Richard Feynman on Physics VS Mathematics | Explorer’s Odyssey
The mathematicians only are dealing with the structure of the reasoning and they do not really care about what they're talking they don't even need to know what they're talking about or as they themselves say or whether what they say is true now i explain that if you state the.
Axioms you say such and such a so and such and such and so on such and such and so what then then the logic can be carried out without knowing what the such and such words mean in other words mathematicians prepare abstract reasoning that's ready to be used if you will only have a set.
Of axioms about the real world but the physicist has meaning to all the phrases and there's a very important thing that the people who a lot of people who study physics that come from mathematics don't appreciate the physics is not mathematics and mathematics is not physics.
One helps the other but you have to have some understanding of the connection of the words with the real world and this is a problem which is not a problem of mathematics at all mathematicians also like to make their reasoning as general as possible if you say i have a three-dimensional space ordinary space i want to talk.
About ordinary space you know you're in it that you measure distances and there are three numbers you need to tell where something is you're going breadth width and height space and you begin to ask them about theorems then they say now look if you had a space of n dimensions then here are the theorems well i say.
Yeah but i only want the case three well substitute n equals three and it turns out then it turns out that very many of the complicated theorems they have are much simpler because it happens to be a special case now the physicist is always interested in a special case.
He's never interested in the general case he does he's talking about something when you know what it is you're talking about that these things are forces and these are masses and this is inertia and this is so on then you can use an awful lot of common sense seat of the pants feeling about the.
World you've seen various things you know more or less how the phenomenon is going to behave well the poor mathematician he translates it into equations and the symbols don't mean anything to him and he has no guide but precise mathematical rigor and care in the argument.
The mathematical rigor of great precision is not very useful in the physics nor is the modern attitude in mathematics to look at axioms now mathematicians can do what they want to do one should not criticize them because they are not slaves to physics it is not necessary that just because.
This would be useful to you they have to do it that way they can do what they will it's their own job and if you want something else then you work it out yourself