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This question is inspired by a set of questions at the end of Timothy Gowers' book:

Mathematics: A Very Short Introduction, Oxford University Press, 2002.

The possible relation between mathematics and music is an old open question. In the ancient Greece some philosophers like Pythagoras and Plato strongly believed that there is a mysterious relation between these two completely different subjects. Their arguments were mainly based on the abstract nature of mathematics amongst different fields of science and abstract nature of music amongst different fields of art. Also they argued on the possible similarity between "mathematical beauty" and "beauty of music" based on the philosophical similarity between notions of "pattern" and "harmony" in math and music respectively.

In the recent years the new approach to this old question is mainly focused on the possible positive impacts of listening and training music on improving mathematical abilities of children and adults.

Question 1. Are there any scientific math education research which proves a direct relevance between listening/training music and a meaningful improvement in children/adults' mathematical abilities?

Question 2. If the answer of the question 1 is positive and there is such a relation, do different genres of music (e.g. classic, without vocal, pop, rock, etc.) have different impacts? What the statistics shows?

Question 3. Does listening/training music regularly have a notable impact on notable mathematical and scientific discoveries? Precisely, is there any statistical research which determines the frequency of musical interests of great mathematicians and scientists? e.g. Both Cantor and Einstein were good violinists.

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    $\begingroup$ I don't know of any conclusive research on this topic, but I can offer this anecdotal evidence (also, the whole question is related). $\endgroup$
    – dtldarek
    Mar 29, 2014 at 7:57
  • $\begingroup$ Personally, I find techno very helpful for certain tensor calculus. $\endgroup$
    – James S. Cook
    Mar 29, 2014 at 14:14
  • $\begingroup$ @dtldarek, I can't work without some form of music playing. But even listening to TV helps. So any relationship to genre is tenuous, at best. $\endgroup$
    – vonbrand
    Mar 29, 2014 at 22:17

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Responding to Q1: At the grade-school level, there is considerable evidence that music (and also dance) can be used to teach fractions. E.g.,

"Rhythm and Music Help Math Students." Scientific American. 2012. Article link: "Grade school kids who learned about fractions through a rhythm-and-music-based curriculum outperformed their peers in traditional math classes."

Another article:

"Fractions Curriculum Strikes Right Note In California." NPR. 2012. Article link. "A recent study found that students who went through the program tested better on fractions. "

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  • $\begingroup$ Thank you for your useful answer. It is an interesting observation. $\endgroup$
    – user230
    Mar 30, 2014 at 4:31
  • $\begingroup$ +1 for citing and summarizes articles. $\endgroup$
    – ruler501
    Mar 30, 2014 at 5:01
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A small contribuition; This might help discussion going. I do not have a comprehensive direct answer, however, at the moment I am working on something else that allowed me to see some of the potentially relevant information:

“…Klinedinst (1991), who also found links between retention in an instrumental music programme and scholastic ability, reading achievement, and mathematics achievement.” [from: Evans, P., McPherson, G. E., & Davidson, J. W. (2013). The role of psychological needs in ceasing music and music learning activities. Psychology of Music, 41(5), 600-619. doi: 10.1177/0305735612441736, p.1]

Klinedinst, R. E. (1991). Predicting performance achievement and retention of fifth-grade instrumental students. Journal of Research in Music Education, 39, 225–238.

I also know that it has been lately research in neuroscience with positive answers to Q1, just don't have that reference handy. I will try to find it.

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  • $\begingroup$ The references are very nice. Thanks. $\endgroup$
    – user230
    Mar 30, 2014 at 4:30
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In fact there are only some categories of music (mainly in music engineering or acoustical engineering) really relate to mathematics. For example we will expect the musical instrument manufacturers, the loudspeakers manufacturers or the acoustical engineers should have capable mathematics backgrounds but will not expect the singers should have capable mathematics backgrounds.

Note that the strong bondings between mathematics and music formed only when the developments of e.g. music engineering and acoustical engineering, the ancient greeks' feelings of the relationship between mathematics and music are in fact too farfetched and you should ignore them.

So if you really want to improve mathematical abilities through music, you can for example join some music engineering or acoustical engineering works, but for example listening music are certainly not helpful.

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    $\begingroup$ I'm fairly certain this answers a completely different question than the one the poster was asking. $\endgroup$
    – user614
    Apr 3, 2014 at 20:03

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