The nucleus of an atom of any element is made up of neutrons and protons. If any number of neutrons and protons could form a stable nucleus the number of elements and their isotopes would be unlimited. This is not the case as all combinations of protons and neutrons do not form a stable nucleus. Some combinations do not exist while others are unstable and disintegrate over a period of time and form stable combinations.
Man-made elements are heavy elements created by colliding smaller atoms. When smaller elements are collided, particles can be added to the neutrons of the stable atoms leading to the formation of other elements. Some of these are stable and exist for a time period long enough for them to be detected. Most man-made elements though have a very short half life and exist for small fractions of a second.
For example the element UUS was created by colliding the atoms of the elements Calcium and Berkelium. This is a highly unstable element with the half life of the different isotopes of UUS formed in the range of 0.1–40 ms.