LONG LIVE POLYA!, 14. Juli 2000

i must say that this is one of the most interesting books i've ever read. it is a must for teachers of mathematics and the sciences. polya exposes with an unmatched wit and cunning the art of breaking it down and analyzing parts of parts in order to arrive at a reliable and justifiable solution.

polya is the quintessential teacher and this teacher finds his writings both compelling as well as inspiring. this is NOT the last book by this great mathematician that i plan to read.

a word of advice for teachers: read it and REREAD it until you get the point. the teaching of mathematics is not a mere monkey-see-monkey-do regurgitation process. rather, it is the art of conveying to the student the problem-solving process. once the student has mastered this talent, the sky's the limit. and speaking of limits, the sky may just be a gross underexaggeration.

LOVE IT! got to say again, "BUY THE BOOK!" and this goes doubly for TEACHERS!

       Do You Want Your Kid to Be a Robot?, 7. April 2000

In fact, do you want to be a robot? I talked to a woman who took a whole semester in computer science and came out learning nothing. She told me this. My love affair with Real Math started with this book in a library. I was reading a book which had a bunch of interviews with the most successful programmers in the world. One was Czech and I do not remember his name. But he was asked the following question. "What in your opinion is the biggest mistake that programmers are doing in their educations or their work today?" He answered, "It's simple. They don't know how to solve problems. At our company, we have some simple books that tell you how to do this. The best is Polya's 'How to Solve It'. It has a little diagram in the back that completely runs you through a series of questions on solving math problems. But even in schools, they don't take this approach. Everything is by rote and repetition! You solve a problem and YOU DON'T KNOW WHAT YOU SOLVED! We have a lot of these little books." The late Isaac Asimov wrote a beautiful little book called "The Realm of Algebra". It's out of print. But he explains the entire realm of algebra in something like 150 pages. The best book I've ever seen about math. Math can be fun. Programming can be fun. But only if you ask Polya's questions in the back of this book. "What do I have to do to make this problem complete?""What is missing from this problem?""What could I add to make this problem solved?" A two page diagram in the back. And everybody knows that programming is just "crummy mathematics". BUY THE BOOK! BUY THE BOOK! BUY THE BOOK!. 2 pages in the end of this book and at least 50% of your math/programming problems are down the drain. Buy the books for your son if you are a Betty Crocker. Or your daughter. Or they will end up in the "Valley of the Dead". Solving problems in school for years and years and simply not knowing what they did! Good luck. Oh yes. One last thing. BUY THE BOOK!

       Die Mathematik hat auch eine intuitive Seite!, 13. Januar 2000

Polya's brilliante Anleitung zum Lösen mathematischer Probleme vermittelt auch dem Laien ein überaus stimmiges und nützliches Bild vom täglichen Brot des Mathematikers. Gerade indem sie keine unfehlbare Beweismethode liefert, die einfach ohne kreativ nachdenken zu müssen nur abgearbeitet werden muss, sondern den intuitiven Aspekt mathematischen Denkens betont, vermittelt sie viel von der Schönheit eleganter Lösungen. Anders als beispielsweise ein Ingenieur ist der Mathematiker nicht zufrieden, sobald ein bestimmtes Problem irgendwie gelöst ist, sondern meist beginnt hier erst der interessante Teil der Arbeit: Kann die Lösung noch vereinfacht werden oder gar bei der Lösung anderer, verwandter Probleme helfen? Oft werden ganze Zweige der Mathematik geschaffen, um ein bestimmtes Problem wie z.B. die kürzlich bewiesene Fermat'sche Vermutung anzugehen. Polya's Büchlein hat auch ganz konkreten Nutzen: Wer seinen Kindern, Schülern oder Studenten einfache oder schwere Mathematik beibringen will, tut gut daran, sich mit Polya in den Prozess der Lösungsfindung einzufühlen statt fertige Lösungen zu präsentieren. (Dies ist eine Amazon.de an der Uni-Studentenrezension.)

      Great for its time -- a classic, 22. Oktober 1999

This is a really good book about how to teach and how to think about problems that need to be solved with paper and pencil. Of course, it doesn't treat the way we handle problems today with computers. But it's still a classic book.

       Useful in many areas, 28. April 1999

I used the techniques in How to Solve It to find my latest job. It's an approach to attacking tough questions that should be useful well beyond the mathematical arena.