Category Archives: Math History

All You Need Is…Math?

The Beatles famously shared songwriting credits for all of their songs; throughout history, it’s been gradually revealed whether or not John Lennon or Paul McCartney wrote each famous Beatles song.  However, there’s one song that they were never able to agree on.  Hear how mathematicians have determined who actually wrote The Beatles’ hit “In My Life”.


Listen to the song above.  Then you should read this NPR article and/or listen to the interview (top left of page).

Write a brief paragraph summary explaining in your own words how mathematicians determined the authorship of “In My Life”.  Write a second paragraph hypothesizing:  Where else might this statistical method be used?  Think not just in music, but in the written word as well.  How might historians and archaeologists use this method in other instances?

Finally check out this post, wherein the author used a technique similar to “Bags of Words” to see if a machine could read recipes and create new ones.  The results are…interesting.


Number Gossip


“Can you believe what 56 did?  It’s just so…odious!”

“Oh I know.  And 43 is so lucky, I can’t even stand it.”

You probably know a lot of properties of numbers like “even”, “odd”, “prime”, “square”…but there are so many more that you might have never heard of!  Head on over to Number Gossip to get the scoop!


Pick a favorite or interesting whole number.  It might be your uniform/jersey number for a sport you play, or your home address, or your lucky number, or something else entirely.  Enter it into the search field at Number Gossip.

  1.  List all of the “common properties” of your number that Number Gossip lists.  If any of those properties are unfamiliar to you, you should be able to click for an explanation.   Explain in a sentence next to each property why your number belongs to that property (Where applicable, give a specific reason for *your* number, not just a definition of the property).
  2. Pick one “rare property” (if your number has one; not all do) and do the same thing as in step 1.
  3. Pick one “unique property” (if your number has one; not all do) and do the same thing as in step 1.
  4. Search Number Gossip for the whole number directly before and after the number you chose.  How are the search results different?  How are they similar?  Write a few sentences comparing and contrasting, as well as your thoughts as to why they compare the way they do.




Mayan Mathematics

Certain schools on the Yucatan Peninsula in Mexico are teaching native students the mathematics that was done by their ancient ancestors in the Mayan civilization.  Check it out in the video above.


Watch the video and pay attention to how the Mayans write their numbers and conduct simple arithmetic.  Answer the following questions.

  1.  How would you express the number 19 using the Mayan notation?
  2. In the video, the news reporter shows how to do the arithmetic 16 + 7.  Replicate that arithmetic using drawings.
  3. Now create a drawing/notation using the Mayan method to conduct the arithmetic 18 + 6.
  4. Explain at least three reasons why it is important for these children to be taught this method of arithmetic alongside the “typical” methods (like the way you learned to do addition, for example).


Who Cares If Math is Useful?

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The last time we saw Dr. Eugenia Cheng, she was on The Colbert Show cooking up some fun mathematical recipes.

This time, she’s on PBS talking about how the usefulness is math is…a burden?  What could she possibly mean?

Visit the video to hear what she’s talking about.


Watch the video linked above (less than 4 minutes).  Answer the following questions in a couple of paragraphs.

  1.  Why does Dr. Cheng feel that we should let go of the idea that math is “useful”?
  2. What are some adjectives Dr. Cheng uses instead of “useful”?
  3. Dr. Cheng gives a number of examples of math that wasn’t “useful” until centuries after it was discovered.  Describe a couple of those examples (internet cryptography, viruses, soccer balls, etc.).
  4. How does Dr. Cheng suggest we “break the cycle” of how students (particularly elementary students) view mathematics?



Noise Cancelling Headphones


Ever wonder how noise-cancelling headphones work?  Is it just more insulation than other headphones?  Or is there more to it than that?

Turns out it is mathematical.  And we have one Joseph Fourier (1768-1830) to thank for the equation that makes noise-cancelling headphones work.  Check it out here: (via WIRED)


Read the brief article linked above.

Print off this picture of a sound wave:


Use the information from the article to answer these questions on the page where you printed off the above sound wave:

  1.  Under the picture of the sound wave you printed off, draw another wave that would be higher-pitched sound than the one you printed off.  (NOTE:  When the article mentions “frequency”, it is referencing the wavelength).
  2. Underneath that picture, draw another picture of a sound that would be quieter than the one you printed off.
  3. Explain in your own words how the article describes how an engine roar is “like an ocean in a storm”.
  4. In your own words, explain what noise-cancelling headphones do in order to reduce outside noise.


A Mathematical Analysis of the Electoral College


You may have heard that there’s a Presidential Election this year?

As this is one of the most hotly contested and emotional political races in recent memory, every facet of the election is going to be under scrutiny.  One such facet is the Electoral College.

Mathematician John Allen Paulos wrote an opinion piece back before the 2012 Presidential Election for ABC News criticizing the Electoral College system.  He posits that a candidate could conceivably lose the popular election 70,000,000 to 11 but still win the presidency.

Is that possible?  Does this carry even more weight in 2016 than it did in 2012?  Read on and see:


Read the article.  Explain how a candidate could logically receive only 11 votes but still win the presidency.  Write a paragraph explaining your feelings on the Electoral College (Do you think it is fair?  Should we do it differently?).  Then research one other free, democratic country and determine how their national leader is elected.  (Example:  Prime Minister of Britain, Japan, Canada, Australia, etc.)

Gambling & Mathematics


Many people know that mathematicians have used their knowledge of numbers as an advantage when gambling (For example:

What we might not know is that a LOT of new mathematical knowledge was developed as a result of gambling or “games of chance”.

Check out the Guardian article here:


Read the above article.  Each of the 7 bullet points lists a mathematician (or two) that contributed to this new knowledge.  Pick any three of the mathematicians listed.  Summarize (from the article) what they did to promote a new mathematical understanding based on their “hobby” of gambling.  Then research each mathematician online (Wikipedia is fine) and add a sentence or two (per mathematician) about what else they are known for (in mathematics or outside of mathematics).