Why is Pilates a method to relieve back problems?

 To relieve the lower back, we will strengthen the abdominal strap(the abdominal corset: the rectus , the small and large obliques and the transverse) to relieve the lumbar muscles (The lumbar muscles are extensor muscles of the spine . They straighten the back and are therefore erectors of the spine. If they act on one side only, they cause a lateral tilt. They also rotate the torso. The main lumbar muscles are the long dorsalis and the multifidus or multifidus. The long dorsalis is the most internal muscle, it attaches to the sacrum and to the back of the iliac crests.

How do we proceed?

 1 - We wake up and strengthen the muscles that are less used,
2 - We relax and loosen the overused muscles by stretching them well,
3 - In a third step, the deep muscles are awakened, those that form the pelvic floor. These are the deep muscles of the pelvis, in both men and women.

At the same time, thetransverse abdominals should also be worked on to help the spine to be well aligned:

(The transversus abdominis is the deepest muscle of the abdominal muscles. It is located below the oblique and rectus muscles . The main function of the transversus abdominis is to hold the viscera. It is also involved in the exhalation phase of breathing.)A flat stomach can be achieved bybuilding up the transversus abdominis. 

The effectiveness of Pilates combines belly work and Pelvic floor work,

The Pilates method is a global method which will also require work on the rest of the body, a global muscle chain to be considered as a whole.