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Friday, July 1, 2011

Words in mathematics

If you browse through an index of any mathematics book you will see a lot of words that have a meaning outside mathematics. I don't think this is true for the other sciences in the same degree. Take physics for example. If words from physics are used in some non-scientific conversation, 'speed' or 'force' for example then they still ( roughly perhaps ) have the same physical meaning.

When defining new mathematical ideas, concepts, objects or methods mathematicians often borrow words from the natural language and assign a mathematical meaning to it. The mathematical language is hard to grasp for the non-initiated. When a mathematician hears the word 'group' it isn't likely that he associates it with a group of -people-, groups appear everywhere in mathematics. Ring, field, graph, network, category are also examples of words borrowed by mathematics.

People from the early 20th century already knew the word 'computer'. Becoming a 'computer' was a career-option in those days. The insurance industry needed lots of them. To 'compute' premiums for example. The field of computing life-insurance premiums has evolved in a science of its own, the actuarial sciences. A mix of business administration, statistics ( they maintain 'death-tables' ) , mathematics and law. So the word computer got a different meaning over time. I am not sure but I have the impression we use it less and less. We have laptops, phones, tablets and what have you. Nobody calls their phone a computer although it is more powerful than the first 30,000 dollar costing IBM PC.

I am currently studying Linear Programming. Another borrowed word dating back to the 1940s. Although Alan Turing was coding these days we know he was decades ahead of his time. How many times has it been explained that Linear Programming is not at all like computer programming? Any serious Linear Programming however can't be done 'by hand'. Computers are required to do the number crunching. Think of matrices with hundreds if not thousands of rows and columns. Even the simplest problems have five or more unknowns in canonical form.

Besides Linear Programming there are the fields of Integer Programming and Non-linear Programming. The latest books in these fields have the word Programming replaced by Optimization. Which, incidentally, is also the name of the OU course in that field. Otherwise the course would have been called 'Programming'. Try explaining that to your neighbor.

I have subscribed to Project Euler. I couldn't resist. It is the challenge, I suppose. I have solved the first problem. Well, as long as I practice math every day. Don't try quitting mathematics for a few months or so. You 'think' your brain can handle it, but that is merely memory-recall. Just stay mathematically fit.

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