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Most children learning arithmetic in school -- mostly by rote memorization -- are never even told about the beauty of true, deep mathematics. They graduate and live their lives with no concept that mathematics defines the soul of the universe.Here are a few hints of the depth that is hidden from most people:
- The Square Root of Negative One. What number when multiplied by itself equals negative one? Well, there is no such number. And yet, we define that it exists, call it "i", and use this imaginary number to design electronics. There would be no radio, video, phones, or computers without the square root of negative one. I think this makes electrical engineers true wizards.
- Transforms. If you have a complex mathematical problem to solve, you can often define a new universe with different mathematical rules where it can be solved much more simply. You transform the problem into that universe, solve it, and then transform it back. Does this universe really exist? Well, it works. That's all I know.
- Euler's Identity. If you take "e" and raise it to the product of "i" and "pi", then add 1, the result is zero. This equation has the base of the natural logarithms "e", the square root of negative one "i", the ratio of the circumference to the diameter of a circle "pi" (which shows up virtually everywhere in mathematics and physics), the multiplicative identity "1", the additive identity "0" -- and nothing else.
Stanford University mathematics professor Dr. Keith Devlin has said, "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence."I look at the very deep work currently being done in mathematics, and am chastened by this thought: All of the great mathematicians of the past had no idea that their purely theoretical work would become the basis of vast technological industries. What will tomorrow bring?
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