As children, we all loved mathematics and working out **puzzle**s. Mathematics was an all-important tool to answer questions, like "How many," "Who is older," "Which is larger." And **puzzle**s were of course everywhere. We did not stop to check a dictionary to ascertain that a **puzzle** is *something, such as a toy or game, that tests one's ingenuity*. We did not care about our ingenuity a little bit, but just thrived on learning new things and skills that the nature made us curious about. Growing up was a great fun.

Time brought a change. In school we were made to realize that learning is a serious business, and for many of us much of it has ceased to be entertaining. Although not for all. Some could not give up their erstwhile pursuits of mental entertainment. There are enough of **puzzle** lovers to provide a living for the selected few who invent and publish **puzzle**s - in accordance with the dictionary definition to challenge one's ingenuity, **puzzle**s old and new. The luckiest of the breed grew to become scientists, mathematicians in particular. Mathematicians solve **puzzle**s as a matter of vocation. Puzzlists seek **puzzle**s in newspapers, books, and now on the Web.

There are many kinds of **puzzle**s - **jigsaw** **puzzle**s, slider **puzzle**s, sliding blocks **puzzle**s, logic **puzzle**s, mazes, cryptarithms, **crossword**s, strategy **game**s, dissections, magic squares - it's hard to enumerate all known kinds. Puzzlists and mathematicians have their preferences. Most of mathematicians will probably deem classification of their occupation as **puzzle** solving a misnomer. (Due to their mindset they will likely to inquire as to the definition of * puzzle solving* - just in case.) Mathematicians call their

Solving both **puzzle**s and mathematical problems require perseverance and ingenuity. However, there is a profound difference between solving **puzzle**s and what mathematicians do for a living. The difference is mainly that of the attitude towards either activity. For a puzzlist, solving a **puzzle** is a goal in itself. For mathematician, solving a problem is an enjoyable and a desirable occupation but is seldom (with the exception, for instance, of great problems of a long standing, like Fermat's Last Theorem) a satisfactory achievement in itself. In most cases after solving a problem mathematician will try something else: modify or generalize the solved problem, seek another proof - perhaps simpler or more enlightening than the original one, attempt to understand what made the proof work, etc., which will lead him to another problem and so on. Whatever he does, he eventually gets a hierarchical network of interrelated solved problems - a theory. Why does mathematician seek new problems?

The reason is in that mathematics, even if perceived by many as a not very meaningful manipulation of abstract symbols, embodies in its abstractedness a rare power of explanation. Some mathematics directly explains natural phenomena, some sheds light on other portions of mathematics or other sciences. (A famous Russian mathematician V.I. Arnold even categorized mathematics as *that part of physics in which experiments are inexpensive.*)

Understanding in mathematics is born not only from formulas, definitions and theorems but, and even more so, from those networks of related problems. The process is very much like distilling the many meanings of a word in a Thesaurus into a unique shade of the concept that it represents. Mathematics - the most exact science of all - is least of all a dictionary of term definitions. Mathematicians seek knowledge. In search of knowledge, they enjoy themselves tremendously inventing and solving new problems.

The Interactive Mathematics Miscellany and **Puzzle**s site makes an attempt to present mathematics as an evolving and entertaining subject in which an unsuspecting visitor may take an active part.

Dr. Alexander Bogomolny is a former associate professor of mathematics at the University of Iowa and currently a developer of an award winning site **Interactive Mathematics Miscellany and Puzzles**.The site is an encyclopedic collection of K12 math articles, problems,

Dr. Bogomolny is a graduate of the Department of Mathematics of the Moscow State University (1971) and holds a Ph.D. in Mathematics (1981) from the Hebrew University of Jerusalem, Israel.

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