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You don't think that a little historical perspective helps bring the subject to life? I think it's great for both the mathematically inclined students and their

by cik2e 10y ago

You don't think that a little historical perspective helps bring the subject to life? I think it's great for both the mathematically inclined students and their not so interested counterparts. Context helps those who care see the bigger picture and those who don't to at least understand why this might be important.

kxyvr 10y ago
I work as an applied mathematician and in my opinion trying to work though the historical context can sometimes hurt. Basically, there are two issues at play. One, everyone has a finite amount of time to learn things, so working through historical methods to add context can take away from gaining time and experience with flat out better, modern methods. Two, it often confuses people as to what methods to use. I work a lot in optimization theory and solvers. In modern optimization theory, you essentially never formulate, use, or look at the Euler-Lagrange equations. However, whenever I work with engineers, they was to use these equations because they learned them in school and think that it's necessary to use them to optimize. It's not. Just discretize everything and use the KKT conditions. Hell, don't discretize everything and use the KKT conditions because they work just fine in Banach spaces. It's not that the E-L equations are wrong, but they're covered for historical context and it cheats people out of the time they need to learn modern methodology. As another example, when people learn iterative linear system solvers, they often start with the Jacobi method or Gauss-Seidel. However, these methods are almost never used because they're absolutely terrible compared to modern Krylov methods. Again, though, I often work with engineers who learned about them in school and want to use them when they should have been learning the differences between things like MINRES and CG and what needs to be done to precondition the system. For full mastery of a field, sure it helps to know the historical record. Certainly, I think there are little historical tidbits that can keep a class more interesting and put some things in context. However, by in large, I often see people use completely terrible algorithms because they were taught in what I consider a historical manner and they did not have the time, nor perhaps the instruction, to learn more modern methods, which can often be formulated in an independent way without regard to older algorithms. Fields evolve and sometimes we realize there's just flat out better ways of doing things that don't need earlier results.
- Animats 10y ago
  Reading the above, I wonder if the people who are writing the linear equality/inequality parts of SAT solvers for program proof know that. Internally, numerical equalities and inequalities become rows in a sparse matrix. The columns represent program variables. Solution is done with rational arithmetic. The original Oppen-Nelson prover of the 1970s solved those with a Gauss-Jordan approach, and most follow-on work through at least the 1990s was basically the same machinery.

by cik2e 10y ago

kxyvr 10y ago

I work as an applied mathematician and in my opinion trying to work though the historical context can sometimes hurt. Basically, there are two issues at play. One, everyone has a finite amount of time to learn things, so working through historical methods to add context can take away from gaining time and experience with flat out better, modern methods. Two, it often confuses people as to what methods to use. I work a lot in optimization theory and solvers. In modern optimization theory, you essentially never formulate, use, or look at the Euler-Lagrange equations. However, whenever I work with engineers, they was to use these equations because they learned them in school and think that it's necessary to use them to optimize. It's not. Just discretize everything and use the KKT conditions. Hell, don't discretize everything and use the KKT conditions because they work just fine in Banach spaces. It's not that the E-L equations are wrong, but they're covered for historical context and it cheats people out of the time they need to learn modern methodology. As another example, when people learn iterative linear system solvers, they often start with the Jacobi method or Gauss-Seidel. However, these methods are almost never used because they're absolutely terrible compared to modern Krylov methods. Again, though, I often work with engineers who learned about them in school and want to use them when they should have been learning the differences between things like MINRES and CG and what needs to be done to precondition the system. For full mastery of a field, sure it helps to know the historical record. Certainly, I think there are little historical tidbits that can keep a class more interesting and put some things in context. However, by in large, I often see people use completely terrible algorithms because they were taught in what I consider a historical manner and they did not have the time, nor perhaps the instruction, to learn more modern methods, which can often be formulated in an independent way without regard to older algorithms. Fields evolve and sometimes we realize there's just flat out better ways of doing things that don't need earlier results.

Animats 10y ago
Reading the above, I wonder if the people who are writing the linear equality/inequality parts of SAT solvers for program proof know that. Internally, numerical equalities and inequalities become rows in a sparse matrix. The columns represent program variables. Solution is done with rational arithmetic. The original Oppen-Nelson prover of the 1970s solved those with a Gauss-Jordan approach, and most follow-on work through at least the 1990s was basically the same machinery.