“A computer gives the average person, a high school freshman, the power to do things in a week that all the mathematicians who ever lived until thirty years ago couldn’t do.” That’s Ed Roberts quoted in Hackers, a book published in 1984. So let me update his quote with my own: “My laptop gives me the power to run simulations in an afternoon that the fastest computers thirty years ago would have struggled with”.
This power has a downside. Computers are so fast these days that I’ve become lazy—mathematically speaking. A few decades ago, in my field of physical oceanography, it was routine to manipulate partial differential equations and solve complex integrals. I can do these things, if I put my mind to it. But I seldom do; there’s no need. These days, even ordinary differential equations that I learned to solve in undergrad get plugged into Mathematica most of the time or relegated to some less-than-perfect numerical method. And I can’t remember the last time I did multiplication longhand:
Brushing Up Science 