Depends on how far back you go. For a Roman, mental multiplication was exceedingly difficult. Clearly this implies that there was a period of upward trend. If we believe that we're dumber than some of our forefathers, then there must have been a peak at some point in the past (or perhaps even multiple peaks, but we don't have enough evidence to suspect more than one, so let's assume it's an approximately parabolic trajectory).
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.
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
I'm sorry, but being able to perform arithmetic does not equate to higher intelligence or mental capacity. As society begins to perform more calculations via computer, it will allow us to begin address more abstract and higher level mathematics, problems which would be near impossible to address had we been required to do the math with grease pencils.
If you can't do arithmetic in your head, the other problems are considerably more involved. I can't see a time where the ability to do mental multiplication is not a prerequisite for higher maths.
If by "fine", you mean, "with Bronze Age math", then sure. The Greeks figured some great things out in their time, but your average math undergrad would school their best in most things. We've done more with math in the last 20 years than they did in their entire 600 year history.
They didn't need to multiply in their heads to lay out the foundations of geometry and discover irrational numbers. Every generation of math grads from then on begins studies from their achievements.
> 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.
They would be wrong. Calculus is huge. Linear algebra is huge. Boolean logic is insanely huge. The things we can do with numbers now make possible our modern world, something that members of HN don't need me to tell them.
All of the fields you mentioned get by mostly with modes of mathematic proof introduced by Greeks. In that sense there wasn't much new since Pythagoras until the infamous proof of map coloring theorem recently.
Performing math in your head requires concentration and a working memory. These improve with practice and are useful for more than just math (like following complex writing or multiparty discussions).
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.
> As society begins to perform more calculations via computer, it will allow us to begin address more abstract and higher level mathematics, problems which would be near impossible to address had we been required to do the math with grease pencils.
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.
I think there's a point where further mathematical prowess no longer holds any sort of competitive advantage for the average person. That point is probably grade 6.
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.
They weren't meant to. The purpose of Roman numerals was to be a convenient notation that you would read on and off of an abacus. All actual calculations were done on an abacus.
You bring up good points, but mental multiplication is a bad example. That's certainly more related to an inadequate notation for the task than any trend in human intellect.
Well, since the entrance exam would likely be geared toward people graduating high school, wouldn't the entrance questions have to be at that level of educational experience?
Considering construction finished just 3 years before this exam was published, and the charter was formalized just 10 years before, I would say that MIT (known as Boston Tech from 1866-1916) was not among the foremost technical institutions. At the time.
From the wiki page, it seems like it was actually one of the first technical unis around: "a new form of higher education to address the challenges posed by rapid advances in science and technology in the mid-19th century that classic institutions were ill-prepared to deal with." (http://en.wikipedia.org/wiki/History_of_the_Massachusetts_In...)
The problem with anything built for military/medical/emergency service use, is that by the time you have ruggedized it, packaged it, setup service and support and got it approved by a dozen different agencies - well even a simple flashlight really does end up costing $100
I thought we were all supposed to have been dumbed down compared to our illustrious forefathers?