Are CASs useful in mathematics? I understand that computer-algebra systems are useful for physists, engineers, or other users of mathematics.  But are they useful in mathematics itself?
Specifically,


*

*Are they usually taught in undergraduate or graduate education in (pure) mathematics?

*Do the majority of professional mathematicians use them?

*Can they be replaced with free and open source ones like Maxima, PARI/GP and Sage?

*Would there be a serious problem if a student or a resercher in mathematics did not use them?


My main concern is that if mathematics students or reserchers have to use blackbox software like Mathematica, it seems to me against the spirit of mathematics: never treat results as truth until their proof is provided.

The answer is a big YES. Computers and CAS have brought experimentation to Mathematics. Here are some links that you may find interesting:


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*Wikipedia page on Experimental Mathematics.

*Link to the Experimental Mathematics journal.

*Experimental Mathematics: Computing Power Leads to Insights.

*Ten Problems in Experimental Mathematics, by David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor and Eric W. Weisstein, in the Mnhly.


Or just Google experimental mathematics.
