In short, there is no boundary between physics and mathematics; their similarity is such that they are inseparable.
With the permission of our contributors and readers, I present my personal experience:
1- After graduating, I was appointed a lecturer and researcher at Cairo University's MTC, within the Chair of Basic Sciences.
2- At the time, the Chair of Basic Sciences included physics, mathematics, probability and statistics, and descriptive geometry.
3- Obtaining a master's degree was a difficult experience and required a miracle: I first had to take 12 advanced mathematics courses and 12 advanced physics courses as prerequisites, culminating in rigorous exams, before putting my final thesis into practice. 3- After obtaining my MSc, I was appointed lecturer and head of the four sub-chairs mentioned above, working one to one with top Russian and Czechoslovak experts.
Imagine a situation where a professor excuses himself and you have to give a lecture in his place, knowing the topic from one of the four sub-chairs' specializations only 10 minutes in advance.
4- Now, after a long journey of theoretical and experimental research and publishing more than 60 original papers, believe me, I don’t know who I am, whether I am a physicist or a mathematician.
In short, there is no boundary between physics and mathematics; their similarity is such that they are inseparable.
5-But I can assume that I am a physicist with love and passion for mathematics in my heart for a long time since my MSc and all the difficult exams on endless prerequisite topics in mathematics.
6- I recently discovered that all my research focuses on mathematics generated by physics.
For example,
i- Solving partial differential equations in classical and quantum physics using physical techniques.
ii- Pure mathematical problems of integration and differentiation using physical techniques, completely neglecting the finite difference method (FDM).
iii- Probability and statistics, and the derivation of statistical distributions such as the Gaussian-normal distribution.
iv- Revolutionary foundations of original theories that have remained unanswered for over 100 years, such as artificial intelligence and unified field theory.
I am using physics to generate mathematics.
All these boring analyses and anecdotes are a gift I offer to our young master's researchers, in the hope that they can better identify with themselves.
Finally, the initial question remains valid: are you a mathematician or a physicist?
On physics laws and parallel universes, “does the God play with infinitely many dices?” What can be expected on physics laws in parallel universes? In our universe there exist some physical quantities and interactions for example mass, electric charge, gravity, electromagnetism, gravitational and electromagnetic radiation. Galileo, Newton, Kepler, Kopernic, Nasîrüddin Tûsî, Maxwell, Einstein etc, very important scientists studied and derived the physics laws [1, 2, 3, 4, 5, 6, 7]. It is possible to study the Dynamics of our universe from infinitely small to infinitely large scale. Our universe has its own physical quantities, physical laws. But it is not certain that in other parallel universes there exist same physical quantities (mass, electric charge etc), interactions, radiations. They may have new exotic different physical quantities, their different interactions. Even if same quantities, interactions exist, it is certain that their magnitudes and ratios may not the same. Despite in our universe the ratio of (electromagnetism/gravity is nearly 10^40), this ratio maybe reverse or largely different. In that case how can be governed the contact and information exchange among them. In other parallel universes new exotic physical quantities and interactions are possible, same kind periodic table may not exist. Some restrictions in quantum mechanics are valid in our universe, such as Heisenberg uncertainty principle, Pauli exclusion principle. In other universes very different kind exotic structures massless, chargeless may exist, and very different exotic quantum rules. In our universe there exist some limit points such as speed of light, absolute zero Kelvin degree, event horizons of black holes. It is completely possible to study and analyze all physics until these limit points, but unfortunately physics laws do not work beyond them. But two points are clearly definite, first one is basic primary school calculus (addition, subtraction, multiplication, division) and second one is Einstein covariance of the physics laws in parallel universes. A parallel universe has its own physical quantities, interactions, laws etc., and naturally these physical laws must be written in the same mathematical form totally independent of any reference frame. Two observers from from two different reference frames must observe the same physics and must study same physics formulas, despite two reference may move relatively to each other uniformly, or with acceleration a, or higher order acceleration a^(n>1). In our universe, velocity dependent potentials, special relativity with uniform motion, general relativity with acceleration, the contancy of speed of light , absolute Kelvin zero degree (- 273 degree), event horizon of a black hole, atomic and nuclear structures in quantum mechanis are well studied concepts. Einstein field equations result in so many, nearly infinitely many, solutions. Most of them do not have physically correspondence in this universe. Gödel universe is a very good and intelligent example for this case. Against quantum mechanics probabilistic interpretation, Einstein has said that “the god does not play dice”. But in this case for infinitely many parallel universes “the God prefers to play with infinitely many dices”. References: 1- Nasir al-Din al Tusi: Tusi (1201-1274 a.d.) was an Arabic scholar whose writings became the standard texts in several disciplines for several centuries. They include editions of Euclid's Elements and Ptolemy's "Almagest," as well as other books on mathematics and astronomy, and books on logic, ethics, religion. He wrote the "Tadhkira," to be "a summary account of astronomy' presented in narrative form. The details are expounded and proofs of the validity are furnished in the "Almagest." Indeed, ours would not be a complete science if taken in isolation from the "Almagest" for it is a report of what is established therein." It is thus not only a sort of running commentary on the "Almagest," but also an account of medieval Arabic cosmology. Jamil Ragep has not only translated the text of the "Tadhkira," but has also provided a lengthy introduction with a biography of Tusi and a discussion of the context in which the "Tadhkira" was written and its influence, as well as a detailed and thorough commentary on each section of the text. 2- Einstein : The Foundations of the General Theory of Relativity “Die Grundlage der allgemeinen Relativit ̈atstheorie’.Annalen derPhysik, 49, 769–822 1916” 3- Maxwell James Clerk, A Treatise on Electricity and Magnetisim, 1873, 4- Galilei Galileo “Dialogues Concerning Two New Sciences” 5- Isaac Newton “Philosophiae Naturalis Principia Mathematica 6- Johannes Kepler, “The Harmonies of the World” 1619 Nicolaus Copernicus, “De revolutionibus orbium coelestium – On the Revolutions of the Celestial Spheres” 1543
After all these perfect answers, I can't add anything other than a funny anecdote or joke a mathematician friend told me about the difference:
Two friends, one a mathematician and the other a physicist, went to a conference and slept in the same room at a high-end hotel.
Late one night, a fire broke out in the room. The mathematician was the first to wake up, turned on the faucet, and wrote on his paper:
We have fire and water, the solution exists! Then he went back to sleep.
When the fire grew bigger, the physicist woke up and began working on turning the water into fire.
But despite this, I still don't understand the difference between physics and mathematics.
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