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I'm a senior applying for admissions to Ph.D. programs in mathematics. The departments I'm applying to all ask for three recommendations and encourage (but don't usually require) them to be from math professors.

I have three math professors whom I plan to ask for letters, and I believe all of them will be strong, but perhaps not superlative. In addition, I know a professor who is primarily from the philosophy department (whose interests are related to math) who I believe would write a stronger letter than the other three. (He supervised an unusual independent study course for me and it was fairly successful).

The subjects I studied with him were entirely mathematical (logic), but his own work is more distinctly on the philosophy side (philosophy of science/math and related topics, not mathematical logic) .

Could asking this professor to write a fourth letter harm my application in any way? I think the letter itself would represent me in a good light and highlight an unusual aspect of my resume, but I don't want it to replace a letter from a mathematician for fear of admissions committees looking negatively at a letter from someone in the wrong department.

EDIT In response to the comment: I've worked closely will all three math professors. I've done long-term research projects with two of them (my university requires a junior and senior thesis; they were my advisors), and a year-long independent study with the third. I believe they were all reasonably happy with my performance, but I'm not sure I was able to blow them away. The independent study project I did with the professor from the philosophy department was more unusual, took more initiative on my part, and I believe I made a stronger positive impression.

I'm a senior applying for admissions to Ph.D. programs in mathematics. The departments I'm applying to all ask for three recommendations and encourage (but don't usually require) them to be from math professors.

I have three math professors whom I plan to ask for letters, and I believe all of them will be strong, but perhaps not superlative. In addition, I know a professor who is primarily from the philosophy department (whose interests are related to math) who I believe would write a stronger letter than the other three. (He supervised an unusual independent study course for me and it was fairly successful).

The subjects I studied with him were entirely mathematical (logic), but his own work is more distinctly on the philosophy side (philosophy of science/math and related topics, not mathematical logic) .

Could asking this professor to write a fourth letter harm my application in any way? I think the letter itself would represent me in a good light and highlight an unusual aspect of my resume, but I don't want it to replace a letter from a mathematician for fear of admissions committees looking negatively at a letter from someone in the wrong department.

I'm a senior applying for admissions to Ph.D. programs in mathematics. The departments I'm applying to all ask for three recommendations and encourage (but don't usually require) them to be from math professors.

I have three math professors whom I plan to ask for letters, and I believe all of them will be strong, but perhaps not superlative. In addition, I know a professor who is primarily from the philosophy department (whose interests are related to math) who I believe would write a stronger letter than the other three. (He supervised an unusual independent study course for me and it was fairly successful).

The subjects I studied with him were entirely mathematical (logic), but his own work is more distinctly on the philosophy side (philosophy of science/math and related topics, not mathematical logic) .

Could asking this professor to write a fourth letter harm my application in any way? I think the letter itself would represent me in a good light and highlight an unusual aspect of my resume, but I don't want it to replace a letter from a mathematician for fear of admissions committees looking negatively at a letter from someone in the wrong department.

EDIT In response to the comment: I've worked closely will all three math professors. I've done long-term research projects with two of them (my university requires a junior and senior thesis; they were my advisors), and a year-long independent study with the third. I believe they were all reasonably happy with my performance, but I'm not sure I was able to blow them away. The independent study project I did with the professor from the philosophy department was more unusual, took more initiative on my part, and I believe I made a stronger positive impression.

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Is it ever harmful to submit extra recommendation letters from somebody outside of my department?

I'm a senior applying for admissions to Ph.D. programs in mathematics. The departments I'm applying to all ask for three recommendations and encourage (but don't usually require) them to be from math professors.

I have three math professors whom I plan to ask for letters, and I believe all of them will be strong, but perhaps not superlative. In addition, I know a professor who is primarily from the philosophy department (whose interests are related to math) who I believe would write a stronger letter than the other three. (He supervised an unusual independent study course for me and it was fairly successful).

The subjects I studied with him were entirely mathematical (logic), but his own work is more distinctly on the philosophy side (philosophy of science/math and related topics, not mathematical logic) .

Could asking this professor to write a fourth letter harm my application in any way? I think the letter itself would represent me in a good light and highlight an unusual aspect of my resume, but I don't want it to replace a letter from a mathematician for fear of admissions committees looking negatively at a letter from someone in the wrong department.