# The math of physics

1. Jun 26, 2017

### thetexan

Since math is such an important part of physics I was wondering....

Why so? Is it assumed that any physical phenomena (and I mean any conceivable physical phenomena from quantum to cosmological) that exists, known or yet unknown, can be explained with a mathematical formula or equation thus necessitating the endless math involved?

Or.....and in conjunction with the above...the math will prove the phenomena or at least predict it. Take e=mc^2 for example. Was Einstein searching for a formula or did it reveal itself by accident? (retorical question)

Let's say string theory as another example. Why all the math? What is the purpose? (this is more than a stupid question). Is the goal to find a formula that works each time it is applied to string ideas thus making a prediction that works every time thus proving the theory?

It just seems to me that there is a universal belief that there will be a math equation or formula for anything. Or better stated...anything that can be observed can be modeled with math, and if that math hasn't been found...YET....it will be with enough research? In other words, all puzzles CAN be solved with math given enough effort. Is this the idea?

tex

2. Jun 26, 2017

### A.T.

Because the goal of physics is to make quantitative predictions.

3. Jun 26, 2017

### Bandersnatch

I think, you're overthinking it. Maths is just a hardcore approach to logical reasoning. And if your goal is to describe reality in a rigorous fashion, what else would you use? Faulty reasoning? Illogical reasoning? Magical thinking?

The only assumption necessary for this approach is that the universe is indeed logical.

4. Jun 26, 2017

### thetexan

I guess I made my question more complicated than it needed to be. Here is the real issue that I think will answer my main wonderment...

Is it assumed to be a fact that any physical phenomena, regardless of what it is, from quantum physics to the biggest cosmological physics, can be represented with mathematical equations?

It seems that if any phenomena, known or unknown, exist, then it exists and works in some way that must, as you say, be logical. And if it operates logically, then the language of logic, mathematics, must, by definition, be able to represent it. It just becomes a matter of figuring out the representation.

Is this correct?

tex

5. Jun 26, 2017

### Staff: Mentor

Nobody assumes this. A physical phenomena is something which can be measured or in general be observed. A measurement is by its nature a comparison with a scale, which gets numbers and units involved. It is furthermore often a change of state, so time as a parameter comes in. The requirement to express all these as uniquely as possible, and at the same time as understandable as possible, brings in logic, numbers and mathematics in a natural way. And the big advantage is: If there is no mathematical language to express an observation, no problem, then a calculus will be developed. Such mathematics is not at the beginning of physical observations as your statement suggests, but their natural fellow traveler.

6. Jun 26, 2017

### sophiecentaur

Firstly, when considering well known classical Physics, situations are just better explained using Maths. When you read the laboured way that phenomena used to be described 'just' in words, it is not surprising that Science was highly esoteric. You could say that, literally, "word's cannot express" some things. Appropriate Maths was devised to make such descriptions possible. Over the years, Maths has developed to follow the demands of Science. Trust me, they didn't invent maths just to annoy you.

7. Jun 26, 2017

### nasu

There are cases when math was developed to "follow the demands of Science". The most famous example is possibly the "calculus of fluxions" invented by Newton.
However, most of the time the math was developed for its own sake and physicist just found more and more parts of it to be "useful". A real mathematician cannot care less about the applications of the new concepts he develops. If he does, he is not a "real" mathematician. :)
I think there are also cases when physicists developed "new" mathematical methods just because they did not know they were already known to mathematicians.

8. Jun 26, 2017

### TeethWhitener

9. Jun 26, 2017

### Krylov

I hope this is ironic, but I fear that it is not.

10. Jun 26, 2017

### nasu

As a physicist, I like to believe that math is developed for the sake of applications, especially in physics. Or even that math was developed by physicists.
However this is not the case. I did not intend to be disrespectful to mathematicians. Just to give them what is theirs.

To put it in a mathematical format, there are (and were) at least some mathematicians who believe that math is done for its own sake, for its beauty and for the intellectual satisfaction. Do you disagree with this?

Sure, the part with being or not real was a joke.
If you are a mathematician developing applications of mathematical methods, of course you are a real mathematician. Without quotes. :)

11. Jun 26, 2017

### Krylov

No, on the contrary.

12. Jun 26, 2017

### Staff: Mentor

It's not always physics. It wasn't QM that started probability theory. It was in fact simple gambling
And RSA might be related to ERH, but they didn't induce each other. I still find my picture of travelling companions more suitable than any implications are, in which direction ever and how well hidden ever. And who expected to find graded algebras or cohomology theory in modern physics? Lie theory on the other hand arose from the need to solve differential equations which again likely had their origin in physical requirements, but not exclusively.

13. Jun 26, 2017

### ZapperZ

Staff Emeritus
This is rather puzzling.

Would you ask a mechanic why he/she needs all those "tools" to repair a car? Or would you ask a linguist why we need all these words just to convey a message or an idea?

Zz.

14. Jun 26, 2017

### sophiecentaur

You need not worry. Mathematicians (the really hot ones) do not care what we lessor mortals say or think about them. They are only worried about what their fellow mathematicians think. They tend to get just as excited about solving Rubic's Cube as with developing some Maths that is of use to Science or Engineering. But we would be lost without them so we have to treat them gently.
I think that may be far too much to hope for. There will be problems that can never be solved with Maths to a level that is entirely satisfactory. For a start, there are many Differential Equations which relate to Physical processes which do not have Analytical solutions. For instance, the only way to solve the Equation that describes 'simple Frequency Modulation is by using numerical methods. There are many more instances of that and it must really upset non pragmatic users.
Also, the mathematical models are only as good as the evidence that's used to build them, which is down to measurement, in the end.

But, if you want a world with No Maths in it, the level of Scientific understanding will be very low.

15. Jun 26, 2017

### nasu

That was the reason for my post. I was afraid that some of the hot ones will read this thread and get offended by the idea that they work for the benefit of these scientists back there.
https://imgs.xkcd.com/comics/purity.png

16. Jun 26, 2017

### sophiecentaur

I think they 'know' they are smarter than 'us' and wouldn't care. Most of them are aware of the esteem in which they are held.

17. Jun 26, 2017

### nasu

Not all are so self-reassured. There was one of them who felt the need to "apologize" for the applied math. :)
https://en.wikipedia.org/wiki/A_Mathematician's_Apology
(Available online)

"Any genuine mathematician must feel that it is not on these crude achievements that the real case for mathematics rests, that the popular reputation of mathematics is based largely on ignorance and confusion, and there is room for a more rational defence."

The "crude achievements" are the practical applications of math. He mentions Einstein's relativity between them.

18. Jun 27, 2017

### Staff: Mentor

Why all the math? Because it works. The rest is philosophy, so thread closed.