Stuart, 29, of North Pickenham asks: "What are the roots/is the history of maths? Was it developed independently by various people around the world?"
|A hypercube unfolded into three dimensions so you can see it|
To answer the second question first: yes.
The answer to the first question is a little trickier to manage in a paragraph, but here goes: The roots of human mathematical understanding are in a few mental capabilities common to all humans. These include: spatial reasoning, counting, logic and abstraction (the ability to notice common properties in different objects). The interplay between these properties is the key here, I think. By applying logic to spatial reasoning you get Euclidian Geometry and you can abstract from those principles to imagine four-dimensional hypercubes that we could never actually see. A similar process will get you from counting sheep to imaginary numbers. As discussed last month, I see this process as discovery not development - it so happens that conditions on this planet have been such that creatures with brains sufficiently complex to comprehend mathematical truths have evolved. It's a big Universe, I bet it's happening all over the place. And the truths will be the same, whatever is comprehending them.
Clare, 32, of Southampton doesn't like numbers. She wants to know "Why do you think humans feel the need to quantify things?"
Well Clare, as usual it is the farmers who are to blame. Pre-agricultural societies such as the Piraha lack number words. Crucially, they do not lack the cognitive ability to understand numbers, so when a culture needs to develop a complex counting system - due to the development of farming, say, or the sudden arrival of hordes of Anthropology students demanding that they count batteries (this happens more frequently than the development of agriculture) - they can, as dismaying as that may be for you.
Anonymous sets up a false dichotomy with his question: "Do you think there's a logic to the mathematics of quantum physics that we haven't discovered yet? Or is it truly random?"
As I understand it, there are several competing explanations for observed quantum phenomena, none of which are compatible with the relativity we observe in the Macro-Universe. When dealing with large numbers of repeated experiments, probability theory can be used to make fairly accurate predictions.
Finally, Tim, 62, of Weymouth wants to know "Since when was elfs the plural of elf?"
It never has been. The plural of "elf" is "elves". I used the word "elfs" in a list of non-existent supernatural entities. So whatever the hell "elfs" are, I don't believe in them. (Still undecided about elves.)