Isn't it strange to think that modern high schoolers undoubtedly know more about mathematics and various disciplines of sciences than ancient or even not so ancient scientists who devoted their entire lives to certain subjects? I mean, if you think about it, it's not too ludicrous. They definitely have a greater grasp on mathematics than, say, Pythagoras, who's crown jewel of a discovery is currently being taught to 6th graders around the world. Take Isaac Newton, for example, a man who appears in textbook after textbook as the late-renaissance wonder man who invented integral and differentiable calculus. He discovered the basics for physics, including the laws of motion, gravity, and optics. However, they are exactly that, the basics. Now, do not think I am bashing Newton by any means. Nor am I saying that high schoolers know all that he knew or are more intelligent than him. He is possibly the greatest thinker in the history of man; however, modern education has advanced so much so that today's teenagers now take the knowledge that past scientists and mathematicians spent their lives discovering for granted. More and more advanced knowledge and problem solving skills are being exposed to a younger and younger audience in today's education system. That is not to say that past "ground breaking" discoveries were by any means easy. It was no more easy than a scientist today discovering the secrets to the quantum world.

Because of this, it is no surprise that seeming "amateurs" use frequency analysis and other cryptanalysis strategies that took centuries to develop. Let's take the credentials of a possible "amateur" cryptanalyst into consideration. He/She probably has some sort of upper level (comparative to a few hundred years ago) mathematic training including calculus and statistics and probably multiple years of taking English courses, all of this learned from high school. According to my previous assertion, wouldn't this count as a "sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics" (Singh 15)? I think so.