Do the Math

If you can convert your problem into a math problem, then you have done two things: (1) you have simplified the problem and (2) you have brought the full power of mathematics to bear on your problem. Translating a problem into a mathematical one is called mathematical modeling. Once a math model is chosen (which means that certain specific assumptions are made), there are centuries of mathematical techniques that can be used to answer your question. In this way, you tap the brains of mathematicians who have already solved your problem.

Unfortunately, many students have been permanently turned away from the power of mathematics by the "story problems" they were forced to solve (or at least forced to struggle with) in grade school.

"A train leaves San Francisco traveling south at 45 miles per hour. Meanwhile, another train leaves Los Angeles traveling north at 50 miles per hour. A fly, traveling at 100 miles per hour flies from the first train to the second train and continues back and forth until the trains collide. Assuming San Francisco and Los Angeles are 380 miles apart—how far does the fly fly?"

If this kind of problem makes your head spin, or makes you feel like you're about to go crazy, or simply breaks your heart—then you are not alone.

There were at least good intentions on the part of the math teachers who introduced story problems that had to be converted to math (arithmetic, algebra, or geometry). But they picked such awful problems. Who cares how far the fly flies? The teachers forgot about ganas—desire. Students must have a strong reason for solving the problem.

Albert Einstein was the world's greatest scientist, but he did not care about calculating numbers for the sake of exercising his mathematical dexterity. Actually, Einstein was only an average mathematician. He often made simple calculation errors, some appearing in his published works. Einstein said he did not care about how a particular atom vibrated. He wanted to understand how the universe was constructed. His Big Picture approach was so driven by his desire to know, that he slogged through the horrible complexities of tensor calculus.

Einstein viewed math as a necessary tool for communicating his findings to other scientists. In fact, Einstein explains that he used his physical intuition to solve problems—a combination of visual imagery and muscular feelings. In a visceral way, he knew when he had the solution. Then he would have to prove the results of his thought experiments to the scientific community by writing down the attendant mathematics. Einstein's advice to the rest of us is "Do not worry about your difficulties with mathematics; I can assure you that mine are still greater."

If your problem can be written as a mathematical statement, then you have a great advantage in solving your problem because there are vast mathematical resources at your disposal.

Rocket scientists find math indispensable for calculating the flight of a spacecraft to another planet. Not all rocket scientists are great mathematicians, but they all have a great desire to make their mission succeed. Even Einstein did not know about tensor calculus when he started his quest for the general theory of relativity.

Mathematics may not be your cup of tea, and this may be due in part to painful experiences in school. Mr. Escalante demonstrated that he could teach advanced calculus to underprivileged high school students in East Los Angeles. He instilled in his students a great desire to learn, and they proved themselves brilliantly on the standard placement tests.

Math is not the problem—lack of desire is.

(By the way—if you're still curious—the fly flies four hundred miles before the trains collide.)

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