The Mathematical Image

The proof is elegant and the result profound. Still, it is typical mathematics; so, it’s a good example to reflect upon. In doing so, we will begin to see the elements of the mathematical image, the standard conception of what mathematics is. Let’s begin a list of some commonly accepted aspects. By ‘commonly accepted’ I mean that they would be accepted by most working mathematicians, by most educated people, and probably by most philosophers of mathematics, as well. In listing them as...

 Thomas Jefferson was a Scientist

Thomas Jefferson was a scientist. That's how he described himself. When you visit his home at Monticello, Virginia, the moment you enter its portals you find ample evidence of his scientific interests - not just in his immense and varied library, but in copying machines, automatic doors, telescopes and other instruments, some at the cutting edge of early nineteenth-century technology. Some he invented, some he copied, some he purchased. He compared the plants and animals in America with Euro...

 We Must Interrogate Nature

Greek mathematics was a brilliant step forward. Greek science, on the other hand - its first steps rudimentary and often uninformed by experiment - was riddled with error. Despite the fact that we cannot see in pitch darkness, they believed that vision depends on a kind of radar that emanates from the eye, bounces off what we're seeing, and returns to the eye. (Nevertheless, they made substantial progress in optics.) Despite the obvious resemblance of children to their mothers, they believed ...