Advanced Maths with Sage, AI, GPT? How? Why?

Summary — Read codes on abstract structures, match them with books, and make new structures with the help of books alone. Train on Sage-like software.

We need some structured information to automate abstract and applied math. Let’s focus on abstract math today. If we have pre-written structures of mathematical entities, their shapes, forms, and instantiations, why not use them with deep learning that reads advanced texts? Instantiate it and give it a form?

Sage is one such software. Here is a snippet,

We need structures.

Can AI read notes online and create instances of these structures in mathematics, particularly abstract mathematics? How?

Can AI instantiate these structures? How?

Initially AI can use Sage like softwares.

Automatic class creation per new abstract object is a necessary thing, this can be learned from Sage Object Oriented Programming formats.

It can help in doing advance mathematics by researcher if automated classes per abstract object can be determined.

Following the above, if the AI tools can do the exercises on say Nilpotent Groups, it would be a game-changer.

It won’t take away jobs; it would help professors do research with interactive mathematics.

It is needed to reach new heights in mathematics.

You need to read the structures in books, make automated Object Oriented Classes, and then create instances.

Make sure to follow one book, such as Herstein for algebra. In every book, you are faced with different terminology; for example, one book uses left cosets, while another book uses right cosets. Till AI learns this, stick to one book. Then, the research concepts.

Another one of Sage software here, can AI generate such, it can if there is a will to do it.

Once AI understands the codes of these Maths written by humans, things may change.

Internally, AI can now understand coding, as it can code.

Humans write these codes, let’s make AI read these, and then instantiate examples with it and generate more.

So, would we need more coders to code all the math into Sage-like Software Tools? Or can AI make more code for Sage-like software? AI should be able to automatically generate codes for all structures of Mathematics and end up in its own AI Software in line with Sage?

Can AI use Sage then to prove concepts and theorems?

Time to ask some Professors?

Thanks for reading,