The Dance of Mathematical Notations

Though the introduction of symbolic mathematics in its modern form is generally credited to the French mathematician Fran¸cois Vi`ete in the sixteenth century, the earliest appearance of algebraic notation seems to have been in the work of Diophantus, who lived in Alexandria some time around 250ce.

"Just like a page of sheet music represents a piece of music; the music itself is what you get when the notes on the page are sung or performed on a musical instrument. The same is true for mathematics; the symbols on a page are just a representation of the mathematics.

When read by a competent performer (in this case, someone trained in mathematics), the symbols on the printed page come alive—the mathematics lives and breathes in the mind." - Keith Devlin

Is Keith Devlin distorting and creating just a fancy desire? OR Is this a possibility where one can breathe life into his study of mathematical objects? Can one dance to these mathematical notations?

  • $\begingroup$ I think it depends on the area of math. Are you asking for examples (btw, this is a beautifully worded question :) ? $\endgroup$ Apr 29, 2020 at 16:15
  • $\begingroup$ There is no distortion. Symbols and notation are what we use to communicate mathematics. $\endgroup$
    – John Douma
    Apr 29, 2020 at 16:21
  • $\begingroup$ I don't understand what the question is here... Are you concerned that the author of that passage is using language that is too flowery and poetic to be attributed to the sciences and are suggesting that mathematics should be emotionless and mechanical? Have you heard the phrase "Beauty is in the eye of the beholder"... $\endgroup$
    – JMoravitz
    Apr 29, 2020 at 16:24

1 Answer 1


Physically dance? No, I doubt many can actually dance to a piece of printed sheet music either.

But what's on the paper is indeed not the actual math, it is merely an attempt at transferring the mathematics going on in one person's head into someone else's head. And when mathematicians read an engaging paper (at least when I do it), then what's going on in the reader's head is definitely not unlike dancing, and some times even hand movements (including, but not limited to, scribbling) may be required to fully appreciate the thought one is thinking. At least that's my philosophy on the matter.

  • $\begingroup$ A paper can be lucid in its prose as well as its symbolism. I believe the question was specifically about symbolism. $\endgroup$
    – John Douma
    Apr 29, 2020 at 16:27

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