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Lest we forget that Albert Einstein once said that when he ran into a problem in he would play the violin until the solution would present itself.

“If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music.” Albert Einstein.

I suspect that if you asked if we were good at literature, painting - or just about anything cerebral or that required dextrous ability we would average as, well, better than average (did I just say my math skills were good ! )...
I'm not sure it's that musicians are mathematical, more that mathematicians (or engineers) are musical. Along with doctors. University and amateur (community) orchestras, I think you'll find these two groups very much over-represented.
I was an engineer before I went into music full-time

if you asked any group of people about any skill you would have got much the same answer, do not know how you would get anything statistically significant, I suppose one could set up a test and see if there were correlations... If you asked mathematicians what their interests were outside mathematics most would say music and walking.
Malcolm's comment agrees with my experience of amateur adult orchestras, but I would add that teachers (not necessarily of music) also seem to make up a significant proportion of such orchestras.

My degree is in maths, pure maths, as in that legendary toast at the annual Dinner of a University Mathematics Faculty - "Here's to Pure Mathematics, and may it never be of any use to anyone". Quite untrue, of course.
I selected excel, but only due to years of experience in the "real world", in school I thought of myself as average, but that has a lot more to do with who I hung out with.
Both music and math are concerned to a great extent with patterns - recognizing, reproducing, manipulating them. So it would make sense that someone good at one might also be good at the other.
I selected excels, though that would have been in my youth. I have almost purposely avoided math, programming and the like for the last decade or more. Since I became Mr. Mom I have been trying to live the stereo type. Well, not really, but its a good excuse to focus art and music. The problem I found with Math is that after 13 years of non-use I can say the old adage "use it or lose it" is very true when it comes to math, and most things probably. I just can't remember.
At high school, I was brilliant at advanced level mathematics but I am 'less than adequate on the violin' so I do not believe that there is any correlation between the two. Some people may be good at both, but then, some people seem to be good at everything !
I hold a Master's degree and taught various college courses in mathematics for more than a decade, including at a music school.

Sometimes I would describe music to my students as audible math and dance as kinesthetic math.

Had I applied for one, I might have gotten myself into a university to study math. My grades were good enough for most universtities but probably not Oxbridge - however I was offered a Music Scholarship at Cambridge and took it. Seemed a good idea back then ! No regrets.
PS - During my formative years, there were lots of violinists to be heard on the radio, but NEVER anyone proclaiming about trigonometrical identities of one angle and such. No-one ever explained to me what higher Math was FOR !!!
Well, I have to say that math never was my strong subject... In fact it's my worst.

I use to think that there was a strong connection between math and music, but now I am not sure. Math is great, being able to do multiplications up to a hundred, i.e. 50*78=390, really helps with building your working memory and short term memory. A strong working memory is going to help us be better overall musicians, but I don't think it's an essential key to playing. Math also helps us with focusing though, and being able to focus and stay calm is an essential key in playing music. But I find that meditating and a great diet are much stronger factors towards strong playing than great math skills.

If you want to practice your math and strengthen your working memory you can go here

I am well above average with spatial, mechanical and mathmatical ability. So the tests say---??? Actual math? Nooo.
I do believe that if a person's brain was wired to excel in math, that person would be a far better musician. To some of us, we will have to work harder because our heart is wired for music.

My son goes to school with a boy who, at 11, is playing the Mendelssohn concerto well--not just for fun. He studies in the most prestigious violin studio in one of America's largest cities. In 2013, he tested into high school calculus by the school district's math coordinator. When asked how he can remember new music so quickly, he says that he sees the patterns in the music. In this case, I'd say there's definitely a connection : )!
Violinist.com ... where the math skills are above average.

I think perhaps a better question is whether one really enjoys math. The challenge of math and of music are similar in certain ways -- both are limitless, in both breadth and depth, and both have aspects that are aesthetically pleasing and deeply logical. But Hofstadter probably has made the best case. Hard to believe that was 35 years ago.

I'm great at math, but for some inexplicable reason I can't seem to count to four or divide by 3 or 5 reliably when playing.

I have taught and do teach a significant number of students that excel in mathematics, participate and compete in math clubs and teams, take high school AP math, enroll in after-school private advanced math classes, and really, really like math.

Perhaps if parents are going the extra 100 miles to support a child's violin studies, it isn't too much of a stretch to assume these parents will also go another extra 100 miles to support a child's interest in math.

Not my subject though...

Mathematics is easy for me; arithmetic, on the other hand, is difficult. One works abstraction and applies patterns to solve problems; arithmetic is simply to solve problems. It's like the difference between theoretical physics and applied physics.

I believe that musicians can fall into either (or both) categories and it's based on how we individually process information. Some of us (I don't know how many...) start by reading the music, looking for patterns (or themes), decomposing the music, listening to it in our heads, studying the scores, and so on ~ then finally picking up the instrument to try it out. Others begin with learning by opening the case and playing the notes, figuring out comfortable/effective bowing, memorizing the piece, then going to a lesson to learn about the music ~ but with the notes under their fingers.

Recognizing how an individual processes information might be useful in deciding what technique would best work with a learner. If I don't understand the foundational physics principles that underly Schrodinger equations, for example, I would never be able to memorize and apply the complex relationships. Similarly, if I didn't use my highlighter to identify thematic passages in a piece, I would never be able to memorize a piece. I can't memorize notes; I have to memorize lyrics and sequences of notes that comprise a passage. There's sort of a song in my head.

Hmmm... Maybe there is a similarity.

I don't think there is a connection. Here is why.
My husband, math wiz when he was young, computer engineering major and Director of Technology Services of one of the leading companies, always was and still is tone deaf. If he is very happy, he is humming, though always the same hard to define 5 notes tune. He would fall asleep listening to classical music in Symphony Hall. He would ask how much longer until the end of that sonata if we go to my son's school concerts and take an i-phone with him to read.

Now, my son, is totally different story. He is 8 yo, his math is about 6-7 grade level now. He would say the answer before my brain wheels even start to turn. Not to mention, that he doesn't need pen and paper for his calculations. Where I need to work on the problem step by step, he would blurt out the answer and I'd have to ask him to redo slowly, only to be able to check. He is playing violin and piano, although would happily loose the last and just play the violin.
And I- I would honestly say,- mediocre in both.

I would suspect that I have normal to above normal math skills. Having said that I have a graduate degree in quantitative genetics(applied statistics) and I do think that I have a better than average grasp of picking up patterns and cues in data. I think playing violin has something to do with it… maybe it's because I can focus intensely on my work for a longer period of time than the average Joe…. maybe it is because music rewired my brain.