When talking about modern mathematics and physics, one cannot miss mentioning Dr. Ruggeo Santilli. The PhD physicist was born and educated in Italy, and later he moved to the United States in 1967 after Nasa requested his services in conducting some research at the University of Florida in Miami. Over the years in America, he has taken up many roles in teaching in different universities across the country. He still holds many offices were he helps in science and research. Dr. Santilli has been the President of and Dresser of Physics at the Institute for Basic Research, which moved to Florida in 1990 from its previous location in Harvard University. Dr. Santilli has also written many technical articles, (250 to be specific) and 18 post PhD level theses in different fields of mathematics, physics, cosmology, chemistry and biology. Dr. Santilli is also known to have contributed a lot to the modern physics and mathematical theories. He has made some crucial discoveries which include: series of new numbers in mathematics, hadronic mechanics in physics, hadronic chemistry in the field of chemistry. Due to his many contributions to science, he has been rewarded with many awards. He has been given two gold medals at an Australian research centre for merits in science. He has also been recommended for nominations for Nobel Prize by scholars worldwide.
Currently, Dr. Santilli is the head scientist in Thunder Energies Corporation, which is a company that deals in coming up with the cleanest possible and most efficient combustion of synthetic fuels or fossil 
One of his latest works is the development of a telescope and discovery of invisible terrestrial entities. The telescope commonly referred to as the Santilli telescope is made up of concave lenses and can be used to observe objects that are invisible when using the conventional or normal Galileo's convex telescope and to our naked eye.
The journey followed to the creation of the telescope.
Dr. Santilli used the theory of isodual light that is produced by antimatters to come up with this telescope. Antimatters can be defined as a composition of the antiparticles in material and correspond to elements of normal matter . Both the matter and antimatter have same characteristics such as same mass. The two, however, contrast in that they different quantum numbers and opposite electric charge of the particles and antiparticles respectively. This means that if the particles are positively charged, the antiparticles will be negatively charged.
This concept of antimatter having negative energy was first proposed by Dirac. In his discovery, Dirac noted that Particles possessing negative energy behave in an unconventional physically manner . He came up with a theory known as "hole theory" that led to antimatter field being dealt with or studied to second quantization level only. An imbalance was created in this field, and there was a need to come up with a way to resolve the imbalance. Most importantly, the use of this 20th-century mathematics can lead to probable catastrophic variations when it is used to represent both the antimatter and matter. In 1993, at the Joint Institute for Nuclear Research in Russia, Dr. Santilli launched the making of new mathematics that will be useful to antimatter. It led to the formulation of isodual numbers which consist of negative numbers that are opposite those of matter. This is just but a topic in the in the wide Santilli's isodual mathematics, which allowed for the construction of isodual quantization, quantum mechanics and classical mechanics. The isodual mathematics considered the consistent classical treatment of neutral antimatter that did not exist before or are not included in Newton's mechanics, Galileo's relativity, Einstein's special and general relativities since their only conjugation is the sign of the charge.
For example, theories by Einstein predict that matter and antimatter light experience attraction (gravitational bending) while the isodual theory predicts that antimatter and matter light experiences gravitational repulsion from one another . According to the new theory on isoduality, these antimatters give off or emit a new light that can only distinguish from normal light through gravitational interactions. The matter and antimatter convert their masses into light at mutual contact a process referred to as annihilation.
In 1996 at an International Workshop on Anti-matter held in Italy, Dr. Santilli predicted that light emitted by antimatter is different from the normal light and this can be verified experimentally . He based his argument on the fact that normal light does not possess any charge, therefore, by using the map under isoduality of other physical characteristics of light, one can differentiate conjugate light produced by matter from that emitted by antimatter.
In 2006, a monograph was presented showing the systematic study of the results isodual theory of antimatter. The study included Galileo relativity, Newtonian mechanics, Einstein special and also general relativity with the first ever gravitational field of antimatter bodies representations. It is at this point that he concluded that light emitted by antimatter is repelled or keep away by a matter's gravitational field
In 2012, Dr. Santilli at an International Conference of Numerical Analysis and Applied Mathematics convection held Greece, predicted that Isodual light has the opposite or negative index of refraction when traversing a transparent matter-medium, therefore making it impossible to focus images formed by this light through a convex lens.
It led to him creating the first ever telescope that uses the concave lenses.
The main Principles of detection of the telescopes
a) Santilli's telescope-The light from regular matter is dispersed by this concave telescope hence allowing images of light emitted by antimatter to be formed in the camera with no light emitted by matter.
b) Galileo's telescope- The antimatter-light is dispersed into the internal walls of the convex
lens, therefore, allowing only matter-light to focus an image onto the camera with no interference from the light from the antimatter.
In 2014 the first ever images of antimatter galaxies, asteroids and cosmic rays being observed when using 100mm Santilli's and Galileo's telescope attached to a digital camera and given an exposure of 15 seconds 
A black streak was seen on the common background of the camera attached to the Santilli telescope while no streaks were observed on the digital camera (Canon 600D) attached to Galileo's telescope. The fact that an image was focused on the Santilli's concave telescope prove that there exists light that has a negative refraction index and the formation of these dark streaks proves beyond doubt that antimatter carries negative energy.
Discovery of invisible terrestrial entities (ITE’s)
During a test conducted by Dr. Santilli in Tampa Bay, Florida using the two telescopes attached to a digital camera (Sony). Visible entities that are unidentified were accidentally observed on the screen of the camera attached to Santilli telescope that was invisible to the naked eye and the Galileo telescope. This led to a series of systematic tests to identify and learn about these entities that are in our terrestrial environment. He came up with two kinds of invisible terrestrial entities that he presented at an invited lecture at St. Petersburg Astronomy Club  in 2015.
Dr. Santilli presented evidence on the apparent existence of antimatter cosmic rays, antimatter asteroids, and antimatter galaxies dark images he captured in the digital camera's background attached to a telescope made of a convex lens. He claimed that these astrophysical entities are neither visible to naked eyes nor conventional convex telescopes because the light emitted by the antimatter has an opposite refractive index to that of matter.
Types of ITE’s
He named the two types of entities as ITE-1 and ITE-2 entities. The two entities had been individually being tested by associates but were first presented during this convection.
1. The ITE-1
This kind consists of entities in our terrestrial environment attaining propulsion through the acquisition of antimatter in their interior with significant use of matter-antimatter propulsion, and achieve invisibility through the emission of antimatter-light as a sort of exhaust .
It has the following characteristics
• They are not visible to the naked eye or on the normal Galileo's convex telescope
• They exist in areas of terrestrial or lunar orbit
• They leave a dark image on cameras attached to Santilli telescope.
The black image formed shows that light that forms the image possess negative energy this is because only negative energy can annul or end the conventional positive energy that is found the camera's pixel, therefore, the dark image can only mean that the light is either same or equal to antimatter-light.
The ITE-2 entities are found in our terrestrial environment and not in deep astrophysical and are mainly observed to be pulsing backwards and forwards directly over sensitive industrial, civilian and military installations areas. The entities in ITE-2 are said to be of ordinary matter in composition, even though they emit antimatter light which is kind of exhaust it gives out during its locomotion. This fact backs up the hypothesis of locomotion which is centered on the drawing out of negative energy from space that is referred to as universal substratum
The ITE-2 kind have the following characteristics :
• They are neither visible to the naked eye or conventional convex lens telescope
• When observed using a Santilli telescope they leave a bright image at a digital camera's background. The brightness shows that image observed is composed of normal light yet it has means of becoming invisible through the conversion of positive refraction index to negative index
The main aspects to consider or one should note when using Santilli's concave telescope are;
• The telescope can be used to observe images with negative refractive index clearly without enlarging them
• Because they are made of a concave lens, they are mainly effective in focusing images that have a negative refraction index
• The emission of antimatter light does not necessarily suggest that the observed entity is antimatter, because cataclysmic explosions may be experienced if the antimatter entities existed due to the annihilation caused by a matter-antimatter collision.
• Antimatter-light emitted could be a sign that their propulsion system is centered on the drawing out of antimatter from space projected as a universal substratum of the whole space with a tremendously great energy density also referred to as zero energy.
It is, however, also important to note that the two kinds of invisible terrestrial entities must be made up of matter to avoid a cataclysmic explosion. Also, the ITE-1 and ITE-2 have structures that are beyond 20th-century knowledge for the following reasons including; the classical handling of neutral antimatter and the inapplicability of the century’s knowledge; the alteration of the refraction index, the apparent new typo of locomotion among other factors.
The discovery of the invisible entities in our very own terrestrial environment is very important to the scientific grounds. The finding of the two lights has proved that this new method (isodual mathematics) are effective to consider neutral antimatter at both classical and particle level, unlike the 20th-century physical knowledge.
The Santilli telescope and its invisible terrestrial entities can not only be used for astrophysical novelty but also on issues relating to personal grounds, industrial grounds and matters concerning national security.
2. Antimatter, https://en.wikipedia.org/wiki/Antimatter
3. P.A.M. Dirac, The Principles of Quantum Mechanics(Clarendon Press, Oxford, 1958)
4. Bhujbal, P. M. "SANTILLI ISODUAL THEORY OF ANTIMATTER ." n.d.
5. R. M. Santilli, "Does antimatter emit a new light?" Invite paper for the proceedings of the International Conference on Antimatter, held in Sepino, Italy, on May 1996, Hyperfine Interactions vol. 109, 1997, pp. 63-81, http://www.santilli-foundation.org/docs/Santilli-28.pdf
6. R. M. Santilli, "Apparent detection of antimatter galaxies via a telescope with convex lenses," Clifford Analysis, Clifford Algebras and their Applications vol. 3, 2014, pages1-26 (Cambridge, UK),http://www.santilli foundation.org/docs/Antimatter-telescope-2013-final.pdf
7. R. M. Santilli, "The Mystery of Antimatter," Lecture delivered on September 25, 2015, at the St. Petersburg Astronomy Club, http://www.world-lecture-series.org/level-ix
8. R.M Santilli, Isodual theory of antimatter: applications to antigravity, grand unification and cosmology(Dordrecht: Springer, 2006)
9. R. M. Santilli, "Compatibility of Arbitrary Speeds with Special Relativity Axioms for Interior Dynamical Problems," American Journal of Modern Physics, in press (2016) http://www.santilli-foundation.org/docs/superluminal-speeds