Monotype Bodoni looked like a good candidate for the title on the first page, but not a great match for the text:
http://www.myfonts.com/fonts/mti/bodoni-mt/

New Caledonia seems to be a better match, though this metal or early phototypesetting version has a distinctly different italic f:
http://www.myfonts.com/fonts/linotype/new-caledonia/

Thanks very much! I will change the post now. Regarding the symbols for formulae, would you have any additional information as to how they were typeset?

Any of several Scotch Romans, including New Caledonia as suggested by Kevin.
In the days of metal typesetting, the character sets of a font were limited. To set special characters such as mathematical symbols the printer had to resort to an additional font of symbols, sometimes called, particularly in the US, a "Pi" font because it usually included the letter π.
I don't know if this particular page was hand set or in a font that could be used in a Linotype or similar machine.
By 1957 photo-composition was replacing metal. So this is also a possibility for your page.
For a digital substitute there are specialized math fonts or you could use a Scotch Roman with a good math component. You might look at Nick Shin's Scotch Modern https://www.myfonts.com/fonts/shinn/scotch-modern/
For more info on typesetting you might start with this wiki http://en.wikipedia.org/wiki/Typesetting
Don

The font in the mathematical formulae (which differs from the font used for variables in the text) is not far from Computer Modern (default with TeX) that was based on Monotype Modern 8a. Here is Computer Modern

(The default spacing between f and P given by TeX is larger; I had to use some negative kerning to match the sample)

Don, I based my ID mostly on the italic subhead at the lower right of the sample. Though the italic f in the sample still gives me pause, New Caledonia was the best match I could see:

Kevin, I agree with your call of New Caledonia -- a Scotch Roman -- as the closest digital to the 1957 Italic subhead. The rest of the text is not detailed enough to say 100% but New Caledonia would certainly make a reasonable substitute.

As for the math, anyone familiar with TeX could use Computer Modern, as suggested by Michel. Some info on Computer Modern at
http://en.wikipedia.org/wiki/Computer_Modern
http://www.ctan.org/pkg/cm-unicode

I'm not certain the math it could be set in New Caledonia or any of the other Scotch Romans.
I wonder which regular fonts might have this capability?
Don

I wonder which regular fonts might have this capability?

I’m not sure what you consider a “regular” font, but there are non-TeX fonts especially suited for setting math. Most notably Cambria Math and Stix (http://www.stixfonts.org).
List of fonts with a MATH table: https://developer.mozilla.org/en-US/docs/Mozilla/MathML_Project/Fonts#MA...

I looked at the maths in the rest of the paper and the typesetting does not meet the mathematical standards of that period. It would also be hard to reproduce formulas that are that badly formatted with currently available tools.

For a historical overview, there is a nice little publication entitled "Mathematical Typesetting" available from Tiro typeworks at http://www.tiro.com/projects.html

There is also Daniel Rhatigan, The Monotype 4-Line System for Setting Mathematics, Essay submitted in partial fulfilment of the requirements for the MA in Typeface Design, University of Reading, 2007 http://ultrasparky.org/school/pdf/Rhatigan_Monotype_4-line_math.pdf,