> I don't really see sympy and the like surpassing Mathematica. Given enough time, it will happen. There are several reasons. One, people who publish mathemati

> I don't really see sympy and the like surpassing Mathematica. Given enough time, it will happen. There are several reasons. One, people who publish mathematics academically are reluctant to use a closed-source tool to create their results, because those results can't be examined and verified at their source. This issue pushes people toward sympy/Sage/Jupyter and other similar open environments, even though at the moment they aren't as powerful as the Wolfram environment. For example, imagine that the four-color map problem (the first significant computer-aided result in mathematics) had been solved by a close-source environment (instead of an open, freely readable source as it was). If that had been true, people would still be arguing about whether the result was valid. Two, an open-source environment like sympy attracts technically skilled people intent on improving it, knowing that they're contributing to a tangible kind of progress that's clear to everyone, and then freely copied by like-minded people into different environments, all with the intent to advance human knowledge, rather than make stockholders happy. Three, this may not be apparent, but the existence of environments like Sage and sympy are putting tremendous pressure on Wolfram to price their products more reasonably. Instead, and so far, Wolfram's strategy has been to design enticing free samplers like Wolfram Alpha as gateways to their expensive offerings. > If when I'm buying Mathematica I'm paying for a proper implementation of the risch (integration) algorithm, it will have been money well spent. This is a perfect example -- until Mathematica is open-sourced, no one can know whether the existing algorithm is either complete or optimal. Also, given that research into this algorithm has enormous practical value in both mathematics and computer science, it's a shame that a large segment of the effort is being carried out in secret. I'm sure those responsible for its present form would love to publish their results, if only for the fact that this would get them fired and possibly prosecuted. There was a time when people who made an original contribution to human knowledge would publish their results in the open (think Einstein) and take pride in their contribution to the common good. It seems those days are past.