George Boole and the wonderful world of 0s and 1s


Ems Lord in Plus Magazine:

The story of George Boole (1815-1864) is an extraordinary example of collaboration across the centuries. Boole's work provided the foundations for today's computers and mobile phones, yet he died many years before the first computers were invented. How did a mathematician who lived, and died, in the nineteenth century have such an impact on our twenty-first century technology? This is the tale of self-taught mathematician George Boole and the modern day engineers who recognised the power of his ideas.

Boole's early life

George Boole's early life did not mark him out as a ground-breaking mathematician. Born in Lincoln in 1815, he was the son of a local cobbler and would have been expected to work in the family shoe making business as he grew older. But his father's business collapsed and Boole became a local school teacher instead. By the age of 19, he was already a head teacher, spending his evenings and weekends exploring his mathematical ideas. His initial writings appeared in the Cambridge Mathematics Journal and his work soon attracted the attention of the Royal Society. In 1844 Boole was awarded the Royal Society's Royal Medal for his paper On a general method of analysis. His increased profile led to the offer of a professorship in mathematics. Boole left behind his Lincolnshire teaching career and headed off to Cork University to pursue his mathematics full-time, and make the break-through that still impacts on our lives today.

The breakthrough

During his time in Ireland, Boole focused on combining logical deduction with algebra. He argued that the logical approach taken by the ancient Greek philosopher Aristotle and his followers was insufficient for addressing certain types of problems. He focused on those problems where individual statements, or propositions, could either be described as true or false. Boole's work required the development of a new branch of algebra and its associated arithmetical rules.

To introduce Boole's ideas, consider these two propositions:

A = David Beckham is a footballer

B = Quidditch is an Olympic sport

We know that one of them is true and the other is false (I'll let you decide which is which!). But what about the statement A AND B: David Beckham is a footballer AND Quidditch is an Olympic sport? It's clearly false! For it to be true, we would need each of A and B to be true, which isn't the case. Therefore, the statement A AND B is false. If we assign the truth value 0 to a false statement and the value 1 to a true one, then we can write the AND connective as a kind of multiplication: AB stands for A AND B, and since one is true and the other false, we see that AB has the truth value 0 x 1 = 0.

More here.