… for those who love to talk math.
September 26, 2011 Leave a comment
Every wonder about the origins of your favorite mathematical symbol? Did someone find it under a rock? Was it someone’s idea of a cruel joke? Well, wonder no more. Thanks to Douglas Weaver and Anthony D. Smith from Taperoo High School (Australia), you can now learn the origins of many of the mathematical world’s favorite symbols.
To begin the fun, click here: http://www.roma.unisa.edu.au/07305/symbols.htm#Index
September 7, 2011 1 Comment
Recently, Time Magazine took the time to analyze 171 college majors to determine which majors earn the most and least amounts of money. Below is the list of the 10 highest and 10 lowest earning majors. And – what a shock – the highest earning majors all involve a great deal of mathematics!
Read more: http://www.time.com/time/specials/packages/completelist/0,29569,2073703,00.html#ixzz1Vg4a0U4x
August 18, 2011 2 Comments
Kudos to Google!
Anyone who loves math knows how rare it is for mainstream society to be exposed to mathematics of any kind. However, yesterday, Google exposed tens of millions of people to one of the most famous mathematicians of all time, Pierre Fermat. To honor his 4o1st birthday on August 17, Google created the Doodle seen above. What is the Doodle about? Well, written on the chalkboard is what is known as Fermat’s Last Theorem. Simply put, the theorem states that the equation 
has no integer solutions for n>2 and x,y,z ≠ 0.
However, what has become more famous than the actual theorem is the mystery Fermat left behind. The theorem, discovered after his death and written in the margin of his copy of Arithmetica, included the note “I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain.”
For the next three centuries, legendary mathematicians tried hopelessly to recreate the proof that Fermat claimed he had discovered. Finally, in 1993, the mathematician Andrew Wiles (with a little help from others to fill in some gaps) found a proof. Beyond putting the mystery to rest, Wiles put to rest the idea that Fermat ever had a legitimate proof of the theorem as the mathematics he used had only been developed in the 20th century.
So, if Fermat never left a proof, then why call it a theorem? Any high school geometry student will tell you that a theorem requires a proof. It all has to do with the fame of the person making the claim. Fermat was about as famous as any mathematician could be and was, therefore, given the benefit of the doubt. Unfortunately, for us mere mortals it would have been called a conjecture and, more importantly, lost to the sands of time.
July 18, 2011 Leave a comment
Beauty … perfection … words many non-math people don’t expect to hear when it comes to mathematics. But talk to any math person and, sooner or later, one of these words will be used to describe the subject. As the legendary number theorist G.H. Hardy once described it, “Beauty is the first test: there is no permanent place in the world for ugly mathematics.”
For most people, their first opportunity to see such beauty and perfection comes with a course in high school geometry. Studying the properties of polygons or learning that the ratio of a circle’s circumference to its diameter is exactly pi are opportunities to witness first hand the elegance of the subject.
Unfortunately, as math people know too well, the perfection of geometry exists only in our minds. Thanks to the laws of physics, in the “real world”, the perfect forms of geometry just do not exist. A rhombus is never quite a rhombus. The ratio of a circle’s circumference to its diameter is close to pi but never exactly pi.
However, before we all run into the woods to hide from the hideous and ugly real world of imperfection, TAKE A DEEP BREATH! It turns out that there is new hope for us!
According to recent research from Imperial College in London, we need not look farther than the electron to see geometric perfection – well, almost perfection. Previously thought to be a distorted sphere (aspheric), scientists were surprised when they discovered just how spherical an election is. According to their research, the electron differs from a perfect sphere by only 1×10^-27 cm or, if you are a more visual person, .000000000000000000000000001 cm. To understand this in more practical terms, if the electron were blown up to the size of our solar system, it would differ from a perfect sphere by the width of a human hair! (Thanks to sciencedaily.com for the example.)
So, lovers of beauty and perfection, fear not – maybe mathematics in the real world isn’t that ugly after all.
If you are interested in reading more about this on sciencedaily.com, click here: http://www.sciencedaily.com/releases/2011/05/110525131707.htm
If you would like to read the official abstract for the paper, click here: http://www.nature.com/nature/journal/v473/n7348/full/nature10104.html
March 17, 2011 8 Comments
March 17 celebrates the anniversary of one of the most lopsided business deals in mathematical history. Before the days of companies and colleges employing mathematicians, one of the few ways for a mathematician to earn money was to be employed by a nobleman. You might earn your keep by tutoring, consulting on finances, surveying the lands or anything else involving numbers.
In the late 17th century, the great mathematician Johann Bernoulli was looking for a way to earn money while doing what he loved, mathematics. Enter the Marquis de L’Hospital. L’Hospital was a nobleman who was fascinated by mathematics, particularly calculus, which was in its infancy at the time. And he knew that Johann had worked with Gottfried Leibniz with the development of calculus.
However, unlike the great ones, L’Hospital lacked the skill necessary to understand the finer points of this new field of calculus. So, he had an idea. If he hired Bernoulli as a sort of mathematical consultant, Bernoulli would be available to help L’Hospital with any difficulties he might encounter.
So, on March 17, 1694, The Marquis de L’Hospital and Johann Bernoulli entered a financial relationship in which L’Hospital would pay Bernoulli an annual salary to be available as a mathematical consultant. Bernoulli would answer any questions L’Hospital might have and, here’s the big one, send any new mathematical discoveries directly to L’Hospital without announcing these discoveries to the world. Basically, L’Hospital believed that he should have some sort of ownership over Bernoulli’s ideas since it was he who was paying Bernoulli to research mathematics. In other words, any great breakthroughs would be credited to L’Hospital instead of Bernoulli. Sound strange? It was. But remember the times. It was almost impossible to get a paying job as a mathematician. So Bernoulli saw this as his only opportunity to earn a living as a mathematician.
What was the result of this arrangement? One of the first books in calculus … Analyse des infiniment petits … written by … wait for it … L’Hospital! Included in the book were many of Bernoulli’s ideas. However, since L’Hospital was the author, he was viewed as the mathematician who made the discoveries.
Now, L’Hospital knew full well that he was essentially ‘stealing’ the ideas of other mathematicians so he included the following statement in the book: “I have made free use of their discoveries, so that I frankly return to them whatever they please to claim as their own.” As history will show, his book became quite popular. In fact, one of the most famous and important ideas from the book became known as L’Hospital’s Rule … a great rule for evaluating limits when the limit yields the indeterminant form 0/0 … known by calculus students worldwide! Poor Bernoulli.
If you are interested in reading more about this scandal and many others, there is a great book on the subject … Mathematical Scandals by Theoni Pappas. Included on pages 16 – 21 is a more detailed account of the scandal involving L’Hospital’s Rule.
Musings on Math 