Keith Kendig compares math to the Hawaiian islands:
Hawaii may look like a group of separate islands, but actually the islands are just the highest peaks of an immense, mostly-submerged mountain range. All that water hides their underlying connectedness, their oneness. Mathematics may similarly seem like an archipelago of different areas — geometry, analysis, topology, number theory, applied math, and so on. My philosophy is that we’re really just seeing a few peaks of a huge mathematical mountain range. Our ignorance is like the water surrounding Hawaii and hiding its true mountain-rangeness. In mathematics, when we remove ignorance by making discoveries and advances, the water level in effect goes down, and when it drops far enough, separate islands are connected.
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