Atiyah: The point that I was trying to make there was that really important progress in mathematics is somewhat independent of technical jargon. Important ideas can be explained to a really good mathematician, such as Newton or Gauss or Abel, in conceptual terms. They are in fact coordinatefree— more than that, technology-free and in a sense jargon-free. You don’t have to talk of ideals, modules or whatever—you can talk in the common language of scientists and mathematicians. The really important progress mathematics has made within two hundred years could easily be understood by
people such as Gauss and Newton and Abel. Only a small refresher course in which they were told a few terms—and then they would immediately understand. Actually, my pet aversion is that many mathematicians use too many technical terms when they write and talk. They were trained in a way that, if you do not say it 100 percent correctly, like lawyers, you will be taken to court. Every statement has to be fully precise and correct. When talking to other people or scientists, I like to use words that are common to the scientific community, not necessarily just to mathematicians. And that is very often possible. If you explain ideas without a vast amount of technical jargon and formalism, I am sure it would not take Newton, Gauss, and Abel long—they were bright guys, actually!