Welcome to Musings on Math!

“A mathematician is a device which turns coffee into theorems.”

– Alfréd Rényi

Hello.  Welcome to musingsonmath.com!  My goal when creating this website was to give my high school and college math students a place to go to learn more about the information I presented in class – ideas that we didn’t have time for during the confines of our class time (not necessarily the technical aspects of the class, textbooks do an O.K. job of that).  Rather, what I wanted was a place to go where the more human side of the subject could be explored: the people and events that shaped the thinking and understanding of the mathematicians who discovered (or created) the beautiful world of mathematics.   That doesn’t mean that I don’t ever delve into the mathematics.  I do, from time to time, offer up some more technical posts as well as some more interesting problems to solve.  However, I want this site to show that mathematics is not some technical, dry and emotionally void subject that is written in a complicated and cold language.  Instead, it is a subject that is a lively and colorful, full of interesting characters and fascinating stories that make mathematics into a living, breathing subject to be enjoyed by all.  So, whatever your reason for visiting this site, I hope you enjoy it and learn from it.

Before I leave you to your explorations, just a few last points …

The Navigation Bars:

  • The top menu bar contains my website pages.  On these pages, you can find all sorts of mathematical links, articles, problems, books, gift ideas, etc.
  • The bottom menu bar contains the categories of my posts.

My Top 5 most visited pages and posts:

One last item … new posts can always be found below this Welcome post and to the right listed under “Recent Posts.”

Please feel free to contact me with your suggestions, additions or advice by leaving a comment or sending me an email at musingsonmath@gmail.com.

Enjoy the site!

The Month in Math: December

Interested in the highlights from the historical world of mathematics for the month of December?  How about the answers to these questions?

  • In 1742, Euler presents the first concise statement of what famous theorem?
  • In 1908, Scientific American offers $500 to anyone who can come up with “a simple explanation” of what famous idea?

Click here to find the answers to these questions and more:  December

Looking for a different month?  Click here for all 12 months.

The Month in Math: November

Interested in the highlights from the historical world of mathematics for the month of November?  How about the answers to these questions?

  • Which mathematician’s burial was described as follows – “He was buried more like a robber than what he really was, the ornament of his century.”
  • Which mathematician described his discovery of non-Euclidean geometry as “From nothing I have created another entirely new world.”?

Click here to find the answers to these questions and more:  November

Looking for a different month?  Click here for all 12 months.

The Month in Math: October

Interested in the highlights from the historical world of mathematics for the month of October?  How about the answers to these questions?

  • In 1843, what does Sir William Hamilton invent during a walk along the Royal Canal in Dublin?
  • In 1903, Frank Cole gives his famous silent presentation about what unsolved math problem?

Click here to find the answers to these questions and more:  October

Looking for a different month?  Click here for all 12 months.

Mathematical Poetry Month?

It is a relatively well-known fact that, in the United States, the month of April is National Poetry Month.  What is far less-known (unfortunately) is that April is also Mathematics Awareness Month.  Intending to capitalize on the overlapping celebrations, science writer Stephen Ornes proposes that April should become Mathematical Poetry Month.  His compelling argument can be read here:  April Should Be Mathematical Poetry Month.

Should we start a petition????

Why don’t people appreciate math?

“It saddens me that educated people don’t even know that my subject exists.” – Paul Halmos

Why is it that so many people have no idea what mathematics is really about?  Why is it that the general public views math as boring and ugly?  Because most people view mathematicians as human calculators, computing gigantic multiplication problems in their heads.  While, in some rare cases, this is certainly true, I have learned from some brilliant mathematicians who couldn’t even master their times tables.

What the general public doesn’t realize is that mathematics is so much more than computation.   It is about discovering patterns and relationships between ideas.  In many cases, there is something beautiful when a mathematical idea makes a clever connection between two concepts, especially when it is unexpected.

Recently, in an OP-ED piece in the New York Times, Manil Suri attempts to explain what mathematics is about and why it is something to appreciate, much in the same way one appreciates art or music.  As he puts it in his piece,  “you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music.  Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, ‘When will I use this?'”

Click here to read his article titled “How to Fall in Love with Math.”  You will not be disappointed.

THE BOY WHO LOVED MATH: The Improbable Life of Paul Erdős


Three weeks from today, math-lovers around the world will be enjoying a new look at Paul Erdős!  June 25th is the release date of the newest book on Paul Erdős, THE BOY WHO LOVED MATH: The Improbable Life of Paul Erdős by Deborah Heiligman with illustrations by LeUyen Pham.

I can’t wait!  Click here to read the first review of the book.  Click here to see some amazing illustrations and read an article about the book in the New York Times.  21 days and counting …

Happy Birthday to Carl Friedrich Gauss!

Happy Birthday to Carl Friedrich Gauss!  Born on April 30, 1777 in Brunswick, Germany, Gauss is considered by most to be the greatest mathematician of all time.

Like many great mathematicians, Gauss showed his incredible mental abilities at a young age.  Before the age of three, Gauss taught himself to read by simply asking his parents for the pronunciations of the letters.  By the age of three, Gauss had a mastery of arithmetic as is often retold in the story of him finding a mistake in the arithmetic of his father’s payroll calculations.  During his teen years, Gauss was improving upon the proofs of NewtonEuler and Lagrange, determined to make the proofs more rigorous in nature.  In fact, this effort forever changed the way mathematical proofs are written.

However, despite all of these early achievements, Gauss was still considering a career in linguistics instead of mathematics.  Thankfully, for the sake of mathematics, this changed on March 30, 1796.  It is on this day that Gauss wrote in his diary that he had discovered a solution to one of the greatest unsolved problems of Euclidean geometry, the construction of regular polygons.  So impressed with the solution to this problem, Gauss decided to dedicate his life to mathematics.  It wasn’t long before Gauss would impress himself again.  On April 8, 1796, Gauss proved the Law of Quadratic Reciprocity.  His favorite of all the theorems, he is credited with at least a half-dozen proofs of it during his lifetime.

As Gauss’ life continued, so did his achievements.  Too many to mention specifically, Gauss made groundbreaking contributions in Number Theory, Differential Geometry, Statistics, the Method of Least Squares, Complex Analysis and non-Euclidean Geometry.  In 1801, Gauss published Disquisitiones Arithmeticae, considered by many to be one of the greatest achievements in all of mathematics.  Beyond mathematics, Gauss also rewrote physics with major contributions to the fields of electricity and magnetism.  As if that weren’t enough, Gauss was also a bit of an inventor.  He is credited with inventing the heliotrope to help with his job as a surveyor.  And, with colleague Wilhelm Weber, he was the first to invent the telegraph.

If there is to be one major criticism of Gauss, it is with his reluctance to publish his discoveries.  Gauss, ever the perfectionist, did not like to publish many of the results of his research, fearing that they were never perfect enough.  Or, as Gauss would describe it later in life, “pauca sed matura” (few, but ripe).  In fact, most of what Gauss discovered was not known until after his death when colleagues went through his mathematical diary.  Looking at this as a major travesty to mathematics, it is the opinion of the famous mathematician, historian and mathematical romantic E.T. Bell that Gauss’ reluctance to publish his discoveries set mathematics back at least 50 years.

If you are interested in learning more about Gauss, please check out some of these resources:

If you would like to see my mathematical collection, some of which is dedicated to Gauss, you can click here.