Mathematics originally meant measuring. Today mathematics is stll about measuring, but counting livestock seems trite. It seems to me better to consider mathematics to be a study of a special branch of truth.
I consider mathematics to be the study of that which can be proven in the geometrical sense. Today fashion in education precludes proofs in algebra. I wonder too, if it precludes real education.
But I have not defined algebra. I was rude to use the word algebra before defining it. I apologize, and hereby define algebra as the study of truth by use of equations. That definition should hurt the ears, because I have not defined equations, either.