk about the history of the ACT and how it has evolved over the years. Although the ACT has not been around as long as the SAT, it has become just as popular and is now accepted by all universities and colleges in the US.

Throwback Fact: The Equals Symbol

For this week Throwback Fact we decided to investigate the origins of the equals symbol. You may be surprised, the equals symbols hasn't been around for as long as you may think.

Where did the equals symbol come from?

Throwback Fact: Mancala

An example of a modern Mancala board from Europe
Source: https://en.wikipedia.org/wiki/File:Bao_europe.jpg

        Many historians believe that Mancala is the oldest board game in existence. Since Mancala is one of our favorite games in the office we decided that for the throwback fact of the week we would take a look at Mancala.

        Mancala is a/the term used to describe a collection of similar games, of which there are over 800 around the world. Some of the variations include Bao, which is played across the east coast of Africa, Oware, which is played in the Caribbean, and Kalah, which is the modern game played in the US and Europe, which we call Mancala. It is unclear exactly where Mancala originated but many historians believe it was in Africa where players used to carve holes in the ground and use pebbles to play.

Bao players in Zanzibar 
Source: https://en.wikipedia.org/wiki/File:Bao_players_in_stone_town_zanzibar.jpg

        There are many different theories as to what the original purpose of the game was for ancient people. One theory is that it was a record keeping system used to manage debit and credits, which were represented by the two sides of the board. Another theory is that Mancala was a ritual at funerals, weddings and other ceremonies. It could also have just originated as a game, which is its main use now.

        Whatever the origins of Mancala one thing is for sure, ancient people needed to count to play, just like we do now. Mancala is a great game for teaching kids how to count and work on strategic thinking skills as they age. 

Tell us, what are some of your favorite board games?

Source: 1, 2, 3

Throwback Fact: Ada Lovelace and the Analytical Engine

Portrait of Ada Lovelace
image: commons.wikimedia.org

Ada Lovelace was born in London, England in 1815 to a poet father and math-loving mother. After her father left the family when she was just four, Ada’s mother raised her on a strict regiment of science, logic, and mathematics. Due to this she developed an early love for machines and technology, a passion that would lead her down a path of scientific discovery. 

Relationship with Charles Babbage:

In 1833, at around seventeen, Lovelace was introduced to Charles Babbage, a mathematician and inventor who was famous for his work with calculating machines. Babbage became a mentor to Lovelace who was captivated by his innovative work. Soon, Babbage would ask Lovelace to work with him on his newest invention called the Analytical Engine, which was meant to perform mathematical calculations just like a computer.

Lovelace’s Work:

Babbage asked Lovelace to translate an article on the analytical machine written by Italian engineer Luigi Federico Menabrea. While translating the text from French to English, she also added her own thoughts and ideas on the machine. She theorized that the machine could repeat a series of instruction, a process known as “looping” that is still used today by computer programmers. She also created codes so that the device could handle numbers, letters, and symbols. Due to these findings and theories, Lovelace is often considered the first computer programmer. 

Lovelace’s Legacy:

Ada Lovelace envisioned a world where machines would be an integral part of human imagination. At the time, these ideas where dismissed by the scientific community because they were too difficult to comprehend. Just like many other visionaries of her era, only time and knowledge could lead to the acceptance of her work. In the 1970’s, engineers at the United States Department of Defense, inspired by her work on the calculation of Bernoulli numbers, named a computer programing language Ada in her honor. Today, Lovelace also serves as an inspiration to many women in the STEM fields, who see her as a visionary who lived before her time. They celebrate Ada Lovelace Day on the second Tuesday of October in her honor. 

Sources: 1, 2

Throwback Fact: Stokes' Theorem

George Stokes (1819 - 1903)

The University of Cambridge, founded in 1209, has produced many of the greatest scientific minds of all time. It makes sense that Sir George Stokes, famous in both the fields of mathematics and physics, spent the entirety of his career within those halls.

On this day in 1850, Stokes' theorem appeared in writing for the first time. Stokes' theorem is used in multivariable calculus to relate a line integral to a surface integral. To view the notation used for Stokes' theorem that isn't supported in Blogger, click here; Mathworld did excellent work of describing the math behind the theorem. As a sidenote, this theorem appears as a topic in this Center of Math textbook.

A pictoral representation of Stokes' theorem

At the time that his most famous mathematical theorem was first discovered, Stokes was one year into his position as a professor of mathematics at Cambridge. He kept this position until his death 54 years later in 1903. During his career, Stokes made contributions many fields of science. He published several papers relating to fluid dynamics and motion, fluorescence, polarization, and light. His published, and unpublished, works have done much for the development of mathematical physics.

Throwback Fact: Sally Ride in Space

Sally Ride in space.
image: commons.wikimedia.org

On this day in 1983, Sally Ride became the first American woman in space (Valentina Terishkova was the first woman in space, as part of the Soviet program in 1963). In her biography on NASA's site, Dr. Ride's listed experience includes earning a Physics Ph.D. from Stanford University, developing the space shuttle's Canadarm arm, two space missions, and serving on the committee investigating the Challenger disaster.

Ride was not a mathematician, but an astrophysicist. However, I'd like to take the time to chat briefly about mathematics as it relates to space.

Throwback Fact: German Tank Problem

A WWII-era German Tank
image: commons.wikimedia.org

Last Saturday, June 6th, marked the 71st anniversary of D-Day, when the Allies invaded the beaches of Normandy and began to turn the tide of World War II. So, though it is not linked to any particular date in math history, it's fitting that we showcase a WWII era math problem.

The German forces had an advantage that the Allies had to overcome: more, and technologically superior, tanks. Knowing how many tanks the Germans were producing was the first step to figuring out how to take care of this threat. So, the Allies tried conventional methods of gathering intelligence: interrogation, spies, and decoding messages.

Throwback Fact: Emmy Noether's Math Journey

Emmy Noether

The way we name proofs in mathematics, most often after their founder, immortalizes mathematicians who could otherwise slip into history unnoticed. But 96 years ago today, an event occured that helped to keep one particular female mathematician from obscurity.

Emmy Noether (1882 - 1935) almost missed her chance at mathematical fame. Born to a Jewish family in the German town of Erlangen, Noether showed few signs of her mathematical talent until she reached a college age. Noether originally planned to learn to teach English and French, but she attended math courses at the University of Erlangen where her father lectured. There, she earned her doctorate in mathematics in 1907, and worked at the same university for 7 years, but didn't earn a single payment for her research. 

Throwback Fact: The Birthday Problem

image: www.flickr.com

In 1939, mathematician Richard von Mises proposed a problem. The answer was so counter-intuitive to many people, including mathematicians across the globe, that it continues to be one of the most discussed math problems ever. It is very difficult for people to understand, not because the mathematics behind it are hard, but just because the answer is so different from what anyone would expect. That problem is stated as follows:

Suppose you are in a large room that random people generally enter. How many people must be in the room before the probability that some share a birthday becomes at least 50 percent?

Throwback Fact: The Origins of Pi

We've mentioned pi quite a few times on the blog (our pi day post in particular). However, we've never discussed the reasoning behind the symbol.

Pi, of course, has existed in approximations since the time of the Babylonians (who got to 28/8 = 3.125) and the Ancient Egyptians (who found (16/9)^2 = 3.1605 on the Rhind Papyrus). Approximations have become better and better over time, but it will never end. Pi is transcendental- it is irrational, and cannot be found as the result of an algebraic function. We can continue to calculate more and more digits, but the number of trailing digits is an uncountable infinity, and therefore we will never know exactly what pi is.

Throwback Fact: Quaternions

A digital representaion of a Julia set quaternion

In 1843, Irish mathematician Sir William Hamilton was walking across Dublin's Brougham Bridge when inspiration struck him. He had been working on finding a method to multiply together points in space (three dimensions) instead of just points on a plane (two dimensions.) On his walk with his wife that morning in october, he realized that while he could not "multiply triples," he could multiply points in four dimensions. He carved this basic rule for multiplication into the bridge:

i² = j² = k² = ijk = -1

Hamilton named a quadruple of this type a quaternion and he devoted the rest of his career to their study. The simplest definition of such a number is a four-dimensional number. Quaternions are still studied today, and present a number of uses in modern mathematics. According to The Math Book by Clifford Pickover, they've been used to describe the dynamics of motion in three dimensions, and have been applied to fields including virtual reality computer graphics, game programming, robots, bioinformatics, and flight software of spacecrafts.

The plaque on Brougham Bridge in Dublin, Ireland

The invention, or discovery, of quaternions represents a moment of great ingenuity in math history. You can actually still visit Brougham (Broom) Bridge today, and see the plaque commemorating Hamilton's discovery. There is even an annual commemorative walk following Hamilton and his wife's path on that fateful morning. Perhaps we should have added this location to our list of math destinations!

One more fun fact about quaternions is that they generated such polarizing responses from the math community. Scottish physicist William Thomson(1824 - 1907) considered them an "unmixed evil to those who have touched them in any way," while mathematician Oliver Heaviside thought of their invention as a feat of human ingenuity. Curiously, one mathematician (who gained his fame from a harshly different circumatance) who studied quaternions was Theodore Kaczynski, the "Unabomber."

Throwback Fact: Perfect Numbers

Tori's handwriting demonstrates a few properties of the first two perfect numbers

We've mentioned the cult of Pythagoras and his followers a few times in the past. And we know that their mathematical findings did not stop at the Pythagorean theorem. One mathematical idea that fascinated the group was perfect numbers.

A perfect number is defined as a positive integer that is equal to the sum of its positive divisors, excluding itself. The definition appeared as early as Euclid's Elements, and only four of these numbers had been discovered before the Renaissance. The discovery process was so slow because these numbers are inredibly rare- the first is 6. It's a relatively small number, and makes the viewer think that the numbers may common. The next perfect number is 28, and then 496. A Greek mathematician (circa 100 CE) named Nicomachus is credited with the discovery of the fourth perfect number: 8128. Then, more than a millenium passed before an unknown mathematician recorded the fifth perfect number, 33,550,336, for the first time.

Cinco de Mayo Mathematician Highlight

After doing a little research, I’ve discovered that Cinco de Mayo is a holiday celebrated possibly more in the United States than in Mexico, its country of origin. Cinco de Mayo began as the celebration of a battle- it commemorates the Mexican army’s victory over France at the Battle of Puebla in 1862. This victory was particularly important in the Franco-Mexican war because it was an impossible feat as the Mexicans won against a much better equipped army.

In the United States, it is often utilized by Mexican Americans as a celebration of Mexican culture, including festivals and parades in some cities. In typical Center of Math fashion, we will use this opportunity to feature a prominent Mexican mathematician, Fray Diego Rodriguez!

Throwback Fact: Gauss's Birthday

Carl Friedrich Gauss

On this day in 1777, Carl Friedrich Gauss was born. The Prince of Mathematics was an important part of our Math Madness competition, and made it to the Final Four round. But in his short bio on our webpage, we missed some facts about Gauss that make his life even more interesting and impressive.

The great mathematician would have been 238 years old today, but there was a time that he did not know the date of his birth. Gauss was born to poor, working-class parents, and his mother was not quite literate. She did not record the date of Gauss's birth. Years later, she could just recall that Gauss was born on a Wednesday, and it was 8 days before Ascension Day, which lies on the calendar 40 days after Easter Sunday.

Throwback Fact: The AMS

An image from our Instagram, when the Center
attended JMM (by the AMS) in January

Friday, April 24th (misaligned slightly from our Throwback Thursday) marks the 118th anniversary of the first sectional meeting of the American Mathematical Society in 1897. Founded nine years previously in 1888, the AMS was the result of Thomas Fiske's vision to create a version of the London Mathematical Society in his home country. Soon after being founded, the AMS began to publish a research journal periodically.

Today, the AMS has nearly 30,000 individual members across the country, with physical locations in Providence, Rhode Island, Ann Arbor, Michigan, and Washington, D.C. And the AMS works today, like in the earliest days of the society, to publish math content- they've upped their postings from one research journal to 8(!), plus 4 translations journals, and two open source journals. The AMS is a wealth of mathematical knowledge.

The AMS works each year with the Mathematical Association of America (MAA) to put on the annual Joint Mathematics Meeting. In fact, the Center of Mathematics regularly attends- we were at JMM San Antonio this past January!

To read more about the American Mathematical Society, click here or visit their webpage.

Throwback Fact: Leonardo Da Vinci

Da Vinci self portrait

Choosing just one topic for a throwback was difficult this week. On this day in 1705, Isaac Newton was knighted by Queen Anne at Trinity College. If you'd like to read a little more on Newton, a past intern did a throwback fact on him here. And Wednesday, April 15th marked two anniversaries- the birth of our Math Madness Champion Leonhard Euler in 1707, and the birth of Leonardo Da Vinci in 1452. 

While he is definitely not a mathematician, Leonardo Da Vinci was a polymath, and contributed many quality works in his lifetime that interest mathematicians today. The original renaissance man, Da Vinci was a master in many areas. His paintings are likely to remain famous for all of human history, and his notebooks fascinate scientists to this day- he worked with codes, he fantasized about flying machines, sketched human anatomy, and much more.