I loved how you wrapped it up! humor at its best.
Another issue to consider, though, is specialization. 100 years ago, even 50 years ago, people could master all the breadth of their subjects (in math/sciences). Who is the current Gauss or Einstein? Hard to tell, possibly no one can now have that effect alone.
Even 20-30 years ago, when Woz singlehandedly invented the personal computer, it was very different. (he says he had it all in his head at once, really amazing). You can read a beautiful interview here: http://www.foundersatwork.com/steve-wozniak.html
Conrad Wolfram recently gave a wonder TED talk on the subject. http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_m...
> We've done more with math in the last 20 years than they did in their entire 600 year history.
What Greeks did with advancing the math profoundly affected technology and sciences. What was done in the last 20 years does not even begin to compare in impact.
With computers, people won't perform the basic calculations in their head. But their strategy-forming about what, of the gigantic possibility space, they could or should ask the computer next will still require the same old concentration and working memory... and more.
This is quite likely true, especially for scientists and mathematicians. An interesting question for me though is whether the average citizenry is becoming better or worse at mathematics over generations.
The average person will do just fine in their lives without needing to factorize a quadratic equation. They will do swimmingly without knowing the relation between ln and e. The average person will, after high school, never again have to utter the word "pi" in a non desert-related setting. Similarly, "'x' equals" will become nought but a forgotten dream.
Modern life makes no mathematical demands of 98% of humanity. The only mathematical skill beyond basic arithmetic that most people need to know is compound interest, and most people don't know that.
Knowledge is driven by need, and there's simply no need for most people to be anything but marginally proficient in math.
Obviously, it was the men and women of the 1950s, who built computers and airplanes from nothing with little more than their wit, a grease pencil, and some twine, who were of the utmost in mental capacity and grit.
Since we're only 60 years from 1950, whereas 1869 is 81, we must be smarter than them. In fact, we're about as smart as people were in 1890. Ten years ago, we were as smart as people in 1900, but sadly such intelligence is ten years gone.
A corollary: in another 21 years, people will look back at this exam and just barely understand it. A few years after that, all hope is lost.