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Programming is 10% science, 20% ingenuity, and 70% getting the ingenuity to work with the science
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To type code,you don't need university,because people who went there make possible that no matter what computer you use,processor instructions,cpu memory management,and all the rest of your hardware, if you open your IDE, in 2 minutes you can make your monitor print Hello World
So, only if you want to innovate,to create something new
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That's correct
You can code and make programs in your house,but like every other professional occupation,you need something that certificate you know the business,in this case, architecture, metrics,methodologys,best practices,and as you said, mathematic,logic and algorithm fundamentals
If you go to a doctor,you need to see something that certificates he knows whats he is doing
Same with a lawyer,architect
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If you want to be ALWAYS a coder, a operative level person,you don't
You only need to demonstrate that you can do the job (experience, certifications, and so on)
If you want to negotiate contracts,estimate projects,design software architecture, management of resources you need some kind of professional education
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If you want to make machine learning software, you must have intense knowledge in Physics and Computer Engineering.
Most companies make ads at StackOverFlow, gave a minimum requirements of a degree in Physics or Math.



