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.
Conrad Wolfram recently gave a wonder TED talk on the subject. http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_m...