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I no longer understand my PhD dissertation

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Re: I no longer understand my PhD dissertation

#3
> Beyond scarcely stretching the boundaries of obscure mathematical knowledge, what tangible difference has a PhD made to my life?

The same thing a bachelors degree does for everyone else. You've proven that you can start, stick with, and complete a task that takes multiple years and a complicated set of steps.

Re: I no longer understand my PhD dissertation

#4

As a PhD in spplied math, I must say I concur wholeheartedly with the author. The true value of a PhD in a quantitative field is less about specific domain knowledge, and more in the set of general problem solving skills you pick up.

This raises an interesting question. Is the PhD process the best way to acquire those general problem solving skills? Or is there a better way to learn them?

Re: I no longer understand my PhD dissertation

#7
Math seems to have a very ephemeral lifetime in the brain. I skipped a year of college once, and when I returned I realized I had to basically abandon any major with a math requirement, because I had seemingly forgotten everything.

I'm currently struggling with an online Machine Learning class (the Coursera one... at the tender age of 43), and I can only take it (so far, at least... just failed my first quiz... fortunately I can review and re-take) because I was rather obsessed with matrices, oh, about 28 years ago. "You mean I can rotate things in an n-dimensional space without using trig?"

Re: I no longer understand my PhD dissertation

#9
First, I am not sure Functional Analysis is as obscure as some other areas. But, second, this just shows, once again, that one ought never to use "clearly," "obviously" etc in proofs.

It is the same principle as writing programs so they are easier for the next programmer to read. That person may be you.

Re: I no longer understand my PhD dissertation

#10
> Mathematics is an excellent proxy for problem-solving

I went to a special, maths focused high school class and this rings true on that lower level too. I am a reasonably successful programmer/architect today and I have -- repeatedly -- attributed my successful attitude toward solving my problems to the 1200 or so problems we solved during those four years. Our maths education was literally nothing else but solving one problem after the other.

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