[annie123 (OP)]

 Physicists like Brian Greene (Until the End of Time etc.)  in lectures, discussions online . frequently 'explain' concepts like string theory that have no experimental evidence by saying  it's all there in 'the math'. Sometimes graphics help visualize the concepts but in terms of evidence to justify the ideas, understanding stops at 'the math'. Is there anywhere ordinary non mathematicians can learn enough about 'the math' to see how the equations explain physics concepts that have no experimental evidence or are difficult to grasp ?
And what is meant b y a 'beautiful equation'? Are there any simple examples?

[PmbPhy]

Physicists like Brian Greene (Until the End of Time etc.)  in lectures, discussions online . frequently 'explain' concepts like string theory that have no experimental evidence by saying  it's all there in 'the math'.

I hate it when people say those things.

[Bill S]

  it's all there in 'the math'

Undoubtedly, this is true, but they rarely tell you what is in the “math”.

Barrow: “The Infinite Book”, says: 

“Gradually mathematicians lighted upon a new concept of existence.  Mathematical ‘existence’ meant only logical self-consistency and this neither required nor needed physical existence to complete it.  If a mathematician could write down a set of non-contradictory axioms and rules for deducing true statements from them, then those statements would be said to ‘exist’.” 

So, if you put in the time and effort to study the maths (I wish I had), you will be able to explore a world of mind extending wonder and undoubted truth; but it will be mathematical truth which may never be complemented by physical examples.

[alancalverd]

It's all there, but in reality, not in the maths.

Physics is the business of constructing mathematical models of reality, using whatever tools do the job.

We can start with the rules of arithmetic to lay down simple conservation laws, and the idea of conservation of mass is supported by pretty well everything that happens in chemistry: two grams of hydrogen and sixteen grams of oxygen makes 18 grams of water, and vice versa.

We can generalise from arithmetic to algebra and derive the conservation of energy, where we can predict the rise in temperature of stirred water from the apparently alien concepts of mass and velocity, without having an actual experience of "energy" but simply inventing it as "that which is conserved". Now we can use the maths to predict how much useful work you can get out of a gallon of petrol or a cheese sandwich, and the tools of calculus give us insights into rates of change and total content of our invented parameters.

Vectors are a useful mathematical tool, and conservation of the momentum vector, another invented concept, gives us ballistics and astronomy.

The idea that the sum of mass and energy is conserved gives us nuclear physics, and the conservation of electric charge leads us to understand atomic physics and the physical basis of chemistry. At each step we introduce a concept, propose its conservation, and look at how successfully that predicts the outcome of an event or interaction.

The big mystery remains as to how the observable universe, which seems to have a finite age, came into existence. Any hypothesis demands a conserved quantity if it is to be testable, and that's where we need a whole bunch of new mathematical tools like string theory to peer into the "pre existence". But the truth is in the reality (i.e. we are here) not the maths that helps us predict the future or reconstruct the past.     

[evan_au]

And what is meant by a 'beautiful equation'? Are there any simple examples?

I think one of the most elegant is Euler's identity: e^πi + 1 = 0
It contains:
- 1: fundamental to the counting numbers
- 0: fundamental to solving equations (for a long time it was even rejected as a reality)
- Slightly rephrase it to "e^πi = -1" and you get the negative numbers, fundamental to banking
- π: fundamental to circles
- e: fundamental to natural logarithms, simple electrical circuits, radioactivity and the spread of the coronavirus pandemic
- i: fundamental to a whole new spectrum of numbers, the "imaginary numbers"
- ...and the whole thing has a close relationship to sine and cosine, fundamental to music, surveying and the electric power grid
See: https://en.wikipedia.org/wiki/Euler%27s_identity

'explain' concepts like string theory that have no experimental evidence by saying  it's all there in 'the math'.

There is a contrast between "Pure Mathematics" and "Applied Mathematics":
- Pure mathematicians are happy with a purely conceptual framework; it doesn't need any connection to the real world
- Applied mathematicians start with the real world, and try to find a mathematical framework that can explain and predict it. But often the real world is "messy" with multiple effects interacting in complicated ways, so the result is not always elegant.
- And, surprisingly often, something that was purely hypothetical (like imaginary numbers) has application to the real world (the electricity grid)

There is a parallel with "Theoretical Physics" and "Experimental Physics":
- Theoretical Physicists are happy with a purely conceptual framework; it doesn't need any connection to the real world
- Experimental Physicists start with the real world, build experiments and try to obtain consistent results. But often the real world is "messy" with multiple effects interacting in complicated ways.
- And, surprisingly often, something that was purely theoretical (like quarks) has application to the real world (protons and neutrons)

Surprisingly often, something that is purely theoretical in mathematics (Group Theory) is applicable to the real world (subatomic particles).
- Some of the best results occur when these 4 specialized groups interact with each other.
- Experimental results make theoretical physicists go "back to the drawing board"
- Theoretical predictions make applied physicists build new experiments to confirm them (or not)

....and sometimes theoretical predictions like gravitational waves and black holes (Einstein) take a century to carry through to a successful experiment (LIGO and the Event Horizon telescope).

[Bill S]

Some months ago I came close to leaving TNS. It's threads like this that make me glad I hung on. 

I'm still with Sabine Hossenfelder, though:

“You can’t lie with math.
But it greatly aids obfuscation.”