Sometimes when you move a shape around in front of you, you end up with the same shape. Maths people call this symmetry, and have lots of names for different ways you can get back to the same shape.
For instance, if you flip a square around you get back the same square. This is called reflective symmetry.
If you spin a triangle around you sometimes end up with the same triangle. This one is rotational symmetry.
Galois spent a lot of time thinking about numbers instead of shapes. What he realised is that when you add and multiply numbers in lots of different ways, you sometimes end up with the same number at the end. And sometimes different numbers, when added and multiplied in the same way, also give you the same number at the end.
For instance, if you take 1, multiply it by itself and subtract 1, you get 1x1-1=0.
If you do the same with -1, you get (-1)x(-1)-1=0. A different number, using the same pattern, gives us the same result.
What we're seeing here is that there are some symmetries in numbers, not just shapes! Galois theory is all about the nitty gritty of how these number symmetries work, how to find them, and how to use them to do interesting mathematics.
For instance, if you flip a square around you get back the same square. This is called reflective symmetry.
If you spin a triangle around you sometimes end up with the same triangle. This one is rotational symmetry.
Galois spent a lot of time thinking about numbers instead of shapes. What he realised is that when you add and multiply numbers in lots of different ways, you sometimes end up with the same number at the end. And sometimes different numbers, when added and multiplied in the same way, also give you the same number at the end.
For instance, if you take 1, multiply it by itself and subtract 1, you get 1x1-1=0.
If you do the same with -1, you get (-1)x(-1)-1=0. A different number, using the same pattern, gives us the same result.
What we're seeing here is that there are some symmetries in numbers, not just shapes! Galois theory is all about the nitty gritty of how these number symmetries work, how to find them, and how to use them to do interesting mathematics.