Advanced Mathematics & Software Tools.

... there are many tools.

i think that Skilled Mathemathicians solve challenging problems, far quicker, far more precisely than less skilled mathematicians and/or computer programmers.

i suspect that using Basic Tools with Abstract Methods of Advanced Mathematics can outperform crude software automations by far.

... i think Knowledges, Theories, Experiences, Theorems, Proofs, Lemmas, etc. - are also Tools, 'Mental Tools'.

... i think not only Strict Sciences - as for example: Mathematics, Computer Sciences, etc. - can have 'Mental Tools'.

... can 'complex integrals' be solved better using Algebraic Structures as Rings, Groups, etc ... with/or without other Mathematics Tools ?

... i supsect it's possible & efficient.

... etc.

There are Software Tools as Wolfram Mathematica, MathWorks MatLab, Microsoft Excel, probably more.

... i know so little, but i suspect that there are 'extension points', 'plugins', 'scripts', etc.

... should we investigate?


... i think Wolfram Alpha should be mentioned as well, it's more than 'Mathematics Search / Computation Engine'.