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

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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 …

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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.

Google honors Euler!

Euler doodle

Kudos to Google!

Today marks the 306th birthday of Leonhard Euler and, thanks to Google, millions of non-math people are being exposed to some of his incredible achievements through this great doodle.

If you are interested in reading more about Euler, here are some great resources:

Happy Birthday, Euler!

Happy 100th Birthday to Paul Erdős!

Happy 100th!

Happy 100th!

March 26 is the birthday of one of the greatest mathematicians of all time, Paul Erdős.  Considering this fact, it should be easy to write some sort of tribute, right?  Well, maybe not.  When I originally wrote this post a few years ago to celebrate his birthday, I was very intimidated.  I was worried that, no matter what I wrote, I wouldn’t write enough to honor his memory.  I even wondered what I should write about.

Maybe I should write about the fact that he was gifted mathematician?  Erdős is said to rival Leonard Euler as the most prolific mathematician in history, having produced some 1500 mathematical papers, many with collaborators.

Maybe I should write about his quirks?  He could be known to appear at your doorstep, unannounced, for an extended visit, announcing that his “brain is open”.  Legend has it that he had trouble tying his shoes, buttering his toast and opening containers of orange juice.  He loved ping-pong.  Even his childhood was unique.

Maybe I should write about Erdős as the philanthropist?  Erdős had little need for money so most of the money he earned was donated … whether to charities, needy friends or to set up scholarships.  If there was someone, anywhere, who needed financial help, Erdős was there.

Or, maybe I should leave it up to a professional wordsmith?  In 1996, columnist Charles Krauthammer wrote a beautiful and touching tribute to Erdős, titled “Paul Erdős, Sweet Genius”.   I think I made the right choice.

If this isn’t enough and you are interested in learning more about Paul Erdős, you can read a more academic biography by clicking on this link.  If reading a book is more to your liking, here are three to consider.

  • The Man Who Loved Only Numbers by Paul Hoffman  (Click here to read my brief synopsis.)
  • My Brain is Open by Bruce Schechter  (Click here to read my brief synopsis.)
  • THE BOY WHO LOVED MATH: The improbable life of Paul Erdős by Deborah Heiligman – available in June 2013 (Click here to read the first review.  Click here to see some of the AMAZING illustrations and read an article about it in the New York Times.)

If you are interested in a few items that I have written about him, you can consider reading these.

Happy 100th Birthday, Paul!

Erdős and √2

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I asked you to tell me at every step if you don’t understand something. You said nothing!

In honor of Paul Erdős’s 100th birthday (March 26), I wanted to share one of my favorite stories involving his attempt to prove the irrationality of the square root of 2 to a non-mathematician.

Now, before we get to the story, a quick mathematical refresher.  Remember that the proof uses the popular technique of “proof by contradiction” or “Reductio ad Absurdum“.  (For example, if you are trying to prove some claim “A” true, first assume instead that “the opposite of A” is true.  Then, show that the new assumption leads to some logical contradiction.  This contradiction means that “the opposite of A” is wrong and “A” must be true after all.  Tricky, isn’t it?)  I love how G.H. Hardy explains it, “it is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.”

(Still need a little more of a refresher with the proof?  Click here.  Don’t worry if you’re not a great mathematician – it doesn’t require a lot of math to understand it.  In fact, that’s what makes it so beautiful – or “from the book” as Erdős would say!)

Now, on to the story …

One afternoon, Erdős was visiting with his life-long friend and fellow mathematician Andrew Vazsonyi.  (This is the same friend who many years ago told Erdős that he was thinking of majoring in something other than mathematics.  Erdős responded by saying that if he chose that path, “I’ll hide, and when you enter the gate of the Technical University, I will shoot you!”)  Anyway, Erdős decided to explain the magic of mathematics to Vazsonyi’s non-mathematican wife, Laura, by proving the irrationality of the square root of 2.  Unfortunately for Erdős, things didn’t go according to plan!  As Vazsonyi tells the story:

One day, Erdos got reckless and told Laura, my wife, that he will prove to her the Pythagorean “scandal,” that the square root of 2 is irrational. (According to legend, the disciple of Pythagoras, who revealed the secret to laymen, was put to death.) He started with an almost blank sheet and started the proof .  “Laura, if you do not understand a step, let me know, so I will clarify the proof,” he said. Let us assume that the square root of 2 is rational, that is it equals a/b, where a and b are whole numbers. “OK?,” Laura agreed. Then he went down, step-by-step and reached a contradiction. “See, the assumption is wrong, the square root of 2 cannot be rational.

But Laura did not like the proof. Erdos got annoyed. “I asked you to tell me at every step if you don’t understand something. You said nothing.”

“Why didn’t you tell me at the beginning that this is all wrong?” said Laura. Erdos flipped his top.

I recalled that when Albert Einstein gave one of his last talks, at the end they unscrewed the black board and sent it to the Smithsonian. So I asked Erdos to certify the document, so I could keep it for history. He signed his name and p g o m a. d, signifying Poor Great Old Man Archeological Discovery. At age 70 he started to use LD for Legally Dead, and at 75 CD for Count Dead, for reasons unknown to me. 

Here is the actual “document” from that day:

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Beautiful, isn’t it.  Happy 100th, Paul!  Thanks for all the great memories – and, of course, mathematics!

If you are looking to read a little more about Erdős, you can read any of these:

Here are the sources for this post::