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I get a little bit dyslexic/dyscalculia-like, when I try to interpret the more complicated arrangements of numbers [and symbols], used to describe set-theory and calculus. So I've taken to writing psuedocode, and drowning my statements in unnecessary parentheses [to help me nullify the need to remember an "order of operations"]. I'm even working on a new personal standard math-markup-language, to help myself grasp an ever expanding range of topics. But that begs the question; assuming I find something that works for me and does not fail/contradict itself: "Will I universally be expected [by the academic community of mathematicians] to translate my work into the pre-existing "standard notation" for it to be taken seriously; or is the academic field willing to accept different standards of mathematical expression, so long as they are fully realized [syntactically-standardized notations]?

If a new way of describing the same maths/math crops up [alongside the tradional way of describing those maths]: does it have a fighting chance? Or is it something that is universally frowned upon and considered disreputable [in an academic setting]?

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    $\begingroup$ You might gain more traction in the computer science and programming community, where different notations (non-decimal bases, postfix, prefix, and infix come to mind) are standard. $\endgroup$ Dec 21, 2017 at 18:21
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    $\begingroup$ If you develop a math-based programming language based on your syntax, it might work. $\endgroup$ Dec 21, 2017 at 18:24

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Mathematitians are busy people and don't want to learn new notation unless they have to. You are basically asking "will the global mathematical community adapt to my notation", and sorry, but the answer to that is no. You can't (and shouldn't) expect people to learn replacement notation just so they can read something you wrote.

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    $\begingroup$ @user179283 "more options of expression will accommodate more types of thinkers" and it will greatly decrease the capability of these thinkers to effectively communicate with one another because of the translations. That's just my opinion, of course, but I think most mathematitians will agree with it... $\endgroup$
    – 5xum
    Dec 21, 2017 at 13:59
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    $\begingroup$ Programmers are very busy people too and we have to learn new ways of expressing our thoughts and new notations with absurd frequency. I'm able to write a bit of functional code in at least seven different notations, for example. You can argue that it is not usual to learn new notations, but by no means there isn't such thing as "too busy to learn new things unless needed". My own productivity in math-related projects shoot up in the sky when I started using my shorthand notation. Sure, I'm not working on academia, but I wouldn't loathe to learn a new notation if that would bring me cool stuff $\endgroup$
    – T. Sar
    Dec 21, 2017 at 18:00
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    $\begingroup$ (I'm coming from a corporate, non-academic research viewpoint, however, so there might be a difference in perspective) $\endgroup$
    – T. Sar
    Dec 21, 2017 at 18:04
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    $\begingroup$ @user179283 Objective C, C#, Java and some other C-Like languages may look and feel like C and C++, but they have several big differences and are way more complex than just a different dialect. Some languages, like Perl, Haskel or F# are completely different beasts relative to the C-Family and still most programmers are okay at learning them. $\endgroup$
    – T. Sar
    Dec 22, 2017 at 8:12
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    $\begingroup$ @MorganRodgers That happens all the time, but in the form of patterns, coding styles, APIs and so on. Change from Business A to Business B, and even if they use the same language the code will be so different that you'll have to re-learn everything from ground up. Try to swap Entity Framework for N-Hibernate, and your data access layer will have a way different look and feel. Heck, new language features pop up all the time! I certainly wouldn't mind having to learn a new notation to read a paper or a piece of code. If it is good, I get a new tool. If it is bad, I learn how to not do something. $\endgroup$
    – T. Sar
    Dec 22, 2017 at 8:19
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I expect there are a few cases where new notations have revolutionized a field. There's an example in my field (CAGD): the development of "blossoming" provided a new way to label points in space, and magically made lots of things trivially easy to prove.

However, I suspect that this is very unusual. More typically, a new unconventional notation is just an inconvenience that adds burden and pain for the reader.

If you use unconventional terminology and notation that adds no significant value, you risk having your papers rejected by research journals. I have rejected papers (partly) for this reason myself.

So, unless you think your new notations will provide significant benefit for large numbers of people, I'd advise you to abandon them and spend your valuable time trying to get comfortable with the ones used by the rest of us.

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    $\begingroup$ Dirac Notation comes to mind too $\endgroup$
    – Matt
    Dec 21, 2017 at 23:27
  • $\begingroup$ That is helpful, to me, because I have been fooling around with new number systems and notational abbreviation systems [that I did not discuss in the original question above], and didn't know at all whether that was normal or not. So: this feedback really helps me contextualize! $\endgroup$
    – user179283
    Dec 22, 2017 at 6:24

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