Having some background in the formal (mathematical) models I can say that most practitioners have no clue how to solve or analyze real problems. Most of them engage in a simple mechanical mathematical methods believing blindly in whatever comes out. Mathematics is a tool, a rigorous formal language, but it says nothing about practitioner's ability to understand what is really going on (and model it properly), which in most cases is very little. As a matter of fact, the more complicated the math (used to obscure the lack of real understanding of the problem) more likely the model is wrong. Formalizing reality in mathematical language is very hard, not to say in some cases nearly impossible unless you start simplifying (and throwing the proverbial baby out of the bath tub along with the water) at which point your model does not reflect the reality any more.
Thanks, that is the sort of understanding that is slowly emerging for me. I only have a very modest talent for math - took a fair number of courses, did some self-study, and I usually did OK if I worked at bit, but found some of it beyond my pay grade.
After short (4y) stint with formal methods, I worked on many cutting-edge ML problems, never, ever have I had to use fancy math to solve problems (well, FFT, FHT, and similar transforms are the top, some integrals & derivatives), but for the most part, addition, multiplication and some form / approx of exp was sufficient. If the author of the paper can not state his case in plain words before throwing at you heavy math he has failed to understand the problem and is just obscuring the fact. To cite Feynman (for whom I have outmost respect): "If you can't explain something to a first year student, then you haven't really understood [it]."
That resonates with me; it is an avenue of intellectual exploration. "If you can't explain something to a first year student, then you haven't really understood [it]." A lot of others have said similar things.
I am currently wrestling with the coherence (or the lack thereof) of frequentist statistics, which I studied in grad school. I just took it on faith that it made sense, decades ago. Now? I have my doubts.
Having some background in the formal (mathematical) models I can say that most practitioners have no clue how to solve or analyze real problems. Most of them engage in a simple mechanical mathematical methods believing blindly in whatever comes out. Mathematics is a tool, a rigorous formal language, but it says nothing about practitioner's ability to understand what is really going on (and model it properly), which in most cases is very little. As a matter of fact, the more complicated the math (used to obscure the lack of real understanding of the problem) more likely the model is wrong. Formalizing reality in mathematical language is very hard, not to say in some cases nearly impossible unless you start simplifying (and throwing the proverbial baby out of the bath tub along with the water) at which point your model does not reflect the reality any more.
Thanks, that is the sort of understanding that is slowly emerging for me. I only have a very modest talent for math - took a fair number of courses, did some self-study, and I usually did OK if I worked at bit, but found some of it beyond my pay grade.
After short (4y) stint with formal methods, I worked on many cutting-edge ML problems, never, ever have I had to use fancy math to solve problems (well, FFT, FHT, and similar transforms are the top, some integrals & derivatives), but for the most part, addition, multiplication and some form / approx of exp was sufficient. If the author of the paper can not state his case in plain words before throwing at you heavy math he has failed to understand the problem and is just obscuring the fact. To cite Feynman (for whom I have outmost respect): "If you can't explain something to a first year student, then you haven't really understood [it]."
That resonates with me; it is an avenue of intellectual exploration. "If you can't explain something to a first year student, then you haven't really understood [it]." A lot of others have said similar things.
I am currently wrestling with the coherence (or the lack thereof) of frequentist statistics, which I studied in grad school. I just took it on faith that it made sense, decades ago. Now? I have my doubts.