Quote:
Originally Posted by Ninguem
What's your take on it?
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Your question is rather vague & open-ended.
If the underlying question you are
really asking is whether higher mathematics is useful and/or necessary as a consumer of the digital age, it all depends upon what are your goals. What do you want to understand?
Higher mathematics is critical to understanding the guts of cryptography, graphics, compression, & search, & here are a few reasons/examples why:
- A number of arguments made in cryptography are based on inductive proofs, discrete statistics, all mixed in with some emerging ideas coming from abstract algebra. Each one of these disciplines is covered in advanced undergraduate courses, but true mastery only comes in post-graduate work.
- Graphics (as does neural networks...) attempts to do very smart things in the smallest number of processor cycles. Although the code which will be executed may seem exceedingly simple, it is based on increasingly sophisticated calculus & physics.
- Historically, compression came as a end result of the work pioneered by Claude Shannon in information theory. From an educational perspective, this material isn't typically seen until graduate school.
- Search used to be based on databases & fast string comparisons. Now, it is using some leading edge research done in machine learning -- teaching machines algorithmically how to discern if any particular solution is more efficient than another, & letting them figure out themselves what data really answers any particular question. The mixture of statistics with linear algebra to deal with millions of variables at the same time is cutting edge research.
This obviously is not meant to be a comprehensive list. It only begins to attempt to tie topics back to their theoretical underpinnings.
Personally, I find this stuff fascinating, but this material isn't learned merely from Wikipedia pages; rather, Wikipedia articles will give only a very high-level summary. To master & understand the underlying theory takes years. Shortcuts don't exist. Patience, tenacity, & curiosity are required.