Most prodigious calculators are, in fact, bad at math.
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Mathematics is often called the "science of numbers," and I believe most people think that the work and fun of a mathematician is doing calculations. This is a gross oversimplification and, between you and me, it often makes mathematicians a little uncomfortable.
The discipline deals with many fundamental concepts – shape, size, movement, set, symmetry, structure, and others – and number is just one of them. Years ago, when income tax returns were still on paper, and we had to do the calculations ourselves, a neighbor kindly invited me to help him. I think he never understood why I didn't jump for joy.
Regularly, individuals emerge with a phenomenal ability to perform long and complicated calculations in their heads with great speed: multiplications and divisions of numbers with many digits, calculations of powers, roots, and even logarithms. The impression caused by these feats is such that in the past many of these individuals were publicly presented as circus attractions. They often exhibit other skills, such as quickly identifying the day of the week for distant dates or accurately estimating areas and volumes just by looking at objects. It is a rare, surprising, and mysterious talent. And it has little or nothing to do with mathematics.
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