To climb a higher mountain, you might have to look somewhere else.
When you’re thinking about next school year, maybe you think, “A lot like this year, but I’ll make improvements and aim even higher.” That’s an admirable motivation.
But it might be futile.
In mathematics, the idea of local maxima and minima helps to describe the fact that in complex mathematical graphs, what seems like the highest point might just be the highest point that you can see. To get to a higher point than the local maximum, you might need to head to a completely different area of the graph.
Put another way: if you want to climb the highest mountain and you head east-ish from Michigan, you’ll eventually be climbing the Appalachian Mountains. You can head up and down Appalachia until you find Mount Mitchell, where you’ll rise to 6,684 feet. But if you want to aim higher than that, you’ll fail – it’s the local maximum. To get anywhere higher, you’ll have to come down from the mountains, go west across long plains, and after more than a thousand miles, you can start scaling much higher peaks than anything in the Applachian Mountains.
You can’t get to the Rocky Mountains by continuing to climb Appalachian Mountains.
In short: if you want to achieve bigger things, you might have to head away from every achievement you’ve already made; the higher peaks might be elsewhere.