Can Karatsuba Help Prof. Arthur Benjamin?

A lecture by Dr. Sarmad Abbasi

The mathemagician Arthur Benjamin squares a 5-digit number in his head.He performs the computation out loud, and this reveals that he is exceptionally talented. 

We show how the feat of squaring a number in the head can be done with considerably less effort. This method uses an idea of Karatsuba, who improved upon the classical multiplication algorithm that was in use for, possibly, “six thousand years.”

The idea that students can perform the same feat as Prof. Benjamin and historical anecdotes about how Karatsuba discovered his method makes this, hopefully,  an engaging talk. 

This lecture tries to generates interest in the classical problem of multiplying numbers, analysis of algorithms, and recreational mathematics. To fully enjoy this talk, we strongly urge the audience to watch Prof. Benjamin’s Ted Talk. 

For copyright reasons, we will not show Prof. Benjamin’s talk online. However, we will see it at the beginning of the talk.

The only prerequisite of the talk is 8th grade mathematics. In particular we will use the algebraic identities like (a+b)^2 = a^2 + 2ab + b^2. Small parts might use a bit higher mathematics but won’t really be needed.

This will be a classical chalkboard lecture.