# The Center of Math Blog

DO the math, DON'T overpay. We make high quality, low-cost math resources a reality.

## Friday, June 24, 2016

### Problem of the Week

Don't miss this week's Problem of the Week!

Solution below the break.

## Thursday, June 23, 2016

### Advanced Knowledge Problem of the Week

Be sure to take this Advanced Knowledge Problem very series-ly. Let us know how you did in the comments!
Solution below the break.

## Tuesday, June 21, 2016

### Problem of the Week

Log some time solving this week's Problem of the Week! Let us know how you did in the comments.
Solution below the break.

## Friday, June 17, 2016

### Happy Father's Day!

Father's Day is a time to celebrate the male hero in your life! Dad's can be our best friends, number 1 supporter's and greatest influences all at the same time. Today, let them how much you really do appreciate them. The Center of Math would like to commemorate some great mathematicians who were also Fathers. Don't miss our gift section at the bottom of the page for the perfect last minute Father's Day presents!

1. Diophantus of Alexandria

(Photo Source: Wikipedia)
Greatest Discoveries: Diophantus studied at the University of Alexandria in Egypt, where he cultivated an intense appreciation and understanding of numbers. He then wrote a series of thirteen books called Arithmatica. Only six of these books survived, however they are still considered crucial for defining modern algebra. These books included over 150 algebra problems that Diophantus solved.
Fun Fact: Not a lot is known about Diophantus, but he is heralded by many as the “Father of Algebra” for his work in defining algebraic solutions and symbols.
2. Blaise Pascal

(Photo Source: Wikipedia)
Greatest Discoveries: Pascal was a crucial force in defining the probability theory. He developed this theory to try and help one of his friends make money gambling, and it ended up revolutionizing statistics. The theory states that events don’t happen purely by chance, but are based on prior events. For instance, if you have a bag of M&Ms and remove six brown ones, the probability of picking a brown M&M from that bag has now changed.
Fun Fact: Pascal turned from math to philosophy after what he described as a “night of fire” in which the world around him was illuminated. After this epiphany, Pascal became one of the first scholars to teach existentialism.
3. Euclid of Alexandria

(Photo Source: Wikipedia)
Greatest Discoveries: Euclid is best known for his work on Elements, a compilation of the work of dozens of mathematicians before him. Elements aimed to translate the observations that past mathematicians had made into concrete rules, called “axioms” that people could use to make more complex deductions.
Fun Fact: Not much is known about Euclid’s personal life, but Elements is still one of the most influential math textbooks in history. It was the basis for early geometry, which is why Euclid is known as “The Father of Geometry.”
4. Pythagoras

(Photo Source: Wikipedia)
Greatest Discoveries: Pythagoras was one of the first mathematicians to attempt to define universal rules for mathematics, rather than relying on strict observation. He developed five main axioms, including the famous discovery that the square of the hypotenuse of a right triangle is equal to the square of its other two sides. Pythagoras also developed number theory, which states that the world is run by a series of integers, and defined prime, perfect, and irrational numbers.
Fun Fact: Pythagoras was involved in the musical arts as well as math. He was a pioneer in music theory, defining the length of notes in terms of numbers, and noted that instruments are only harmonious when they are played in time with these numbers.
5. Isaac Newton

(Photo Source: Wikipedia)
Greatest Discoveries: Newton was a mathematics powerhouse! He discovered that the binomial theorem could apply to non-integer exponents, defined most cubic plane curves, and is one of the founding fathers of calculus. These discoveries revolutionized the scientific world, allowing fields like physics and astronomy to progress beyond what people thought was possible.
Fun Fact: Newton believed that God had chosen him to interpret the bible, and determined that the world would end no sooner than 2060. He made the determination to quell many popular concerns that the world was doomed to end in the near future.
6. René Descartes

(Photo Source: Wikipedia)
Greatest Discoveries: Descartes’ work in mathematics was primarily in the realm of analytical geometry. He was the first person to link algebra to geometry by postulating that algebra can be interpreted in terms of geometrical shapes. He also linked math to philosophy as one of the first scholars to try and use math to define the interrelationship between ideas—which is the basis of our modern scientific method.
Fun Fact: Descartes believed that reason was the only way to reach a higher level of knowledge, rather than relying strictly on anecdotal observations, which is largely what was done before his time. He influenced future mathematicians by defining reflection and refraction, as well as helping to define the laws of motion.
7. Leonhard Euler

(Photo Source: Wikipedia)
Greatest Discoveries: Euler is best known for developing many of the notations used in modern mathematics. He was the first mathematician to define a function, writing equations with the notation “f(x)” to denote that a given function applies to x equation. In addition, he developed notations for trigonometric functions and was the first to use “e” as the symbol for the base of the natural log. He was also the first to use “Σ” to denote a sum, and “i”to denote an imaginary number.
Fun Fact: Euler has always been a popular icon in Europe. His picture was on the sixth series of the Swiss 10-franc banknote, and he has been prominently featured on postage stamps all over Europe.
8. G. F. Bernhard Riemann

(Photo Source: Wikipedia)
Greatest Discoveries: Riemann developed “elliptic geometry,” which differs from Euclidian geometry in that it breaks away from the limitations of the two- and three-dimensional world. This theory extended geometry to infinite dimensions, creating the concept of “hyperspace” and developing the idea of general relativity, which is the basis for much of modern mathematics.
Fun Fact: Riemann is responsible for one of the greatest questions in mathematics. A reward of one million dollars has been offered to anyone who can prove his theory about the relationship between zeroes and prime numbers.
9. Fibonacci

(Photo Source: Wikipedia)
Greatest Discoveries: Fibonacci is responsible for popularizing the Hindu-Arabic number system. He did this through publishing his book, Liber Abaci, meaning, “Book of Calculations.” This book showed how using the 0–9 number system with place values could broaden the scope of western mathematics. He also developed the Fibonacci sequence, in which each number is the sum of the previous two numbers.
Fun Fact: There are many mathematical concepts named after this founding father of mathematics, such as the Fibonacci identity and Fibonacci search technique. However, he’s memorialized by more than just the math community. There’s an asteroid and even a rock band named after him!
10. George Boole

(Photo Source: Wikipedia)
Greatest Discoveries: George Boole invented Boolean Algebra with his book, The Laws of Thought. Boolean Algebra paved the way for the entire field of computer science by stating that there are universal mathematical laws that can be used to form the basis of all reasoning. Based on the probabilities for any system of events, Boole believed you could calculate the probability of any other event that is connected with the initial system of events.
Fun Fact: By the age of 19, Boole had already established his own school in his hometown of Lincoln, England. This would prove to be a stepping-stone for Boole’s future endeavors running Hall’s Academy and then his own boarding school.

Looking for a last minute father's day gift? Look no further, these 5 options will guarantee a smile on your dad's special day!

1) For the Dapper Dad - A great watch is never a bad idea.

2) For the Funny Dad - Got a family of math lovers? You can never go wrong with a math themed tie.

3) For the early-riser Dad - Help him get his day started the right way with this math mug!

4) For the fit Dad - Who wouldn't love a fresh home made juice every morning?

5) For the Dad who loves to cook - A cook book focusing on the best bbq recipes is the perfect present for the Dad who doubles as a chef!

### Some of Infinity

The Center of Math is proud to announce the publication of our first non-academic text– David Craft's Some of Infinity: Peaks in the Landscape of Mathematics!

"But with mathematics, the more we explore, the bigger the world gets, and thus, for those adventurers out there who always want more, welcome to the world of math."

-David Craft, Some of Infinity

Craft's Some of Infinity: Peaks in the Landscape of Mathematics sheds an entertaining light on mathematics, resulting in a perfect read for anyone with an interest in the subject. Some of Infinity examines the roots of mathematics, as each chapter in the novel is dedicated to a different mathematical concept. Craft delivers this wide array of information in a personable and simplistic way that is accessible to all types of readers. This allows his audience to grasp and appreciate the many layers of the book. Shying away from the academic writing style of most math books, Craft aims to show the scope of mathematics and the exploration that is possible. His passion for the subject is contagious and readers will undoubtedly adopt the endless possibilities of mathematics that Craft presents.

Topics covered in Some of Infinity: Peaks in the Landscape of Mathematics
Numbers
Infinity
Probability
Fractals
Geometry
& and many more!

A modern day Renaissance man, David Craft is well versed in many areas. He received his Bachelor's degree in Mechanical Engineering from Brown, and went on to earn his Doctorate in Operations Research from MIT in 2004. Craft currently works for Harvard Medical School in oncology research, developing an algorithm for radiation planning. His many interests include Gallery 263, foraging, and creating music.

For more about Craft's mathematical interests and career, we turn to a 2015 interview conducted by the Center of Math:

So we’ve done a little research on your background, and you have a lot of interests, I can tell. What did you start with? What did you study at school?
At undergraduate I studied mechanical engineering, and I studied… well, I usually say I studied applied math at MIT, but really it was a subject called Operations Research. It’s Applied Math for real world operations.

What do you do now? You are an assistant professor at Harvard Medical?
Right, but it’s a pure research job. I have a nice position where it’s research, and I get to work on whatever I want in the field of radiation therapy for cancer treatment. So the basic idea is this: when you have a tumor that you have to hit with radiation, it’s like a puzzle- how to bring the radiation beams in. We try to conform to the target and try to avoid everything else. That’s the balance, it’s sort of a high dimensional tradeoff because there’s the tumor, but all these different organs around it like the heart, or the liver, or whatever is nearby, and you have to play a sort of balancing game amongst all those things so that’s where the  math comes in.

So after all of these hobbies, jobs, and working in Oncology, what is bringing you back to pure mathematics?
Well, every couple of years I’ve come back to just reading a book on math; popular or in-depth books, but not quite textbooks. I’ve always quite enjoyed that, it reminds me of my school days and I like that. So the reason that I wrote this particular book is that I would be talking to friends and describe some little piece of mathematics. For example, that the number of primes is infinite. Just little topics. And I really enjoyed saying that to people, and then getting them to understand what it would mean to prove such a statement, and then getting them to understand the proof. The fact that you can do that all within like 20 minutes, even for people who wouldn’t consider themselves good at math, is just great.

I never became a math professor because I really like the one-on-one. I have been a math professor [at Williams college] for a year, and it was good, but I like the on-on-one. I’ve had a lot of those one-on-ones with people at bars or parties, and I decided at some point that I could probably cobble these little vignettes into a book.

The book Craft speaks of became a reality titled,
Some of Infinity: Peaks in the Landscape of Mathematics