Celebratio Mathematica

Gilbert Ames Bliss

Gilbert Ames Bliss
May 9, 1876 – May 8, 1951
A Biographical Memoir

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G. Bliss: “The mo­tion of a heav­enly body in a res­ist­ing me­di­um,” Pop. As­tron. 6 (1898), pp. 20–​29.

G. A. Bliss: “The second vari­ation of a def­in­ite in­teg­ral when one end-point is vari­able,” Trans. Amer. Math. Soc. 3 : 1 (1902), pp. 132–​141. MR 1500591 JFM 33.​0385.​01

G. A. Bliss: “The geodes­ic lines on the an­chor ring,” Ann. of Math. (2) 4 : 1 (October 1902), pp. 1–​21. MR 1502291 JFM 33.​0670.​02

G. A. Bliss: “Jac­obi’s cri­terion when both end-points are vari­able,” Math. Ann. 58 : 1–​2 (1903), pp. 70–​80. MR 1511229 JFM 34.​0402.​01

G. A. Bliss: “An ex­ist­ence the­or­em for a dif­fer­en­tial equa­tion of the second or­der, with an ap­plic­a­tion to the Cal­cu­lus of Vari­ations,” Trans. Amer. Math. Soc. 5 : 2 (1904), pp. 113–​125. MR 1500665 JFM 35.​0340.​01

G. A. Bliss: “Suf­fi­cient con­di­tion for a min­im­um with re­spect to one-sided vari­ations,” Trans. Amer. Math. Soc. 5 : 4 (1904), pp. 477–​492. MR 1500686 JFM 35.​0370.​02

G. A. Bliss: “The ex­ter­i­or and in­teri­or of a plane curve,” Bull. Amer. Math. Soc. 10 : 8 (1904), pp. 398–​404. MR 1558133 JFM 35.​0506.​01

G. A. Bliss: “The solu­tions of dif­fer­en­tial equa­tions of the first or­der as func­tions of their ini­tial val­ues,” Ann. of Math. (2) 6 : 2 (January 1905), pp. 49–​68. MR 1503546 JFM 36.​0389.​01

G. A. Bliss: “A gen­er­al­iz­a­tion of the no­tion of angle,” Trans. Amer. Math. Soc. 7 : 2 (1906), pp. 184–​196. MR 1500741 JFM 37.​0490.​01

G. A. Bliss and M. Ma­son: “A prob­lem of the Cal­cu­lus of Vari­ations in which the in­teg­rand is dis­con­tinu­ous,” Trans. Amer. Math. Soc. 7 : 2 (1906), pp. 325–​336. MR 1500752 JFM 37.​0402.​01

G. A. Bliss: “A proof of the fun­da­ment­al the­or­em of ana­lys­is sit­us,” Bull. Amer. Math. Soc. 12 : 7 (1906), pp. 336–​341. MR 1558345 JFM 37.​0495.​02

G. A. Bliss: “Book re­view: The the­ory of func­tions of real vari­ables, by James Pier­pont,” Bull. Amer. Math. Soc. 13 : 3 (1906), pp. 119–​130. MR 1558414

G. A. Bliss: “A new form of the simplest prob­lem of the Cal­cu­lus of Vari­ations,” Trans. Amer. Math. Soc. 8 : 3 (1907), pp. 405–​414. MR 1500795 JFM 38.​0408.​01

G. A. Bliss: “The con­struc­tion of a field of ex­tremals about a giv­en point,” Bull. Amer. Math. Soc. 13 : 7 (1907), pp. 321–​324. MR 1558473 JFM 38.​0408.​02

M. Ma­son and G. A. Bliss: “The prop­er­ties of curves in space which min­im­ize a def­in­ite in­teg­ral,” Trans. Amer. Math. Soc. 9 : 4 (1908), pp. 440–​466. MR 1500821 JFM 39.​0441.​01

G. A. Bliss: “On the in­verse prob­lem of the Cal­cu­lus of Vari­ations,” Ann. of Math. (2) 9 : 3 (April 1908), pp. 127–​140. MR 1502361 JFM 39.​0445.​01

G. A. Bliss: “A meth­od of de­riv­ing Euler’s equa­tion in the Cal­cu­lus of Vari­ations,” Amer. Math. Monthly 15 : 3 (March 1908), pp. 47–​54. MR 1516998 JFM 40.​1031.​08

G. A. Bliss and M. Ma­son: “Fields of ex­tremals in space,” Trans. Amer. Math. Soc. 11 : 3 (1910), pp. 325–​340. MR 1500866 JFM 41.​0437.​01

G. A. Bliss: “Book re­view: An in­tro­duc­tion to the study of in­teg­ral equa­tions, by Maxime Bôcher,” Bull. Amer. Math. Soc. 16 : 4 (1910), pp. 207–​213. MR 1558889

G. A. Bliss: “A new proof of Wei­er­strass’s the­or­em con­cern­ing the fac­tor­iz­a­tion of a power series,” Bull. Amer. Math. Soc. 16 : 7 (1910), pp. 356–​359. MR 1558920 JFM 41.​0286.​03

G. A. Bliss: “The func­tion concept and the fun­da­ment­al no­tions of the Cal­cu­lus,” pp. 263–​304 in Mono­graphs on top­ics of mod­ern math­em­at­ics rel­ev­ant to the ele­ment­ary field. Edi­ted by J. W. A. Young. Long­mans Green and Co., 1911. Zbl 0067.​03101

G. A. Bliss: “A gen­er­al­iz­a­tion of Wei­er­strass’ pre­par­a­tion the­or­em for a power series in sev­er­al vari­ables,” Trans. Amer. Math. Soc. 13 : 2 (April 1912), pp. 133–​145. MR 1500910 JFM 43.​0504.​02

G. A. Bliss: “A new proof of the ex­ist­ence the­or­em for im­pli­cit func­tions,” Bull. Amer. Math. Soc. 18 : 4 (1912), pp. 175–​179. MR 1559180 JFM 43.​0483.​04

G. A. Bliss: “Fun­da­ment­al ex­ist­ence the­or­ems,” pp. i–​ii,1–​107 in The Prin­ceton Col­loqui­um (Prin­ceton Uni­versity, 15–17 Septem­ber 1909), part 1. Amer­ic­an Math­em­at­ic­al So­ci­ety (New York), 1913. JFM 44.​0365.​01

G. A. Bliss and F. B. Wiley: “A meth­od of sub­divid­ing the in­teri­or of a simply closed rec­ti­fi­able curve with an ap­plic­a­tion to Cauchy’s the­or­em,” Bull. Sci. Lab. Den­ison Univ. 17 (1914), pp. 375–​389.

G. A. Bliss and A. L. Un­der­hill: “The min­im­um of a def­in­ite in­teg­ral for uni­lat­er­al vari­ations in space,” Trans. Amer. Math. Soc. 15 : 3 (1914), pp. 291–​310. MR 1500981 JFM 45.​0605.​03

G. A. Bliss: “The Wei­er­strass \( E \)-func­tion for prob­lems of the Cal­cu­lus of Vari­ations in space,” Trans. Amer. Math. Soc. 15 : 4 (October 1914), pp. 369–​378. MR 1500985 JFM 45.​0604.​03

G. A. Bliss: “A note on sym­met­ric matrices,” Ann. of Math. (2) 16 : 1–​4 (1914–1915), pp. 43–​44. MR 1502486 JFM 45.​0262.​05

G. A. Bliss: “A sub­sti­tute for Duhamel’s the­or­em,” Ann. of Math. (2) 16 : 1–​4 (1914–1915), pp. 45–​49. MR 1502487 JFM 45.​0452.​02

G. A. Bliss: “A note on func­tions of lines,” Proc. Natl. Acad. Sci. USA 1 : 3 (March 1915), pp. 173–​177. JFM 45.​0550.​01

G. A. Bliss: “Gen­er­al­iz­a­tions of geodes­ic curvature and a the­or­em of Gauss con­cern­ing geodes­ic tri­angles,” Amer. J. Math. 37 : 1 (January 1915), pp. 1–​18. MR 1507894 JFM 45.​0859.​02

G. A. Bliss: “Book re­view: Leçons sur les fonc­tions des lignes, by Vito Vol­terra,” Bull. Amer. Math. Soc. 21 : 7 (1915), pp. 345–​355. MR 1559651

G. A. Bliss: “Jac­obi’s con­di­tion for prob­lems of the Cal­cu­lus of Vari­ations in para­met­ric form,” Trans. Amer. Math. Soc. 17 : 2 (April 1916), pp. 195–​206. MR 1501037 JFM 46.​0758.​03

G. A. Bliss: “A note on the prob­lem of Lag­range in the Cal­cu­lus of Vari­ations,” Bull. Amer. Math. Soc. 22 : 5 (1916), pp. 220–​225. MR 1559765 JFM 45.​0605.​01

G. A. Bliss: “Book re­view: Top­ics in the the­ory of func­tions of sev­er­al com­plex vari­ables, by Wil­li­am Fogg Os­good,” Bull. Amer. Math. Soc. 23 : 1 (1916), pp. 35–​44. MR 1559859

G. A. Bliss: “A ne­ces­sary and suf­fi­cient con­di­tion for the ex­ist­ence of a Stieltjes in­teg­ral,” Proc. Natl. Acad. Sci. USA 3 : 11 (November 1917), pp. 633–​637. JFM 46.​1458.​03

G. A. Bliss: “In­teg­rals of Le­besgue,” Bull. Amer. Math. Soc. 24 : 1 (1917), pp. 1–​47. MR 1560001 JFM 46.​0383.​01

G. A. Bliss: “The prob­lem of May­er with vari­able end points,” Trans. Amer. Math. Soc. 19 : 3 (1918), pp. 305–​314. MR 1501104 JFM 46.​0758.​04

G. A. Bliss: “Solu­tions of dif­fer­en­tial equa­tions as func­tions of the con­stants of in­teg­ra­tion,” Bull. Amer. Math. Soc. 25 : 1 (1918), pp. 15–​26. MR 1560139 JFM 47.​0940.​01

G. A. Bliss: “A meth­od of com­put­ing dif­fer­en­tial cor­rec­tions for a tra­ject­ory,” J. U.S. Ar­til­lery 51 (1919), pp. 445–​449. Cor­rec­ted copy of earli­er print­ing in vol. 50 (pp. 455–460).

G. A. Bliss: “The use of ad­joint sys­tems in the prob­lem of dif­fer­en­tial cor­rec­tions for a tra­ject­ory,” J. U.S. Ar­til­lery 51 (1919), pp. 296–​311.

G. A. Bliss: Dif­fer­en­tial cor­rec­tions for anti-air­craft guns. Technical report, Ab­er­deen Prov­ing Ground, 1919.

G. A. Bliss: “Dif­fer­en­tial equa­tions con­tain­ing ar­bit­rary func­tions,” Trans. Amer. Math. Soc. 21 : 2 (1920), pp. 79–​92. MR 1501137

G. A. Bliss: “Func­tions of lines in bal­list­ics,” Trans. Amer. Math. Soc. 21 : 2 (1920), pp. 93–​106. MR 1501138 JFM 47.​0382.​02

G. A. Bliss: “Some re­cent de­vel­op­ments in the Cal­cu­lus of Vari­ations,” Bull. Amer. Math. Soc. 26 : 8 (1920), pp. 343–​361. MR 1560316 JFM 47.​0471.​04

G. A. Bliss: “Bira­tion­al trans­form­a­tions sim­pli­fy­ing sin­gu­lar­it­ies of al­geb­ra­ic curves,” Trans. Amer. Math. Soc. 24 : 4 (1922), pp. 274–​285. MR 1501226 JFM 50.​0266.​02

G. A. Bliss: “The re­duc­tion of sin­gu­lar­it­ies of plane curves by bira­tion­al trans­form­a­tion,” Bull. Amer. Math. Soc. 29 : 4 (1923), pp. 161–​183. Pres­id­en­tial ad­dress de­livered be­fore the Amer­ic­an Math­em­at­ic­al So­ci­ety, Decem­ber 28, 1922. MR 1560693 JFM 49.​0264.​01

G. A. Bliss: “Book re­view: Vor­le­sun­gen über Dif­fer­en­tial­geo­met­rie und geo­met­rische Grundla­gen von Ein­stein’s Re­lativ­itäts­the­or­ie, vol. 1: Ele­ment­are Dif­fer­en­tial­geo­met­rie, by W. Blasch­ke,” Bull. Amer. Math. Soc. 29 : 7 (1923), pp. 322–​325. MR 1560739

G. A. Bliss: “Al­geb­ra­ic func­tions and their di­visors,” Ann. of Math. (2) 26 : 1–​2 (September–October 1924), pp. 95–​124. MR 1502680 JFM 50.​0699.​03

G. A. Bliss: “A bound­ary value prob­lem for a sys­tem of or­din­ary lin­ear dif­fer­en­tial equa­tions of the first or­der,” Trans. Amer. Math. Soc. 28 : 4 (1926), pp. 561–​584. MR 1501366 JFM 52.​0453.​13

G. A. Bliss: “A bound­ary value prob­lem in the Cal­cu­lus of Vari­ations,” Bull. Amer. Math. Soc. 32 : 4 (1926), pp. 317–​331. MR 1561219 JFM 52.​0509.​02

G. A. Bliss: “Book re­view: Ele­menti del cal­colo delle variazioni, by G. Vivanti,” Bull. Amer. Math. Soc. 32 : 4 (1926), pp. 392–​393. MR 1561233

G. A. Bliss: “Con­tri­bu­tions that have been made by pure sci­ence to the ad­vance­ment of en­gin­eer­ing and in­dustry. Math­em­at­ics.,” Sci. Mon. 24 (1927), pp. 308–​319. JFM 52.​0036.​11

G. Bliss: “The trans­form­a­tion of Cleb­sch in the Cal­cu­lus of Vari­ations,” pp. 589–​603 in Pro­ceed­ings of the In­ter­na­tion­al Math­em­at­ic­al Con­gress (Toronto, 11–16 Au­gust 1924), vol. 1. Edi­ted by J. C. Fields. Uni­versity of Toronto Press, 1928. JFM 54.​0532.​03

G. A. Bliss: “Book re­view: Cal­cu­lus of Vari­ations, by A. R. For­syth,” Bull. Amer. Math. Soc. 34 : 4 (1928), pp. 512–​514. MR 1561597

G. A. Bliss: “The prob­lem of Lag­range in the Cal­cu­lus of Vari­ations,” Amer. J. Math. 52 : 4 (October 1930), pp. 673–​744. MR 1506783 JFM 56.​0435.​01

G. A. Bliss: “An in­teg­ral in­equal­ity,” J. Lon­don Math. Soc. S1-5 : 1 (1930), pp. 40–​46. MR 1574997 JFM 56.​0434.​02

G. A. Bliss and I. J. Schoen­berg: “On sep­ar­a­tion, com­par­is­on and os­cil­la­tion the­or­ems for self-ad­joint sys­tems of lin­ear second or­der dif­fer­en­tial equa­tions,” Amer. J. Math. 53 : 4 (October 1931), pp. 781–​800. MR 1506854 JFM 57.​0528.​01 Zbl 0003.​25702

Con­tri­bu­tions to the Cal­cu­lus of Vari­ations, 1930. Edi­ted by G. A. Bliss and L. M. Graves. Uni­versity of Chica­go Press, 1931. Zbl 0003.​40002

Top­ics of the Cal­cu­lus of Vari­ations. Edi­ted by G. Bliss. Uni­versity of Chica­go, 1932. Prin­cip­ally a re­port on lec­tures by E. J. Mc­Shane and Richard Cour­ant.

G. A. Bliss: “Ern­est Ju­li­us Wil­czyn­ski,” Sci­ence 76 : 1971 (October 1932), pp. 316–​317. JFM 58.​0995.​07

G. A. Bliss: “The prob­lem of Bolza in the Cal­cu­lus of Vari­ations,” Ann. of Math. (2) 33 : 2 (April 1932), pp. 261–​274. MR 1503050 JFM 58.​0535.​02 Zbl 0004.​15502

G. A. Bliss: “The Cal­cu­lus of Vari­ations and the quantum the­ory,” Bull. Amer. Math. Soc. 38 : 4 (1932), pp. 201–​224. MR 1562365 JFM 58.​0530.​01 Zbl 0004.​15601

G. A. Bliss and I. J. Schoen­berg: “On the de­riv­a­tion of ne­ces­sary con­di­tions for the prob­lem of Bolza,” Bull. Amer. Math. Soc. 38 : 12 (1932), pp. 858–​864. MR 1562533 JFM 58.​0535.​01 Zbl 0006.​25902

G. Bliss: Vari­ation­srech­nung. Edi­ted by F. Schwank. B. G. Teub­n­er (Leipzig and Ber­lin), 1932. JFM 58.​0529.​08 Zbl 0003.​34803

G. A. Bliss: “Eliakim Hast­ings Moore,” Univ. Rec. 19 (1933), pp. 130–​134.

G. A. Bliss and M. R. Hestenes: “Suf­fi­cient con­di­tions for a prob­lem of May­er in the Cal­cu­lus of Vari­ations,” Trans. Amer. Math. Soc. 35 : 1 (1933), pp. 305–​326. MR 1501685 JFM 59.​0497.​02 Zbl 0006.​25903

G. A. Bliss: “Math­em­at­ic­al in­ter­pret­a­tions of geo­met­ric­al and phys­ic­al phe­nom­ena,” Amer. Math. Monthly 40 : 8 (October 1933), pp. 472–​480. Re­prin­ted as Chapter 8 of A math­em­atician ex­plains by M. I. Logs­don (Uni­versity of Chica­go Press, 1936) pp. 146–158. MR 1522896 JFM 59.​0060.​01

G. A. Bliss: “Eliakim Hast­ings Moore,” Bull. Amer. Math. Soc. 39 : 11 (1933), pp. 831–​838. MR 1562740 JFM 59.​0038.​02

G. A. Bliss: The Cal­cu­lus of Vari­ations, mul­tiple in­teg­rals. Uni­versity of Chica­go, 1933. MR 2936825

Con­tri­bu­tions to the Cal­cu­lus of Vari­ations, 1931–32. Edi­ted by G. A. Bliss and L. M. Graves. Uni­versity of Chica­go Press, 1933. Zbl 0006.​40401

G. A. Bliss: Al­geb­ra­ic func­tions. AMS Col­loqui­um Pub­lic­a­tions 16. Amer­ic­an Math­em­at­ic­al So­ci­ety (New York), 1933. JFM 59.​0384.​03 Zbl 0008.​21004

G. A. Bliss: The Cal­cu­lus of Vari­ations in three space. Uni­versity of Chica­go, 1934. Lec­ture notes, Spring 1934.

G. A. Bliss: “The sci­entif­ic work of Eliakim Hast­ings Moore,” Bull. Amer. Math. Soc. 40 : 7 (1934), pp. 501–​514. MR 1562892

G. A. Bliss: The prob­lem of Bolza in the Cal­cu­lus of Vari­ations. Uni­versity of Chica­go, 1935. Lec­ture notes, Winter 1935.

G. A. Bliss: “Book re­view: ‘In­equal­it­ies’, by Hardy, Lit­tle­wood, and Pólya,” Sci­ence 81 (1935), pp. 565–​566.

G. A. Bliss and L. E. Dick­son: “Bio­graph­ic­al mem­oir of Eliakim Hast­ings Moore, 1862–1932,” Proc. Natl. Acad. Sci. USA 17 (1936), pp. 83–​102.

G. A. Bliss: “The evol­u­tion of prob­lems of the Cal­cu­lus of Vari­ations,” Amer. Math. Monthly 43 : 10 (December 1936), pp. 598–​609. MR 1523791 Zbl 0015.​35702

Con­tri­bu­tions to the Cal­cu­lus of Vari­ations, 1933–37. Edi­ted by G. A. Bliss, L. M. Graves, and W. T. Re­id. Uni­versity of Chica­go Press, 1937.

G. A. Bliss and L. E. Dick­son: “Her­bert Ell­s­worth Slaught,” Sci­ence 86 (1937), pp. 72–​73.

G. A. Bliss: “Her­bert Ell­s­worth Slaught — In me­mori­am,” Bull. Amer. Math. Soc. 43 : 9 (1937), pp. 595–​597. MR 1563596

G. A. Bliss: “Nor­mal­ity and ab­nor­mal­ity in the Cal­cu­lus of Vari­ations,” Trans. Amer. Math. Soc. 43 : 3 (1938), pp. 365–​376. MR 1501950 JFM 64.​0510.​01 Zbl 0019.​12303

G. A. Bliss: “Def­in­itely self-ad­joint bound­ary value prob­lems,” Trans. Amer. Math. Soc. 44 : 3 (1938), pp. 413–​428. MR 1501974 JFM 64.​0438.​02 Zbl 0020.​03204

G. A. Bliss: “Her­bert Ell­s­worth Slaught — teach­er and friend,” Amer. Math. Monthly 45 : 1 (January 1938), pp. 5–​10. MR 1524156 JFM 64.​0023.​14

Con­tri­bu­tions to the Cal­cu­lus of Vari­ations, 1938–41. Edi­ted by G. A. Bliss, M. R. Hestenes, and W. T. Re­id. Uni­versity of Chica­go Press, 1942.

G. A. Bliss: “The Cal­cu­lus of Vari­ations for mul­tiple in­teg­rals,” Amer. Math. Monthly 49 : 2 (February 1942), pp. 77–​89. MR 0006022 Zbl 0063.​00455

G. A. Bliss: “Oskar Bolza,” Science 97 : 2509 (1943), pp. 108–​109. article

G. A. Bliss: Math­em­at­ics for ex­ter­i­or bal­list­ics. John Wiley and Sons (New York), 1944. MR 0010480 Zbl 0063.​00457

G. A. Bliss: “Os­kar Bolza — in me­mori­am,” Bull. Amer. Math. Soc. 50 : 7 (1944), pp. 478–​489. MR 1564626

G. A. Bliss: Lec­tures on the cal­cu­lus of vari­ations. Uni­versity of Chica­go Press (Chica­go, IL), 1946. MR 0017881 Zbl 0063.​00459

G. A. Bliss: Cal­cu­lus of Vari­ations, 6th edition. Carus Math­em­at­ic­al Mono­graphs 1. The Math­em­at­ic­al As­so­ci­ation of Amer­ica (Wash­ing­ton, DC), 1971. Zbl 0317.​49001