You are in possesion of a card set. On one side there is a shape, a circle or a triangle. On the other side there is a colour, blue or yellow. There is one rule: If there is a circle on one side of a card, then the other side is blue. You have four cards placed on a surface next to each other, one depicting a circle, one a triangle, one is blue and one is yellow.Which card or cards do you need to turn around in order to confirm the abovementioned rule?
Defining criteria
What is logic and what is mathematics?
The Merriam-Webster Dictionary defines logic as follows: a science that deals with the principles and criteria of inference and demonstration: the science of the formal principles of reasoning
mathematics is the science of abstract structures and patterns, constructed out of different statements, which need to be proven true
Identifiable set of operations & Symbol system
object -> actions -> statements -> relationships
Henri Poincaré distinguished between the memory for steps in a chain of reasoning and the appreciation of the links between propositions. The later was regarded as the more important ability for a mathematician.
There are symbol systems for encoding actions performed upon objects and symbol systems for relations between objects.
1 + 1 = 2 | 2 - 1 = 1 | 2 x 2 = 4 | 4/2 = 2
Prodigies
Extraordinary Individuals are Individuals with...
... remarkable counting abilities, such as Shakuntala Devi: she was able to multiply two 13 digit numbers in 28 seconds in 1980
... intuitive understanding, such as Srinivasa Ramanujan: he wrote down nearly 3.900 new results (theorems, identities and equations)
... insight into abstract structures, such as Alexander Grothendiek: he worked on a rebuilding of algebraic geometry
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