### 1.3.5 Unintended Successes

There are many examples of m pure mathematics which were studied for their own sake but later have been found to be very useful e.g matrices

Matrices were invented by two English mathematicains called Sylvester and Cayley in the mid 1800's

In the 1920's Heisenberg presented his thesis on Quantum Mechanics in Germany. The work was brilliant but the tutor made one comment Why did you not use matrices to do some of your calculations? To which Heisenberg replied what are matrices??

It transpired that this German tutor had actually studied under Sylvester and Cayley many years ago and when he saw the thesis he remembered the strange quantities called matrices that they had played with Today matrices are an indispensable TOOL

There are many strange coincidences where mathematics that was never conceived as being useful has turned out to be useful