In this note, we indicate that the problem of detecting antimatter asteroids, stars and galaxies is fundamentally open at this writing; we identify the basic issues to be resolved for said detection; and we propose novel experiments. One of the largest scientific imbalances of the 20th century was the study of particles at all possible levels, from Newtonian mechanics to second quantization, while antiparticles were solely studied at the level of second quantization. The imbalance was due to

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... fact that Newton's equations, Galileo's relativity, and Einstein's special and general relativities have no means for distinguishing between neutral particles and their antiparticles, trivially, because their sole distinction is the sign of the charge. Even for the case of charged antiparticles, 20th century classical theories had problems, e.g., because the operator image of a classical charged "antiparticle" is a "particle" with the wrong sign of the charge, evidently in view of the existence of only one quantization channel. Since Galileo's and Einstein'a relativities cannot provide a consistent classical characterization of antiparticles, a rather widespread 20th century view was that "antimatter does not exist at the classical level," the sole admitted manifestation of antimatter being that at the level of elementary particle reactions. However, such a view is dismissed by evidence because Earth has been devastated in the past by antimatter asteroids. For instance, the 1908 Tunguska explosion in Siberia was the equivalent of one thousand Hiroshima atomic bombs, but left no crater or residue at all in the ground, thus being solely interpretable via the annihilation of an antimatter asteroid in our atmosphere. Additionally, the entire Earth atmosphere remained excited for two days during which there was full illumination at midnight even in Sidney, Australia. It is evident that such a global atmospheric excitation cannot possibly be interpreted via a matter asteroid, the sole quantitative representation being, again, that permitted by the annihilation of a large antimatter asteroids in our atmosphere. Furthermore, astronauts and cosmonauts have systematically reported "flashes of light" in the upper atmosphere when in darkness that can only be quantitatively interpreted as being due to antimatter cosmic rays annihilating at the first contact with our atmosphere. These, and additional evidence (e.g., in astrophysics indicating the apparent existence in the universe of large aggregates of antimatter), thus mandating its study, not only on scientific grounds, but also for our own safety. On mathematical grounds, the insufficiencies of 20th century theories for antimatter were due to the lack of the appropriate mathematics providing a consistent representation of all classical antiparticles, irrespective of whether neutral or charged. Since the map from a particle to its antiparticle is generally anti-isomorphic, and anti-Hermitean as a particular case, the consistent conjugation from classical particles to classical antiparticles requires an anti-isomorphic image of the entire 20th century applied mathematics used for matter, including anti-isomorphic images of numeric fields, functional analysis, differential calculus, Lie's theory, etc. In the early 1980s, during his stay at the Department of Mathematics of Harvard University under DOE support, the author addressed the above problems and, following various trials and errors, constructed the anti-Hermitean image of 20th century applied mathematics via a map, today known as Santilli isoduality (and denoted with the upper symbol d ), essentially consisting in the anti-Hermitean image of each and every quantity and all their operations of 20th century applied mathematics used for matter. For instance, given a generic vector field or operator O(t, r, v, ψ,...) depending on time t, Euclidean coordinates r, velocities v, wavefunctions ψ, etc., its isodual image is given by The resulting mathematics is nowadays known as Santilli isodual mathematics, where the term "dual" denotes the duality from matter to antimatter and the prefix "iso" is intended in the Greek meaning of preserving the original topology (or axioms). Consequently, isodual mathematics does not introduce new mathematical axioms, but merely