My line of work has always been in the abstract which is a lot more interesting, because in mathematics, as I said earlier, we can play with the rules and see what the outcome is. We get some beautiful ideas which we can use to solve problems. Personally, I am a bit of a mathematical Platonist in that I believe that mathematics is discovered, not invented; that numbers exist, but not as material objects. Interestingly, each branch of mathematics seems to find some physical application. Even complex numbers, and hyper-complex numbers (the quaternions) are being used in your computer right now, yet you won't be able to count apples with them.
As far as I see it, Quantum Mechanics is a remarkable theory which can predict the motions of subatomic particles with an alarming degree of accuracy. Indeed, it even gives a limit to how accurately we can ever make measurements. The idea is that energy is not a completely continuous quantity but comes in packets called quanta. Albert Einstein then demonstrates that there is an equivalence between matter and energy, and so we have a direct impact of quantum mechanics on our material world. We no longer can measure where a particle is, but only where it probably is. Thus, the Quantum Mechanic combines the certainty of classical Newtonian Mechanics with probability and statistics to formulate her theory.
There are startling conclusions to this, which prove to be troubling (I state them in their popular versions, rather than the mathematical formalism):
1) (Heisenberg uncertainty principle) We cannot simultaneously know where a particle is and where it is going. If we know one for sure, then we cannot be sure about the other.
2) It is entirely possible that while a particle is probably right in front of you, it might actually be on the Moon.
3) Our observations of a particle actually affect the motion or state of that particle.
4) (Schroedinger's Cat) "a cat imagined as being enclosed in a box with a radioactive source and a poison that will be released when the source (unpredictably) emits radiation, the cat being considered (according to quantum mechanics) to be simultaneously both dead and alive until the box is opened and the cat observed."
5) (Wave-Particle Duality and The double slit experiment) A single particle of light, when directed at an obstacle with two apertures through which it may pass, passes through both of them. Consequently light can be considered both as a wave and as a particle.
I cite the popular versions precisely because these are the versions that have filtered down into popular thinking. The calculations that this theory makes, as I said above, are supremely accurate and make it a good scientific description of the way things work. However, Quantum Mechanics seems to break down as soon as we introduce gravity, and further, breaks down when we try and reconcile it with another supremely accurate theory - General Relativity. The theory we have for the very small does not match up with the theory we have for the very large.
The five facts that I have stated above do not marry with our experiences of life, and it is how we exaggerate these ideas that perhaps makes more mockery of the beauty of Quantum Mechanics, and our experiences of reality precisely because we misinterpret them.
1) If the Uncertainty Principle could be scaled up to our level, then we would never be able to catch a ball, let alone land a man on the moon.
2) It would take a length of time longer than the lifespan of the Universe for all the particles in your body to transport you suddenly to Mars.
3) If this were scaled up, then football matches would be a hoot!
4) Bishop George Berkeley's philosophy of things existing because we observe them would make a bit of a resurgence.
5) Bilocation would not be reserved to certain saints.
God either exists or He doesn't: there can't be a middle ground, though His existence is not beyond doubt - even St Thomas Aquinas grants that. There is no probability that He exists for the simple reason that if He does, He will not possess a quantum wave function describing His state. If God exists in one universe of the famous multiverse then, by the very attributes that He possesses, He must exist in every universe in the multiverse. It's also a good point to make that the existence of the multiverse is just as much a physical speculation as the existence of God. Evidence that supports the existence of the multiverse can also be explained by other things, such as the possibility that the energy is nor conserved. (How does one even prove that the total energy in the universe remains constant in the first place?) Probability requires a background framework from which values and measurements can be deduced. There can be no background framework to measure the probability of the existence of God.
It is the popular misconception of scientific method and result that gives rise to forms of pseudo-science which give justification to claims that are not only ridiculous but damaging to the framework and stability of Society. It also prevents real science from being done. Paul Feyerabend insists that Science must be a proper anarchy if it is to make inroads into the truth.
Many people now think that the truth must be relative. Mathematics refutes that. Mathematical truth is indeed truth. If one accepts the axioms and the methods of inference, then one is bound to accept the conclusion. Yet mathematics is not necessarily the only access to truth, though it needs to be proved that truth exists beyond the physical world. Physics can't prove that, so it uses Occam's razor to deny that there is anything outside physics. Mathematicians can be tempted to do the same. If we reject the idea of objective truth, then on what basis? Perhaps one needs to reject traditional logic and thus ways of engaging in communicating with other people.
Yet, in all this philosophising and discourse, we often forget something important. Human beings exist, and are not abstract. Our Lord bids us to value them because, if God exists, He wanted to create Human Beings. That's some value. In our dealings with others, we are not allowed to forget their intrinsic value and needs which trounce any theorising and abstract discovery. Love needs to be promulgated, and that's the truth.