Everybody knows that there is a magnetic field in nature. However, most people think that the existense of magnetic field is "given from above" , or, by other words that "this is the way Universe was designed", or by yet another words "it is fundamental physical phenomena which simply is there and which does not come from something else, or can not be derived from anything else", or similar statement/ understanding of the nature of magnetic field.
Yet it (magnetic field) is simply a MATHEMATICAL CONSEQUENCE of 2 things: electric field and relativity. Write down the Coulomb equation of electric field for a point charge. (This equation describes electric force on any other charge being brought nearby). Now, see what happens if you MOVE this charge. According to relativity you then have to use Lorents transformations to find what does the electric field of the moving charge looks like in STATIONARY reference system. (Or vice versa which is completely equivalent: what does the electric field of NON-MOVING charge looks like in MOVING reference system).
Transforming electric field from one reference system to another using Lorents equations immediately gives you much more complex field (= electric force) than the original field of NON-MOVING charge. And the difference between the electric field of the charge in non-moving and the electric field in moving reference system is EXACTLY what we call a "magnetic field" (or "magnetic force").
So, moving charge MATHEMATICALLY creates what we call "magnetic field" (in addition to existing electro-STATIC one). Although "on the surface" a magnetic field looks to be very different phenomenon than electric field, it acts on charges very wierd "sideway" and often seems to be completely unrelated to electric field phenomenon (especially if opposite charges compensate each other and there is no net macroscopic electric field in the system).
Exactly the same way math "creates" a photon ( which is an electric field of ACCELERATING or DECELERATING charge). And a photon has quite different "appearances" - of a light or of a heat (infrared) , or of radio wave, or of a gamma-ray - quite differently behaving objects. But it (appearance of a photon, or as scientist say, its wavelength) just depends on the magnitude of acceleration of electric charge.
Exactly the same way math "creates" each and every object and phenomena in the universe, including universe itself - it is all just a bunch of mathematical objects resulting from more fundamental mathematical objects.