Comments on: Mathematica and The American Mathematical Monthly’s “Problems and Solutions” Section

By: mohamadi

mohamadi — Tue, 25 May 2010 11:01:41 +0000

how i can send my problem(integral)?

By: اخبار

اخبار — Sun, 02 May 2010 14:45:23 +0000

thank you so much

By: Matt Enlow

Matt Enlow — Fri, 06 Nov 2009 19:42:07 +0000

@Barrett: I will leave that as an exercise for the reader, though I will say that one of my favorite quotations is from Michael Murphy: “Behind every technological innovation lies a withered human faculty.”

@Stan: I maintain that there is value in the “journey” just as much as in the “destination”. I may be biased, as a math teacher, but I believe that to be singularly focused on The Answer is to miss so much that is beautiful about mathematics and the patterns contained therein.

Obviously if you are doing complex calculations as part of your job, then most likely you don’t have time to appreciate the journey, and that’s understandable. But I’m guessing the AMM publishes these problems not because they simply want The Answer, but because, as Mr. Pavlyk mentions, they provide challenges and entertainment for many people.

Also, I would have to respectfully disagree with your assertion that “in 10-20 years such problems… will be viewed as no more interesting than computing digits of Sqrt[2].” First of all, the latter is an infinite process, not a problem with a solution. And there is nothing to be gained along the way, as we know that the digits will never terminate or repeat. But there are still other questions to ask. Are there ANY patterns in the digits? Are the digits truly random? Can we notice anything if we look at the decimal expansion in other bases? What are some good rational approximations to Sqrt[2]? Are there patterns in those numbers?

The best questions leave many other questions in their wake on the way to their solutions. And the fact that others have most likely already investigated and answered these questions does not diminish the joy I derive from pondering them myself.

Is there a character limit for these comments? I’m surprised I haven’t exceeded it. Sorry, this is a hot-button issue for me.

By: Alec Mihailovs

Alec Mihailovs — Thu, 29 Oct 2009 05:58:07 +0000

For problems like that, getting the answer is not good enough – the solution is required.

It would be nice if Mathematica could provide it, too, and not just the answer.

By: Stan Wagon

Stan Wagon — Thu, 29 Oct 2009 01:52:02 +0000

Do you send these solutions to the editors. Do they consider them solns? I too use Mathematica on such problems in many journals. I feel that in 10-20 years such problems — having solid algorithmic solutions — will be viewed as no more interesting than computing digits of Sqrt[2]. Yet journal editors and problemists seem not to care that their problems can be solved algorithmically. Re M Enlow comment: I think problemists need to be more imaginative — some journals publish very many constrained optimization problems, but they all have a sameness to them and many (low degree) can be solved algorithmically.

By: Barrett

Barrett — Wed, 28 Oct 2009 21:52:27 +0000

What might technology undo?

By: Matt Enlow

Matt Enlow — Wed, 28 Oct 2009 18:34:21 +0000

This seems, to me, to take a lot of the fun out of solving challenging problems. Sometimes we get so excited about what new technology can do, we don’t bother to step back and think about what it might undo.

By: Luboš Motl

Luboš Motl — Wed, 28 Oct 2009 18:18:14 +0000

It’s doing pretty efficiently!

An e-friend of mine recently complained that in similar calculations, (-1)^(1/3) gives the complex root, rather than -1 as expected by schoolkids – and maybe even high school kids. He thinks that there should exist a high school mode.

By the way, how Nadiya is doing, O.P.?