Yes, I think so. Maths gives a striking example. Many things that to us are elementary concepts you teach to children - some of them even to very young children - were beyond the capabilities of even the most advanced thinkers in the past.
Including:
- Positional notation with zeroes. The Babylonians had a primitive place notation - but without a trailing zero. They had base 60, but if we had the same system to base 10 you could distinguish 36 from 306 but couldn't distinguish 306 from 3060 (you understood what it was by context). See Positional notation
- Idea of zero as a number in its own right - dates back to 9th century India 0 (number)
- Negative numbers - most early civilizations treated them as absurd, and only came into common use after 7th century India for debts Negative number. Mathematicians in the past would rewrite equations in order to avoid the need to use the absurd negative numbers.
- Fractions - our modern idea that you can express the ratio of any pair of numbers e.g. 7/5 as a fraction is surprisingly recent - for a long time they worked with them in what seems to us a clumsy fashion using "Unit fractions" - only fractions with 1 on the top. For instance, 4/5 could be written as 1/2 + 1/4 + 1/20 (or as 1/3 + 1/5 + 1/6 + 1/10 etc.). See Unit fraction and Fraction (mathematics),
- Solution of the quadratic - a long history, originally many special cases and only some could be solved (made more complicated by the special cases you need to avoid negative numbers). Complete solution not until C16 Quadratic equation
- Solution of the cubic - major problem in the C16, is now considered rather basic stuff. Cubic function
I think fair to say, that if you took any of us, and put us back into anywhere in the world prior to say around C7, even our most brilliant mathematicians and scientists - then if brought up in C7, anywhere in the world - they would not understand any of those concepts.
If they became an extremely brilliant mathematician of their time - then they might perhaps come up with a novel way of solving the quadratic equation as a result of their life work in mathematics - or some new proof of a geometrical result or some such. Because that's what brilliant mathematicians did back then.
See for example al-Khwarizm who had six chapters devoted to the six then known types of quadratic equation (all written to make no use of negative numbers as mathematicians of his time didn't recognize them as valid numbers)
Here by squares, he means our x^2 and by roots, our x. His six chapters covered:
- Squares equal to roots.
- Squares equal to numbers.
- Roots equal to numbers.
- Squares and roots equal to numbers, e.g. x^2 + 10x = 39.
- Squares and numbers equal to roots, e.g. x^2 + 21 = 10x.
- Roots and numbers equal to squares, e.g. 3x + 4 = x^2.
See Quadratic etc equations
These various maths concepts are quite tricky to grasp even today for young children. If you haven't tried to teach them, and perhaps don't remember your own childhood too clearly - you might be surprised how very tough it is for young children to get these ideas. But it's not so surprising when you discover how long it took for humans to develop the ideas in the first place. Basically in our schools we attempt to fast forward our children through several thousand years of human mathematical development in a few years.
And similarly if you took any of those mathematicians from the past and they were born and brought up in our society (assuming they made the same choice to be a mathematician in our society), then I'm sure they would learn the concepts of zero, and ratios, and negative numbers as quickly as any of us - as a child - and go on to master algebra quickly.
Things like quadratic equations are child's play to any mathematician given modern education and we have put all the ancient solutions + more in a single one line equation.
They would then go on to prove results in advanced mathematics that we couldn't even begin to explain to our predecessors without giving them a modern education first.
I wonder sometimes - what simple basic concepts we might be missing that our descendants might learn as children.
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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