| Reference number | Title | Date |
| EC/1897/18 | Mathews, George Ballard: certificate of election to the Royal Society | |
| RR/15/291 | Referee's report by George Ballard Mathews, on a paper 'On the theory of consistence of logical class-frequency and its geometrical representation' by George Udny Yule | March 1901 |
| RR/16/209 | Referee's report by George Ballard Mathews, on a paper 'Memoir on the theory of the partitions of numbers. Part III' by Percy Alexander MacMahon | December 1904 |
| RR/16/50 | Referee's report by George Ballard Mathews, on a paper 'Skew refraction through a lens; and on the hollow-pencil given by an annulus of a very obliquely placed lens' by Joseph David Everett | nd [c January 1903] |
| RR/16/89 | Referee's report by George Ballard Mathews, on a paper 'On a generalised Theory of Alternative Inheritance with special reference to Mendel's Laws' by Karl Pearson | nd [c December 1903] |
| RR/16/161 | Referee's report by George Ballard Mathews, on a paper 'On the normal series satisfying linear differential equations' by E Cunningham | January 1904 |
| RR/17/61 | Referee's report by George Ballard Mathews, on a paper 'Second memoir on the compositions of numbers' by Percy Alexander MacMahon | 18 September 1906 |
| RR/16/410 | Referee's report by George Ballard Mathews, on a paper 'The influence of bias of personal equation in statistics of ill-defined qualities: an experimental study' by George Udny Yule | December 1905 |
| NLB/25/526 | Copy letter from Robert William Frederick Harrison, to Professor George Ballard Mathews, Fellow of the Royal Society | 14 November 1902 |
| NLB/27/844 | Copy letter from Robert William Frederick Harrison, to George Ballard Mathews, Fellow of the Royal Society | 9 December 1903 |
| NLB/29/263 | Copy letter from Theodore E James, to Professor George Ballard Mathews, Fellow of the Royal Society | 27 August 1904 |
| NLB/28/279 | Copy letter from Robert William Frederick Harrison, to George Ballard Mathews, Fellow of the Royal Society | 10 February 1904 |
| MC/20/170 | Letter from [George Ballard] Mathews, to [Joseph] Larmor | 1 November 1905 |
| NLB/29/901 | Copy letter from Robert William Frederick Harrison, to George Ballard Mathews, Fellow of the Royal Society | 10 January 1905 |
| NLB/32/633 | Copy letter from Robert William Frederick Harrison, to Professor George Ballard Mathews, Fellow of the Royal Society | 26 April 1906 |
| NLB/35/701 | Copy letter from Joseph Larmor, to George Ballard Mathews, Fellow of the Royal Society | 5 July 1907 |
| NLB/35/710 | Copy letter from Robert William Frederick Harrison, to Professor Joseph Larmor, Secretary, Royal Society | 9 July 1907 |
| NLB/40/32 | Copy letter from Joseph Larmor to G [George] B [Ballard] Matthews | 25 March 1909 |
| RR/17/431 | Referee's report by George Ballard Mathews, on a paper 'An electrical device for evaluating formulae and solving equations' by Alexander Russell and Arthur Wright | April 1909 |
| RR/17/433 | Referee's report by George Ballard Mathews, on a paper 'On the graphical determination of Fresnel's integrals' by J H Shaxby | March 1909 |
| RR/17/318 | Referee's report by George Ballard Mathews, on a paper 'Memoir on the theory of the partition of numbers, part IV' by Percy Alexander MacMahon | July 1908 |
| RR/14/63 | Referee's report by George Ballard Mathews, on a paper 'Memoir on the theory of the partitions of numbers.—Part II' by Percy Alexander MacMahon | 16 January 1899 |
| RR/18/59 | Referee's report by George Ballard Mathews, on a paper 'Memoir on the theory of the partitions of numbers. —Part V. Partitions in two-dimensional space' by Percy Alexander MacMahon | December 1910 |
| NLB/63/76 | Copy letter from James Hopwood Jeans, Secretary of the Royal Society and FRS; to W.E.H. Berwick Esq.
49 Bierley Lane, Dudley Hill, Bradford | 21 June 1922 |
| NLB/62/647 | Copy letter from Francis Alexander Towle, Assistant Secretary of the Royal Society; to Professor [Godfrey Harold] Hardy, FRS | 31 March 1922 |
| NLB/62/779 | Copy letter from James Hopwood Jeans, Secretary of the Royal Society; to Professor [Horace] Lamb, FRS | 4 May 1922 |
| RR/15/356 | Referee's report by George Ballard Mathews, on a paper 'Quaternions and projective geometry' by Charles Jasper Joly | December 1902 |
| RR/16/205 | Second referee's report by George Ballard Mathews, on a paper 'The Basic-Gamma-Function and the Elliptic Functions' by Reverend F H Jackson | 14 July 1904 |
| RR/16/164 | Referee's report by George Ballard Mathews, on a paper 'A memoir on the theory of order as defined by boundaries' by Edward T Dixon | July 1904 |
| RR/16/413 | Referee's report by George Ballard Mathews, on a paper 'A property which holds good for all groupings of a normal distribution of frequency for two variables, with applications to the study of contingency, tables for the inheritance of unmeasured qualities' by George Udny Yule | December 1905 |
| RR/16/399 | Referee's report by George Ballard Mathews, on a paper 'Mathematical concepts of the material world' by Alfred North Whitehead | October 1905 |
| RR/16/204 | Referee's report by George Ballard Mathews, on a paper 'The Basic-Gamma-Function and the Elliptic Functions' by Reverend F H Jackson | December 1904 |
| RR/16/416 | Referee's report by George Ballard Mathews, on two papers 'On a property which holds good for all groupings of a normal distribution of frequency for two variables, with applications to the study of contingency-tables for the inheritance of unmeasured qualities' and 'On the influence of bias and of personal equation in statistics of ill-defined qualities: An experimental study' by George Udny Yule | 13 December 1905 |
| MC/23/293 | Letter from [George Ballard] Mathews, 10 Menai View, Bangor, to [Joseph] Larmor, [Royal Society] | 15 October 1908 |
| MC/20/169 | Letter from [George Ballard] Mathews, 14 Temple Road, Worthing, to the Royal Society | 30 September 1905 |
| MC/20 | Volume 20 of miscellaneous correspondence regarding business matters, sent to the Royal Society | 1905 |