Antihydrogen, the bound state of a positron and an antiproton, has recently been created under controlled conditions in the laboratory. The proposal seeks to build upon this by creating and trapping very cold antihydrogen using a magnetic gradient trap. This is an arrangement of magnetic fields that acts upon the small magnetic moment of the antiatom to produce a trapping force. However, such traps are shallow, and are currently only capable of holding neutral species with kinetic energies equivalent to a temperature below 1 Kelvin. To trap antihydrogen efficiently it must be produced at this temperature, or below. This requires several major changes and upgrades to our apparatus. These include a complete new magnet and cryogenic system, an octupole coil arrangement for the neutral trap, a new antihydrogen annihilation detector and upgrades to the performance of the positron accumulator. These changes are very technical in nature and the detailed case for support seeks to explain and justify them. However, all experiments with antihydrogen are difficult, so the question we address here is; why bother? We will explain this using the example of symmetry.It has been apparent for a while that fundamental asymmetries are hidden deep within nature. For example, in the 1950's it was discovered that the weak nuclear interaction violates parity conservation. However, the defective parity mirror can be mostly repaired by adding so-called charge conjugation, which, loosely speaking, means that interactions are unaffected when every particle is substituted by its antiparticle. For a while it was believed that the laws of nature would obey the combination of parity reversal and charge conjugation. But by the mid-1960's this was found to be untrue for a small class of reactions involving unusual, fleeting, particles called K-mesons. Since then it has been assumed that the small blemish in the combined charge conjugation/parity reversal mirror can be corrected by the application of time-reversal.However, this 3-way switch differs from the three discrete symmetries, or any 2-way combination of them because the charge/parity/time combination exists as a theorem that can be proved using the basic postulates of quantum field theory. Such theories are the cornerstone of our current understanding of the Universe, but are widely recognised as being incomplete. So testing this unique 3-way switch is going to the heart of our understanding of nature. Our current picture of the beginning of the Universe involves the Big Bang, which is thought to have been an energetic event that created equal amounts of matter and antimatter. Why then did they not all annihilate one another and leave a Universe devoid of matter? Searches for large amounts of remnant antimatter in the Universe, have failed to find any trace. Currently it is thought that our Universe is matter dominant; in other words asymmetric. The other fact to add to this is that the amount of asymmetry we can currently identify via numerous studies of fleeting and rare particles isn't enough to explain the existence of the material Universe.Thus, the evolution of the Universe is not fully understood and this makes testing the symmetries of nature of great importance. The creation of cold antihydrogen in amounts suitable for study, has opened a new door on symmetry; hopefully one which will allow precision laser spectroscopic comparisons with the spectral lines of hydrogen. Spectroscopy of hydrogen has recently reached fantastic precision for one line in particular, the two-photon 1S-2S transition, which has been determined to about 2 parts in a hundred million million. Amazingly, due to uncertainties in the properties of the proton, this level of precision is way beyond that achieved by theory. Comparisons of hydrogen and antihydrogen would be free of this effect. Our proposal will help make these comparisons a reality.