What do Christian Scientists mean when they say death is an illusion?

Christianity Stack Exchange Tag: A sect of Christianity founded by Mary Baker Eddy. It is best known for its teaching that all forms of illness are an illusion that can be overcome by prayer alone.

What does it mean, that all forms of illness and even death itself, is an illusion?

Adherents subscribe to a radical form of philosophical idealism, believing that reality is purely spiritual and the material world an illusion. This includes the view that disease is a mental error rather than physical disorder, and that the sick should be treated not by medicine but by a form of prayer that seeks to correct the beliefs responsible for the illusion of ill health... The church does not require that Christian Scientists avoid all medical care – adherents use dentists, optometrists, obstetricians, physicians for broken bones, and vaccination when required by law – but maintains that Christian Science prayer is most effective when not combined with medicine.

[Mary Baker Eddy] dismissed the material world as an illusion, rather than as merely subordinate to Mind, leading her to reject the use of medicine, or materia medica, and making Christian Science the most controversial of the metaphysical groups. Reality for Eddy was purely spiritual... The Holy Ghost is Christian Science, and heaven and hell are states of mind.... She saw Jesus as a Christian Scientist, a "Way-shower" between humanity and God... "there is no doctrine of the soul" in Christian Science: "[A]fter death, the individual continues his probationary state until he has worked out his own salvation by proving the truths of Christian Science." Eddy did not believe that the dead and living could communicate.

[A]ll healing is a metaphysical process. That means that there is no person to be healed, no material body, no patient, no matter, no illness, no one to heal, no substance, no person, no thing and no place that needs to be influenced. This is what the practitioner must first be clear about. Practitioner Frank Prinz-Wondollek, 2011. https://en.wikipedia.org/wiki/Christian_Science

The above extracts, taken from a Wikipedia article on Christian Science, state their views. Make of them what you will.

Partial quotes from a 1947 Christian Science article starting with a quote by Mary Baker Eddy:

"Life is real, and death is the illusion. A demonstration of the facts of Soul in Jesus' way resolves the dark visions of material sense into harmony and immortality."

“God and His spiritual man and universe are the only real, and the real man and universe reflect the Life which is God... [Jesus] rose above matter to give the final proof of the eternality of divine Life, which knows no death, no sorrow or suffering. This was his way of demonstrating the facts of Soul in proving Life to be real and death but an illusion. We as earnest Christian Scientists must work as he worked; his way of overcoming must be our way. It is the way of Spirit, not matter; of eternity, not time; of reality, not illusion; and the goal is the eternal life that we should strive to attain.”

“It is life discerned spiritually, then, that bridges over the interval of death. To discern, understand, and demonstrate spiritual Life is to know God and His Christ and to unknow or cast off the belief that a corporeal mortal is man. It is to discern and prove that the man of God's creating reflects and possesses by reflection all that God is or has. It is to know and prove that all that is unlike God and His reflection is unreal, and that death, the claimed opposite of Life, is therefore but an illusion.”

”May we look beyond the illusion to envision the real, spiritual man, God's likeness, in the spiritual universe of Mind, in the full consciousness of his true selfhood and heritage of eternal life, where Spirit reigns and "sin, sickness, and death are unknown." https://sentinel.christianscience.com/shared/view/15254xk761g