Can an "amateur" today make useful contributions to theoretical physics or mathematics?

This was a question I posed to a friend of mine. We decided to define an “amateur” as someone without a PhD in physics, mathematics or something close.

We came to the conclusion that it is very unlikely that some one with out a PhD could in fact make a real contribution. This is despite the fact that things are far more open today than they ever have been. I mean, we have the arXiv and open access journals online. Almost everyone has the internet at home these days, and if not the local libraries do.

From time to time undergraduate students can contribute, but these are with close supervision. The supervisor will guide the student and nurture the natural ability. This was really the closest to an “amateur” that could contribute we agreed on.

So, why can’t “amateurs” contribute? Here are my thoughts…

1) Without spending some time in academia, “amateurs” are not aware of the culture and what is expected of anyone wishing to contribute to mathematical science. They do not know how to do research.

2) “Amateurs”, although interested and very keen at times do not often realise just how much of a prerequisite can be required to conduct research. They can often lack the mathematical skills to contribute. Claims like “I can solve the Riemann hypothesis using high school mathematics” only suggests that they don’t understand the hypothesis correctly in the first place. Trying to rewrite particle theory using high school maths is also redundant. We have a great construct for doing particle physics, it is called the standard model.

3) Theoretical physics, mathematical physics and mathematics as a whole is split up into smaller sections. One can only hope to get acquainted properly with a small subset of what is out there. Without specialising to a large extent, it is unlikely that one can discover something new and interesting. Trying to find smaller, specialised problems to work on is usually the way forward: unless you are a genius and can discover a whole new branch of mathematics! “Amateurs” seem to be focused on very well-known and published open questions. In number theory the Riemann hypothesis is a great example of this. In physics, a theory of quantum gravity is an example.

4) Because the individual does not understand it, it must be wrong. “Amateurs” fall into this mind set quite often. Finding a simpler more elegant approach to things is a large part of the mathematical sciences. However, trying to show that special relativity or quantum mechanics are mathematically inconsistent or do not agree with nature is futile. This also includes the desire to use nothing but high school maths to explain all of physics.

Not that I want to discourage anyone from thinking about mathematics and physics. I encourage it, but with a caveat: reading Wikepedia and popular accounts of science are not enough for one to start to do research.

UPDATE (15th May 2014)

Please do not post about your pet theories in the comments here. If you have something to say related to this post about the role of amateurs in science then please by all means share it here. Thank you.

26 thoughts on “Can an "amateur" today make useful contributions to theoretical physics or mathematics?”

  1. I must say that I agree that anyone without a degree or background training in any part of what they are trying to contribute to will MOST LIKELY (not for sure) fail at contributing. What I have to add is that I am a 16 year old male who is very interested in quantum physics and has no background whatsoever, but I do believe I have found an “answer” to the theory of time. I would like to know someone that I can be referred to that can confirm, deny, or simply discuss what I have formulated.

  2. I must object to this as an astronomer. This is one field where amateur observers make great contributions all the time, I can’t speak for other scientific disciplines however.

    1. Thank you for your endorsement of “ametuers” in the realm of astronomy. I’m a retired automotive electronics engineer with some fairly strong ideas as it relates to dark energy and matter. For the last 20 years of my career I was involved heavily in quality control and the problem solving skills one develops in sophisticated electrons is honestly not something you can learn in a post or under graduate setting.

      With the strong correlation between super massive black holes mass to galactic observable mass, the ratio cannot exist unless the SMBH is doing something to/with the mass it consumes. I’m unable to find even one hypothesis that considers dark energy or matter as a by-product of the process. Dark energy, by inference, is increasing based on the continued acceleration of the visible universe. General relativity breaks down only because of the “singularity”. If the SMBH is a converting known matter into matter or energy that we currently do not understand, the infinite mass quandary ceases to exist.

      The arrogance of the post prior to your post is, in part, the reason that physics has been at a standstill for over a century now. Half a century was spent trying to understand General Relativity prior to computers and the next half century wasted trying to disprove it. Sorry for my rant, I’m just fed up with the Politics and Arrogance of 21st century Physics. No new ideas and the same amount of progress.

  3. Hello,

    I believe in discussing ‘useful contributions’, one would first have to define the meaning of a ‘useful contribution’. For one, in professional sciences at large, productivity is measured by volume of publications that scientist authors or contributes to. Taking this as a fact, ‘useful contribution’ implies an activity associated with production of a publication. However, an ‘amateur’ won’t be able to engage in such an activity as they don’t have Ph.D. and/or not a part of academic establishment in general. Hence discussing possibility of ‘useful contribution’ by an amateur is nonsensical in the context of professional science.

    Perhaps a better question is whether an amateur can practice science. I consider myself an amateur science practitioner. I have masters in biology, study for masters in computer science and work in business analysis. In my spare time, I program genetic algorithms which evolve programs for data modeling and forecasting. In every step of the way, I believe I follow scientific method, as defined by Descartes, Bacon, etc, and I use knowledge obtained from academic literature on the subject.

    If I was to share my results and designs, perhaps some of them can be used for a meaningful contribution to science. Hence, as I look at my creative pursuit in the context I’ve defined, I’m an amateur with potential to make a meaningful contribution.

    Monte Carlo

  4. iniaes :

    I agree, astronomy is still a science that a reasonably well equipped amateur can contribute. Things that spring to my mind here are the discovery of comets, observations of Jupiter’s belts, observations of meteor showers and I am sure many other things.

    Professional astronomers have limited time on large telescopes, the amateurs really make a contribution in situations where lots of eyes are better that “one big one”.

    Monte Carlo :

    I guess by a useful contribution I do indeed mean a publication, or maybe a preprint. The main point is that it should extend our knowledge in some way. Not having a PhD is by itself, not a barrier to publication. The thing is that typically, one would need to obtain a PhD in order to understand how to do research and get some knowledge of what is interesting to the scientific community.

    Anyway I wish you luck with your work.


    Sorry for the late replies, I have been busy recently.

  5. Would you dare say that for someone who is going to spend a few years studying properly the books ‘Classical Mechanics by Goldstein’, ‘Principles of Quantum Mechanics by R Shankar’, ‘Classical Electrodynamics by J D Jackson’ and before this Theoretical minimum by susskind. After those three books, Study the 13 books on theoretical physics by Griener and finally the 10 volumes on theoretical physics by Landau. For mathematical physics, book by Arfken, Courant, Hilbert – Methods of Mathematical Physics 1 and 2. Moreover in my country (India) most “PhDs” would fail to answer simple questions. I do agree that one has to be under a good teacher or a researcher, but the “PhD” degree doesnt make a great thinker.

    1. Hey….very nice to read your thoughts…I suppose you yourself are doing the research in physics..I am also planning to….I am working right now..can you please share your email id, so that i can discuss in detail.


  6. If you are willing to include very high quality expository work as a genuine contribution, and I think it deserves to be considered as such, that could be one place where a sophisticated amateur could contribute. You might consider it a contribution to math/physics education, rather than math or physics proper, but a contribution to math/physics education actually IS a contribution to math/physics, in my book. Of course the “high-school math” variety of amateur can be ruled out as having much of anything useful to say, but I don’t think it is fair to characterize all amateurs that way (not saying you have, but you don’t seem to give enough weight to the existence more serious amateurs). Some may have gotten a bachelors in math or physics, but then ended up getting a different day job or something like that. The biggest obstacle, by far, I think, is having another career to work about, when serious or math is, by itself, a full time job, and a very demanding one at that.

      1. Amateur simply means you do not make money with a particular craft. Einstein and Faraday were amateurs by this definition but this says nothing about the professionalism of their work before or after they started making money. I will give you an example.

        An amateur published in the peer reviewed Indian Journal of Science and Tech & Bulgaria’s Sofia Technical University presented the research at their 2011 physics conference. Anne Astronomy News actually reported on proof of how large scale wave functions determine precession in binary stars.

        That amature is me and I have never made money for my research. And it is the only proven link between quantum mechanics and gravitational fields. Professional physicist consider such research a threat to the money they have made trying to solve the problem. How many Fundamental Physics Prizes are given out to people for trying to do what I did. Science is more about money and less about discovery. More about promotion and less about announcing discoveries. They have created a culture where science his become philosophy.

        1. Amateur simply means you do not make money with a particular craft.

          That is not quite the definition we should use here. I too have had work published while not actually being employed to conduct research.

          Thus I have used a more subtle definition.

          Einstein and Faraday were amateurs by this definition but this says nothing about the professionalism of their work before or after they started making money.

          But not by my definition employed here.

          An amateur published in the peer reviewed Indian Journal of Science and Tech & Bulgaria’s Sofia Technical University presented the research at their 2011 physics conference.

          I do not know this journal, but a quick look at its website leaves me in doubt it is well respected. But I am willing to be corrected on that.

          Anne Astronomy News actually reported on proof of how large scale wave functions determine precession in binary stars.

          What is Anne Astronomy?

          And it is the only proven link between quantum mechanics and gravitational fields.

          Then it should have been published in a top journal. Why was it not?

          Professional physicist consider such research a threat to the money they have made trying to solve the problem.

          You have asked many about this?

          Science is more about money and less about discovery.

          Unfortunately we all need money to live. Scientists are no exception to that.

          One last thing, do you have any formal physics or mathematics qualifications?

          1. To second the ones supporting Amateurs, I would like to say that, Satyendranath Bose never earned PhD. He agreed he was an amateur, apart from his famous work he never published anything much in Science. When asked about why he is not sad about winning Nobel Prize, he said he did not deserve it as it was meant for people who have worked hard at some problem for years.

            He may be an amateur but he contributed well. What we need to have is an open mindset to idea. Yes, sure there are shit people around plagiarising and creating false theories for fame, but there are smart people out there who are serious about their research.

            Freeman Dyson has always opposed the PhD system and he never got a PhD. It is just certification which separates a group from others, but today’s race for survival (rather than for knowledge) it has become irrelevant.

    1. I am sorry you think that. This is not really the case.

      I expect that your comment comes from not knowing what is really involved in research in mathematics and theoretical physics.

  7. reading the above post and the comments, i like to say a few things: 1) the special theory relativity actually only uses high school mathematics, since it was one of the subjects we studied in my high school. therefore, it is quite possible for a smart high schooler to show that the STR is mathematically incorrect using only high school mathematics. 2) the famous indian mathematician, Ramanujan, did not even pass high school. except for maths he failed all the other subjects. is there any Ph.D mathematician/physicist, in the whole world, who will consider his contributions to mathematics as amateurish? what he had written is not only being used in the most advanced mathematical and physical theories, but, there still remains a large body of this amateur mathematician’s work that seems to be beyond the ken of the smartest “Ph.D mathematician/physicist” alive today. 3) Newton invented the calculus as an undergrad and not after getting his doctorate. 4) the similarity of between Newton and Einstein is that they both considered the physical idea to be primary and the mathematics to be secondary and used it only as a language to give precision to their physical ideas. they were mathematico-physicists, unlike todays physico-mathematicians who consider mathematics to be primary and the physical ideas to be secondary. this is the reason, unless your paper is filled with complex equations it is not considered to be worthy for publication in a “prestigious” journal, even though the physical conclusion, could be either quite simple or even makes no physical sense at all. therefore one comes across many papers in “prestigious” journals that are filled with complex equations with a physically non-sensical conclusion. I recently read a paper in the “prestigious” journal, physical review D, where the author, who is a Ph.D and does full time academic research, in an American university, after a lengthy mathematical argument concluded that the speed of light in vacuum has to be decreasing since the big bang. strangely, he used the relativistic theories in his mathematical arguments to come to this conclusion! This is the opposite of what Newton or Einstein would do. for example, Einstein first formulated the physical idea called the principle of equivalence, then used mathematics construct his gravitational theory based on the physical idea. finally, 4) the professional/Ph.D mathematician and physicist seem to love the idea of showing off to the lay public just how “smart” he/she is and how “dumb” everyone else is, through the use of complex equations to express simple physical ideas. that is why when we are shown a picture of a professor it usually has a black board filled with complex looking, G-D only knows whether they even make any sense, equations as the background. the result of this physico-mathematical paradigm is that the papers that are being published are using longer and longer mathematical arguments to arrive at narrower and narrower conclusions, so much so, that someone with a Ph.D in one field of mathematics/physics has to get another Ph.D to understand a paper from a slightly different field of mathematics/physics. This change of paradigm is the legacy of Hawking. the journals have also been forced to change to the Hawking paradigm in order to remain in business. the journals, by catering only to a select group of readers, have created a vicious circle of mutual positive feedback, resulting in the exclusion of the vast majority of humanity, resulting in wide-spread scientific illiteracy and mushrooming of pseudo-science, such as astrology, the Nostradamus effect/prophecies, ancient aliens building the pyramids and so forth. I believe we are going through a second dark age in science, where the Ph.D mathematicians/physicists have replaced the church fathers. I hope we soon have the arrival of a second “Copernicus”, “Bruno”, “Galileo” and finally a “Newton”, to end this second dark age and return us back to the correct path of doing science and the scientific paradigm.

    1. Thank you for your comments here.

      There are too many for me to address properly, but what I will say is that picking a few very rare examples of ‘amateurs’ ,and we can debate if your examples really are ‘amateurs’, does not diminish my overall conclusion that it is unlikely that ‘amateurs’ can generally contribute to mathematics and physics. No where have I said that it is impossible.

  8. i joined physics ug program fascinated by astronomy, space, quantum physics.then in the first semester we only had to do lengendre,hermite, vector analysis, blah blah, blah.this will seem boring to a lot who were attracted to physics by facts like nothing is faster than light, mass and energy are equivalent, elihu thompson experiment, faraday effect,amplification by THEY MAKE YOU /THEY WILL MAKE you a mathematician first.not that i hate maths or something, but these days even in my classes ,after a professor has delivered a lecture you just have to ask him/her one question to make THEM shit in their pants:SIR , COULD PLEASE GIVE THE PHYSICAL SIGNIFICANCE OF THE EQUATIONS YOU DERIVED/SIR, WHAT IS THE PHYSICAL MEANING OF THIS DERIVATION? hence today amateurs are marginalized, demoralized by THIS UNHOLY CABAL OF PHYSICO-MATHEMATICIAN.I have a counter question WHAT GREAT CONTRIBUTION ARE YOU PROFESSIONAL PHYSICIST MAKING TO THE REALM OF HUMAN UNDERSTANDING OF NATURE?THE BASIC LAWS OF PHYSICS THAT YOU LIKE TO COMPLICATE WERE DEDUCED BY AMATEURS.WHO / WHAT IS A PROFESSIONAL PHYSICIST??? the one who mugged up countless equations, whose significance he /she couldn’t understand, then vomitted them on an sheet of paper to get a degree.the one who did repeatedly only those problems posed by his/her teachers AS HOMEWORK LIKE IN A MIDDLE SCHOOL OR SOMETHING, and those teachers PUT THE SAME HOMEWORK QUESTION in the exam.Those who are willing to SATISFY EVERY NEED OF THEIR PHD GUIDE to JUST GET THAT PRIZED SALUTATION OF Doctorate.
    The so called PROFESSIONAL S are CERTIFIED , HENCE BUREACRATS, BUREACRATS cant think.they also dont allow others to think by making a curricula
    that makes you lose your prime years 15 to 25 rote learning instead of thinking 16 hours a day.YOU SO CALLED PROFESSIONAL S MUST TEACH “HOW TO THINK”NOT “THIS IS THE ONLY THING YOU MUST THINK” TO SEE ANY REAL CHANGE HAPPENING IN THE REALM OF HUMAN UNDERSTANDING.

    1. When I started my undergraduate studied in physics, some of my fellow students made similar comments along the lines of ‘I wanted to learn physics not mathematics’. However, the two disciplines are not as separate as one may first think. Mathematics is the basic framework for physics and so it is inevitable that any physics course will contains lots of mathematical methods. Without the mathematics the physics is quite empty… mathematics is essential in our understanding.

  9. How can you reply that Einstein didn’t meet your qualification for amateur? He had only undergrad training and was working as a patent clerk when he had his “miracle year”. Then, you claim this is just one example. But of course it is the prime example, and honestly should disqualify your entire premise as it illustrates, quite explicitly, that an amateur can make a most monumental contribution to physics. Einstein didn’t know the math he needed to publish his papers at the start of his career, he engaged a mathematician to assist him in that.

    The fact is, it may well continue to be amateurs who pop up in history every so many years, who cause us to think differently about the problems we face in physics.

    Einstein himself argued for the amateur, saying we need a child’s fresh eyes. I’m paraphrasing, of course, but you can look up the quote if you’d like.

    You can do all the proper research you’d like, but if you’re looking down the wrong avenue you won’t contribute in any significant insight. Isn’t it also reasonable to suspect that if an amateur was able to posit a theory, even if his methods of deriving this were unorthodox, and that theory could be tested, and that theory could be disproven, wouldn’t that theory stand as reasonable a chance of contributing as any other?

    It takes a certain amount of understanding, to be sure, but the most likely qualifier may well be an intuitive aptitude for the subject, rather than degree of certification.

    1. Einstein was working on his PhD thesis when at the Patent Office. The usual thing at that time was to take up a teaching position to support oneself while a PhD student. Thus, Einstein would not meet my rather loose definition of am amateur.

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