I forgot an important part of my definition - a vital part of the physics lies in the boundary conditions, which are often crucial to the results. Also, compatibility with other established laws can be important to weed out "non-physical" solutions.

Ihavenofingerprints wrote:I enjoy and get better at applying mathematics to my studies as I get older, as I progress I realize there is more to it than what I learned in high school. Mathematics for me is more about ingenuity and intuition than being a flawless calculator under a given set of rules.

I enjoyed this video where the perception of being "bad at maths" due to experience in school is discussed at some length

I for one, do not "hate" maths, I just resent the incorrect application of maths, that sometimes produces bad predictions, masquerading as new physics.

Rest assured it was a general comment in reference to the OP, I have no position on the ongoing dialogue.

DavidMcC wrote:FURTHER EDIT: The physics, to me, means generating the equations in the first place, rather then solving them. This needs much less mathematical skill than solving those equations.

Math isn't about solving the equations, that's what computers are for (although of course you need sufficient math skills to write the computer code). The real math skill is generating the equations. Newton was able to derive Kepler's laws from his law of gravitation thanks to his knowledge of geometry (he hadn't invented calculus yet). Planck came up with the correct formula for blackbody radiation thanks to his math skills, even though he didn't know at the time why that formula worked.

Math skills in physics isn't about number crunching, it's about seeing connections, finding patterns and creating models.

Thanks everyone for your insights. Very interesting and useful.

Pulsar wrote:Math skills in physics isn't about number crunching, it's about seeing connections, finding patterns and creating models.

Yeah, I'm getting that. In that sense I think he should be just fine.

Pulsar wrote:

DavidMcC wrote:FURTHER EDIT: The physics, to me, means generating the equations in the first place, rather then solving them. This needs much less mathematical skill than solving those equations.

Math isn't about solving the equations, that's what computers are for (although of course you need sufficient math skills to write the computer code).

No, in principle, number crunching by computers is a last resort, when mathematical skills have failed. It is only since computer number crunching that it hasn't been so important to find mathematical solutions to the equations (with the given boundary conditions). Newton's fluxions was a stop-gap measure for that particular bit of physcics concerned with planetary orbits, before computers were invented. The real mathematics is in finding ana;ytic solutions to the equations, when that is possible.

The real math skill is generating the equations.
...

Math skills in physics isn't about number crunching, it's about seeing connections, finding patterns and creating models.

I didn't say maths skill was about number crunching, I meant it was in finding analytical solutions to physics equations, as mentioned above.

Pulsar wrote:

DavidMcC wrote:FURTHER EDIT: The physics, to me, means generating the equations in the first place, rather then solving them. This needs much less mathematical skill than solving those equations.

Math isn't about solving the equations, that's what computers are for (although of course you need sufficient math skills to write the computer code). The real math skill is generating the equations. Newton was able to derive Kepler's laws from his law of gravitation thanks to his knowledge of geometry (he hadn't invented calculus yet). Planck came up with the correct formula for blackbody radiation thanks to his math skills, even though he didn't know at the time why that formula worked.

Math skills in physics isn't about number crunching, it's about seeing connections, finding patterns and creating models.

Of course it isn't! (As previously posted.) There seems to be a generational gap here, with younger people looking to computers as THE way to solve equations (by number crunching)! The mathematical ability for generating a set of equations is far less than that for solving them (analytically), that's for sure! Forget "numerical solutions" for a minute.

.. Maxwell's equations are a good example, where the physics is in generating the equations, and the maths is in finding (when possible) analytic solutions (which may, for example, include Bessel functions, when there is cylindrical symmetry, IIRC).

... I quite agree that, often in practice, in applied physics, no analytic solution is possible, if only because of non-analytic boundary conditions.

The amount of mass = the amount of space-time warpage.

That's the physics.

Pointless hot-air without the maths.

colubridae wrote:The amount of mass = the amount of space-time warpage.

That's the physics.

Pointless hot-air without the maths.

Not so, because it's the basis on which the maths is constructed.

DavidMcC wrote:

colubridae wrote:The amount of mass = the amount of space-time warpage.

That's the physics.

Pointless hot-air without the maths.

Not so, because it's the basis on which the maths is constructed.

The amount of mass = the amount of space-time warpage.

Carries as much weight (no pun intended) as:-

The amount of mass = any old cockammy drivel

Until and only until you do the maths (and, by extension, the measurements).

colubridae wrote:

DavidMcC wrote:

colubridae wrote:The amount of mass = the amount of space-time warpage.

That's the physics.

Pointless hot-air without the maths.

Not so, because it's the basis on which the maths is constructed.

The amount of mass = the amount of space-time warpage.

Carries as much weight (no pun intended) as:-

The amount of mass = any old cockammy drivel

Until and only until you do the maths (and, by extension, the measurements).

If you still don't understand, I guess you never will.
Last shot: "The amount of mass = the amount of space-time warpage" forms the BASIS of the law. Without that, there is no maths! ("The amount of mass = any old cockammy drivel" does NOT form the basis of the maths - OBVIOUSLY!)
(End of discussion, AFAIAC, even though you might well continue to resist rational thought, as you don't seem to know the differeence between "space-time warp" and "cockammy drivel" I suggest you look them up in a dictionary.)