Happy Birthday, Carl Friedrich Gauss!

April 30, 2012 3 Comments

Happy Birthday, 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 Newton, Euler 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.

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Happy Birthday, Leonhard Euler!

April 15, 2012 5 Comments

Happy Birthday!

Happy Birthday to Leonhard Euler!

What can I say about Leonhard Euler that hasn’t already been said?  Not much.  Born in Basel, Switzerland on April 15, 1707, Euler showed his mathematical talents early.  By the age of 7, Euler’s father hired a private mathematics tutor to work with him.  By the age of 13, Euler was attending lectures at the University of Basel.

At the age of 14, Euler began attending the University as a student.  It is here that he caught the eye of the great Johann Bernoulli (It seems that everything this man touched turned to gold!)  According to Euler, “I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. … True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand …”

Once finished at the University, Euler spent most of his professional career in Russia at the St. Petersburg Academy of Sciences.  During his career, Euler made significant contributions to the fields of analytic geometry, geometry, number theory, trigonometry and calculus as well as in several areas of physics.

All was not smooth sailing for Euler, however.  In 1738, he lost one of his eyes in an accident from an experiment involving light diffraction.  In 1771, Euler contracted an illness that left him almost completely blind in his remaining eye.  However, despite being essentially blind, Euler still managed to produce hundreds of original mathematical papers.

By the time of his death in 1783, Euler is credited with over 900 mathematical publications.  He was so prolific a mathematician that the St. Petersburg Academy of Sciences continued to publish his work for nearly 50 years after his death!

If you are interested in reading more about Euler, check out one of these resources:

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

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