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Celebratio Mathematica

Barry C. Mazur


Bibliography

[1]B. Mazur: “Or­tho­topy and spher­ic­al knots,” Publ. Math., Inst. Hautes Étud. Sci. 3 : 1 (December 1959), pp. 121–​140. MR 0116348 Zbl 0119.​38704 article

[2]B. Mazur: “On em­bed­dings of spheres,” Bull. Am. Math. Soc. 65 : 2 (1959), pp. 59–​65. Re­search an­nounce­ment for the au­thor’s PhD thes­is (1959). MR 0117693 Zbl 0086.​37004 article

[3]B. Mazur: “On the struc­ture of cer­tain semi-groups of spher­ic­al knot classes,” Publ. Math., Inst. Hautes Étud. Sci. 3 : 1 (December 1959), pp. 111–​119. MR 0116347 Zbl 0119.​38703 article

[4]B. Mazur: “The defin­i­tion of equi­val­ence of com­bin­at­or­i­al im­bed­dings,” Publ. Math., Inst. Hautes Étud. Sci. 3 : 1 (1959), pp. 97–​109. MR 0116346 Zbl 0119.​38702 article

[5]B. C. Mazur: On em­bedings of spheres. Ph.D. thesis, Prin­ceton Uni­versity, 1959. Ad­vised by R. H. Fox and R. H. Bing. A re­search an­nounce­ment based on this thes­is was pub­lished in Bull. Am. Math. Soc. 65:2 (1959). MR 2613038 phdthesis

[6]B. Mazur: “A note on some con­tract­ible 4-man­i­folds,” Ann. Math. (2) 73 : 1 (January 1961), pp. 221–​228. MR 0125574 Zbl 0127.​13604 article

[7]B. C. Mazur: “On em­bed­dings of spheres,” Acta Math. 105 : 1–​2 (1961), pp. 1–​17. MR 0125570 Zbl 0096.​37904 article

[8]B. Mazur: “Stable equi­val­ence of dif­fer­en­ti­able man­i­folds,” Bull. Am. Math. Soc. 67 : 4 (1961), pp. 377–​384. MR 0130697 Zbl 0107.​17002 article

[9]B. Mazur: “Simple neigh­bor­hoods,” Bull. Am. Math. Soc. 68 : 2 (1962), pp. 87–​92. MR 0137125 Zbl 0105.​17002 article

[10]B. Mazur: “Sym­met­ric ho­mo­logy spheres,” Ill. J. Math. 6 : 2 (1962), pp. 245–​250. Cor­rec­tions were pub­lished in Ill. J. Math. 8:1 (1962). MR 0140102 Zbl 0103.​39503 article

[11]B. Mazur: Dif­fer­en­tial to­po­logy from the point of view of simple ho­mo­topy the­ory, published as Publ. Math. Inst. Hautes Étud. Sci. 15 (December 1963). Cor­rec­tions and fur­ther re­marks were pub­lished in Publ. Math. Inst. Hautes Étud. Sci. 22 (1964). MR 0161342 Zbl 0173.​51203 book

[12]B. Mazur: “Re­l­at­ive neigh­bor­hoods and the the­or­ems of Smale,” Ann. Math. (2) 77 : 2 (March 1963), pp. 232–​249. MR 0150786 Zbl 0112.​38301 article

[13]B. Mazur: “Les théorèmes généraux de lis­sage” [Gen­er­al smooth­ing the­or­ems] in Sémin­aire de to­po­lo­gie com­bin­atoire et différen­ti­elle de l’In­sti­tut des Hautes Et­udes Sci­en­ti­fiques: 1962/63 [IHÉS sem­in­ar on com­bin­at­or­i­al and dif­fer­en­tial to­po­logy: 1962/63]. IHÉS (Par­is), 1963. Ex­posé no. 3, 9 pages. incollection

[14]B. Mazur: “Les théorèmes d’uni­cité de lis­sage” [Unique­ness the­or­ems for smooth­ing] in Sémin­aire de to­po­lo­gie com­bin­atoire et différen­ti­elle de l’In­sti­tut des Hautes Études Sci­en­ti­fiques: 1962/63 [IHÉS sem­in­ar on com­bin­at­or­i­al and dif­fer­en­tial to­po­logy: 1962/63]. IHÉS (Par­is), 1963. Ex­posé no. 4, 6 pages. incollection

[15]B. Mazur: “Cor­rec­tions to my pa­per, ‘Sym­met­ric ho­mo­logy spheres’,” Ill. J. Math. 8 : 1 (1964), pp. 175. Cor­rec­tions to an art­icle pub­lished in Ill. J. Math. 6:2 (1962). MR 0157379 Zbl 0116.​14901 article

[16]B. Mazur: “Com­bin­at­or­i­al equi­val­ence versus to­po­lo­gic­al equi­val­ence,” Trans. Am. Math. Soc. 111 : 2 (1964), pp. 288–​316. MR 0202124 Zbl 0124.​16601 article

[17]B. Mazur: “The meth­od of in­fin­ite re­pe­ti­tion in pure to­po­logy, I,” Ann. Math. (2) 80 : 2 (September 1964), pp. 201–​226. MR 0169224 Zbl 0133.​16506 article

[18]B. Mazur: “Cor­rec­tions to: ‘Dif­fer­en­tial to­po­logy from the point of view of simple ho­mo­topy the­ory’ and fur­ther re­marks,” Publ. Math. Inst. Hautes Étud. Sci. 22 (December 1964), pp. 81–​91. Cor­rec­tions and fur­ther re­marks for an art­icle in Publ. Math. Inst. Hautes Étud. Sci. 15 (1963). MR 0185612 Zbl 0173.​51301 article

[19]B. Mazur: Re­marks on the Al­ex­an­der poly­no­mi­al, 1964?. Nev­er pub­lished, but re­cently a scanned ver­sion was pos­ted on­line by Mazur him­self. misc

[20]M. Artin and B. Mazur: “On peri­od­ic points,” Ann. Math. (2) 81 : 1 (January 1965), pp. 82–​99. MR 0176482 Zbl 0127.​13401 article

[21]B. Mazur: “Morse the­ory,” pp. 145–​165 in Dif­fer­en­tial and com­bin­at­or­i­al to­po­logy: A sym­posi­um in hon­or of Mar­ston Morse (Prin­ceton, NJ, 1964). Edi­ted by S. S. Cairns. Prin­ceton Math­em­at­ic­al Series 27. Prin­ceton Uni­versity Press, 1965. MR 0185613 Zbl 0158.​42202 incollection

[22]B. Mazur: “The meth­od of in­fin­ite re­pe­ti­tion in pure to­po­logy, II: Stable ap­plic­a­tions,” Ann. Math. (2) 83 : 3 (May 1966), pp. 387–​401. MR 0196758 Zbl 0141.​40501 article

[23]M. Artin and B. Mazur: “On the van Kampen the­or­em,” To­po­logy 5 (1966), pp. 179–​189. MR 0192495 Zbl 0138.​18301 article

[24]M. Artin and B. Mazur: “Ho­mo­topy of vari­et­ies in the etale to­po­logy,” pp. 1–​15 in Pro­ceed­ings of the con­fer­ence on loc­al fields (Drieber­gen, Neth­er­lands, 1966). Edi­ted by T. A. Spring­er. Spring­er (Ber­lin), 1967. MR 0230730 Zbl 0188.​53402 incollection

[25]M. Artin and B. Mazur: Etale ho­mo­topy (Har­vard Uni­versity, 1965–1966). Lec­ture Notes in Math­em­at­ics 100. Spring­er (Ber­lin), 1969. A second edi­tion was pub­lished in 1986. MR 0245577 Zbl 0182.​26001 book

[26]B. Mazur and L. Roberts: “Loc­al Euler char­ac­ter­ist­ics,” In­vent. Math. 9 : 3 (1969–1970), pp. 201–​234. MR 0258844 Zbl 0191.​19202 article

[27]B. Mazur: “Loc­al flat du­al­ity,” Am. J. Math. 92 : 2 (April 1970), pp. 343–​361. MR 0271119 Zbl 0199.​24501 article

[28]B. Mazur: “Fi­nite flat struc­tures,” pp. 219–​225 in Ap­plic­a­tions of cat­egor­ic­al al­gebra (New York, 10–11 April 1968). Edi­ted by A. Heller. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics 17. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1970. MR 0257182 Zbl 0221.​14025 incollection

[29]B. Mazur: “Frobeni­us and the Hodge fil­tra­tion,” Bull. Am. Math. Soc. 78 : 5 (1972), pp. 653–​667. See also re­lated art­icle in Ann. Math. 98:1 (1973). MR 0330169 Zbl 0258.​14006 article

[30]B. Mazur and J. Vélu: “Courbes de Weil de con­duc­teur 26” [Weil curves of con­duct­or 26], C. R. Acad. Sci., Par­is, Sér. A 275 (1972), pp. A743–​A745. MR 0320010 Zbl 0241.​14015 article

[31]B. Mazur: “Ra­tion­al points of abeli­an vari­et­ies with val­ues in towers of num­ber fields,” In­vent. Math. 18 : 3–​4 (1972), pp. 183–​266. A Rus­si­an trans­la­tion was pub­lished in two parts in Matem­atika 17:2 (1973) and Matem­atika 17:3 (1973). MR 0444670 Zbl 0245.​14015 article

[32]B. Mazur: “Frobeni­us and the Hodge fil­tra­tion (es­tim­ates),” Ann. Math. (2) 98 : 1 (July 1973), pp. 58–​95. See also re­lated art­icle in Bull. Am. Math. Soc. 78:5 (1972). MR 0321932 Zbl 0261.​14005 article

[33]B. Mazur: “Courbes el­lipt­iques et sym­boles mod­u­laires” [El­lipt­ic curves and mod­u­lar sym­bols], pp. 277–​294 in Sémin­aire Bourbaki: 1971/72, ex­posés 400–417. Lec­ture Notes in Math­em­at­ics 317. Spring­er (Ber­lin), 1973. Ex­posé no. 414. In French. MR 0429921 Zbl 0276.​14012 incollection

[34]B. Mazur: “Notes on étale co­homo­logy of num­ber fields,” Ann. Sci. Éc. Norm. Supér. (4) 6 : 4 (1973), pp. 521–​552. MR 0344254 Zbl 0282.​14004 article

[35]B. Mazur: “Ra­tion­al points of Abeli­an vari­et­ies with val­ues in towers of num­ber fields,” Matem­atika 17 : 2 (1973), pp. 3–​57. Rus­si­an trans­la­tion of part of an art­icle in In­vent. Math. 18:3–4 (1972). Zbl 0251.​14015 article

[36]B. Mazur: “Book re­view: Steph­en S. Shatz, ‘Profin­ite groups, arith­met­ic, and geo­metry’,” Am. Sci. 61 : 3 (May–June 1973), pp. 377. article

[37]B. Mazur: “Ra­tion­al points of Abeli­an vari­et­ies with val­ues in towers of num­ber fields,” Matem­atika 17 : 3 (1973), pp. 114–​136. Rus­si­an trans­la­tion of part of an art­icle in In­vent. Math. 18:3–4 (1972). Zbl 0258.​14009 article

[38]B. Mazur and J. Tate: “Points of or­der 13 on el­lipt­ic curves,” In­vent. Math. 22 : 1 (1973–1974), pp. 41–​49. MR 0347826 Zbl 0268.​14009 article

[39]M. W. Hirsch and B. Mazur: Smooth­ings of piece­wise lin­ear man­i­folds. An­nals of Math­em­at­ics Stud­ies 80. Prin­ceton Uni­versity Press, 1974. MR 0415630 Zbl 0298.​57007 book

[40]B. Mazur and P. Swin­ner­ton-Dyer: “Arith­met­ic of Weil curves,” In­vent. Math. 25 : 1 (1974), pp. 1–​61. MR 0354674 Zbl 0281.​14016 article

[41]B. Mazur and W. Mess­ing: Uni­ver­sal ex­ten­sions and one-di­men­sion­al crys­tal­line co­homo­logy. Lec­ture Notes in Math­em­at­ics 370. Spring­er (Ber­lin), 1974. MR 0374150 Zbl 0301.​14016 book

[42]B. Mazur: “\( p \)-ad­ic ana­lyt­ic num­ber the­ory of el­lipt­ic curves and Abeli­an vari­et­ies over \( \mathbb{Q} \),” pp. 369–​377 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Van­couver, BC, 21–29 Au­gust 1974), vol. 1. Edi­ted by R. D. James. Ca­na­dian Math­em­at­ic­al Con­gress (Montreal), 1975. MR 0439844 Zbl 0351.​14011 incollection

[43]B. Mazur: “Ei­gen­val­ues of Frobeni­us act­ing on al­geb­ra­ic vari­et­ies over fi­nite fields,” pp. 231–​261 in Al­geb­ra­ic geo­metry (Ar­cata, CA, 29 Ju­ly–16 Au­gust 1974). Edi­ted by R. Hartshorne. Pro­ceed­ings of Sym­po­sia in Pure Math­em­at­ics XXIX. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1975. MR 0371896 Zbl 0306.​14011 incollection

[44]B. Mazur: Arith­met­ic in the geo­metry of sym­met­ric spaces. A let­ter writ­ten to John Mill­son in the mid-1970s. misc

[45]B. Mazur and J.-P. Serre: “Points ra­tion­nels des courbes mod­u­laires \( X_{0}(N) \) (d’après A. Ogg)” [Ra­tion­al points of mod­u­lar curves \( X_{0}(N) \) (after A. Ogg)], pp. 238–​255 in Sémin­aire Bourbaki: 1974/75, ex­posés 453–470. Lec­ture Notes in Math­em­at­ics 514. Spring­er (Ber­lin), 1976. Ex­posé no. 469. In French. MR 0485882 Zbl 0346.​14013 incollection

[46]B. Mazur: “Book re­view: S. Lef­schetz, ‘Ap­plic­a­tions of al­geb­ra­ic to­po­logy’,” Am. Sci. 64 : 4 (July–August 1976), pp. 460. article

[47]B. Mazur: “Mod­u­lar curves and the Ei­s­en­stein ideal,” Publ. Math. Inst. Hautes Étud. Sci. 47 : 1 (1977), pp. 33–​186. MR 488287 Zbl 0394.​14008 article

[48]B. Mazur: “Ra­tion­al points on mod­u­lar curves,” pp. 107–​148 in Mod­u­lar func­tions of one vari­able, V: Pro­ceed­ings of the second in­ter­na­tion­al con­fer­ence (Bonn, 2–14 Ju­ly 1976). Edi­ted by J.-P. Serre and D. B. Za­gi­er. Lec­ture Notes in Math­em­at­ics 601. Spring­er (Ber­lin), 1977. MR 0450283 Zbl 0357.​14005 incollection

[49]M. Artin and B. Mazur: “Form­al groups arising from al­geb­ra­ic vari­et­ies,” Ann. Sci. Éc. Norm. Supér. (4) 10 : 1 (1977), pp. 87–​131. MR 0457458 Zbl 0351.​14023 article

[50]B. Mazur: “Book re­view: Ernst Ed­ward Kum­mer, ‘Col­lec­ted pa­pers’,” Bull. Am. Math. Soc. 83 : 5 (1977), pp. 976–​988. MR 1566995 article

[51]B. Mazur: “Ra­tion­al iso­genies of prime de­gree,” In­vent. Math. 44 : 2 (1978), pp. 129–​162. With an ap­pendix by D. Gold­feld. MR 482230 Zbl 0386.​14009 article

[52]O. Za­r­iski: Col­lec­ted pa­pers, vol. III: To­po­logy of curves and sur­faces, and spe­cial top­ics in the the­ory of al­geb­ra­ic vari­et­ies. Edi­ted by M. Artin and B. Mazur. Math­em­aticians of Our Time 12. MIT Press (Cam­bridge, MA), 1978. MR 0505104 Zbl 0446.​14001 book

[53]B. Mazur: “On the arith­met­ic of spe­cial val­ues of \( L \) func­tions,” In­vent. Math. 55 : 3 (1979), pp. 207–​240. MR 553997 Zbl 0426.​14009 article

[54]J.-P. Serre: “Points ra­tion­nels des courbes mod­u­laires \( X_{0}(N) \) [d’après Barry Mazur],” pp. 89–​100 in Sémin­aire Bourbaki, 30e année (1977/78). Lec­ture Notes in Math. 710. Spring­er (Ber­lin), 1979. Ex­posé no. 511. MR 554216

[55]B. H. Gross: Arith­met­ic on el­lipt­ic curves with com­plex mul­ti­plic­a­tion. Lec­ture Notes in Math­em­at­ics 776. Spring­er (Ber­lin), 1980. With an ap­pendix by B. Mazur. MR 0563921 Zbl 0433.​14032 book

[56]B. Mazur: “Book re­view: C. Her­bert Clem­ens, ‘A scrap­book of com­plex curve the­ory’,” Am. Sci. 70 : 2 (March–April 1982), pp. 228. article

[57]B. Mazur and A. Wiles: “Ana­lo­gies between func­tion fields and num­ber fields,” Am. J. Math. 105 : 2 (April 1983), pp. 507–​521. Ded­ic­ated to An­dré Weil for his 77th birth­day. MR 701567 Zbl 0531.​12015 article

[58]B. Mazur and J. Tate: “Ca­non­ic­al height pair­ings via biex­ten­sions,” pp. 195–​237 in Arith­met­ic and geo­metry: Pa­pers ded­ic­ated to I. R. Shar­far­ev­ich on the oc­ca­sion of his six­tieth birth­day, vol. 1. Edi­ted by M. Artin and J. Tate. Pro­gress in Math­em­at­ics 35. Birkhäuser (Bo­ston, MA), 1983. MR 717595 Zbl 0574.​14036 incollection

[59]B. Mazur: “Solu­tion of math prob­lem,” Sci­ence 222 : 4623 (4 November 1983), pp. 456. A let­ter to Sci­ence. article

[60]B. Mazur: “Mod­u­lar curves and arith­met­ic,” pp. 185–​211 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Warsaw, 16–24 Au­gust 1983), vol. 1. Edi­ted by Z. Ciesiel­ski and C. Olech. PWN (Warsaw), 1984. MR 804682 Zbl 0597.​14023 incollection

[61]B. Mazur and A. Wiles: “Class fields of abeli­an ex­ten­sions of \( \mathbb{Q} \),” In­vent. Math. 76 : 2 (1984), pp. 179–​330. To K. Iwas­awa. MR 742853 Zbl 0545.​12005 article

[62]B. Mazur: On the arith­met­ic of curves, 1984. Lec­ture notes dis­trib­uted in con­junc­tion with the col­loqui­um lec­tures giv­en at the 90th an­nu­al meet­ing of the AMS, Louis­ville, KY, 25–28 Janu­ary 1984. misc

[63]N. M. Katz and B. Mazur: Arith­met­ic mod­uli of el­lipt­ic curves. An­nals of Math­em­at­ics Stud­ies 108. Prin­ceton Uni­versity Press, 1985. MR 772569 Zbl 0576.​14026 book

[64]B. Mazur and A. Wiles: “On \( p \)-ad­ic ana­lyt­ic fam­il­ies of Galois rep­res­ent­a­tions,” Com­pos. Math. 59 : 2 (1986), pp. 231–​264. With an ap­pendix by Nigel Bo­ston. MR 860140 Zbl 0654.​12008 article

[65]B. Mazur, J. Tate, and J. Teitel­baum: “On \( p \)-ad­ic ana­logues of the con­jec­tures of Birch and Swin­ner­ton-Dyer,” In­vent. Math. 84 : 1 (1986), pp. 1–​48. MR 830037 Zbl 0699.​14028 article

[66]B. Mazur: “Arith­met­ic on curves,” Bull. Am. Math. Soc., New Ser. 14 : 2 (April 1986), pp. 207–​259. MR 828821 Zbl 0593.​14021 article

[67]M. Artin and B. Mazur: Etale ho­mo­topy (Har­vard Uni­versity, 1965–1966), 2nd edition. Lec­ture Notes in Math­em­at­ics 100. Spring­er (Ber­lin), 1986. Re­pub­lic­a­tion of the 1969 ori­gin­al. MR 883959 book

[68]J. Moser, V. Strassen, J. W. Mil­nor, M. F. Atiyah, and B. Mazur: Talks on the medal and prize win­ners, 1986. 78 minute VHS video­cas­sette. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI). A group of four filmed lec­tures on the work of four prize-win­ning schol­ars in the fields of math­em­at­ics and com­puter sci­ence. Mazur lec­tures on the work of Fields medal­ist Gerd Falt­ings. Filmed at the In­ter­na­tion­al Con­gress of Math­em­aticians, Berke­ley, CA, 3–11 Au­gust 1986. misc

[69]B. Mazur: “On some of the math­em­at­ic­al con­tri­bu­tions of Gerd Falt­ings,” pp. 7–​12 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Berke­ley, CA, 3–11 Au­gust 1986), vol. 1. Edi­ted by A. M. Gleason. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1987. MR 934210 Zbl 0663.​01002 incollection

[70]B. Mazur and J. Tate: “Re­fined con­jec­tures of the ‘Birch and Swin­ner­ton-Dyer type’,” Duke Math. J. 54 : 2 (1987), pp. 711–​750. To Yuri Man­in on the oc­ca­sion of his fiftieth birth­day. MR 899413 Zbl 0636.​14004 article

[71]Al­geb­ra­ic num­ber the­ory: In hon­or of K. Iwas­awa (Berke­ley, CA, 20–24 Janu­ary 1987). Edi­ted by J. Coates, R. Green­berg, B. Mazur, and I. Satake. Ad­vanced Stud­ies in Pure Math­em­at­ics 17. Aca­dem­ic Press (Bo­ston), 1989. Col­lec­ted pa­pers ded­ic­ated to K. Iwas­awa on his 70th birth­day and pa­pers based on the lec­tures de­livered at the work­shop on Iwas­awa the­ory and spe­cial val­ues of \( L \)-func­tions. MR 1097604 Zbl 0721.​00006 book

[72]N. Bo­ston and B. Mazur: “Ex­pli­cit uni­ver­sal de­form­a­tions of Galois rep­res­ent­a­tions,” pp. 1–​21 in Al­geb­ra­ic num­ber the­ory: In hon­or of K. Iwas­awa (Berke­ley, CA, 20–24 Janu­ary 1987). Edi­ted by J. Coates, R. Green­berg, B. Mazur, and I. Satake. Ad­vanced Stud­ies in Pure Math­em­at­ics 17. Aca­dem­ic Press (Bo­ston, MA), 1989. MR 1097607 Zbl 0739.​11021 incollection

[73]B. Mazur: “De­form­ing Galois rep­res­ent­a­tions,” pp. 385–​437 in Galois groups over \( \mathbb{Q} \) (Berke­ley, CA, 23–27 March 1987). Edi­ted by Y. Ihara, K. Ribet, and J.-P. Serre. Math­em­at­ic­al Sci­ences Re­search In­sti­tute Pub­lic­a­tions 16. Spring­er (New York), 1989. For A. Mazur. Avail­able open access here. MR 1012172 Zbl 0714.​11076 incollection

[74]A. M. Gleason, A. Jaffe, B. Mazur, R. H. Her­man, C. H. Clem­ens, J. Kollár, K. Gawędzki, C. Soulé, and M. Sipser: “ICM-90,” No­tices Am. Math. Soc. 37 : 9 (1990), pp. 1209–​1216. Re­port on the In­ter­na­tion­al Con­gress of Math­em­aticians held in Kyoto, 21–29 Au­gust 1990. MR 1076560 Zbl 1194.​01041 article

[75]B. Mazur and J. Tilouine: “Re­présent­a­tions galois­i­ennes, différen­ti­elles de Kähler et ‘con­jec­tures prin­cip­ales’” [Galois rep­res­ent­a­tions, Kähler dif­fer­en­tials and the ‘main con­jec­tures’], Publ. Math. Inst. Hautes Étud. Sci. 71 (1990), pp. 65–​103. In French. MR 1079644 Zbl 0744.​11053 article

[76]B. Mazur: “Two-di­men­sion­al \( p \)-ad­ic Galois rep­res­ent­a­tions un­rami­fied away from \( p \),” Com­pos. Math. 74 : 2 (1990), pp. 115–​133. MR 1047735 Zbl 0773.​11036 article

[77]B. Mazur: “Num­ber the­ory as gad­fly,” pp. 15–​33 in Num­ber the­ory: Pro­ceed­ings of a sym­posi­um (Wash­ing­ton, DC, 4 May 1989). Na­tion­al Re­search Coun­cil (Wash­ing­ton, DC), 1990. From this present­a­tion evolved an art­icle with the same title which was pub­lished in Am. Math. Mon. 98:7 (1991). Zbl 0764.​11022 incollection

[78]B. Mazur, A. Beil­in­son, and B. Fei­gin: Notes on con­form­al field the­ory. Notes, Har­vard Uni­versity. techreport

[79]H. Gil­let, B. Mazur, and C. Soulé: “A note on a clas­sic­al the­or­em of Blich­feldt,” Bull. Lon­don Math. Soc. 23 : 2 (1991), pp. 131–​132. MR 1122898 Zbl 0746.​52021 article

[80]B. Mazur and K. A. Ribet: “Two-di­men­sion­al rep­res­ent­a­tions in the arith­met­ic of mod­u­lar curves,” pp. 215–​255 in Courbes mod­u­laires et courbes de Shimura [Mod­u­lar curves and Shimura curves] (Or­say, France, 1987–1988). As­térisque 196–​197. So­ciété Math­ématique de France (Par­is), 1991. MR 1141460 Zbl 0780.​14015 incollection

[81]F. Gouvêa and B. Mazur: “The square-free sieve and the rank of el­lipt­ic curves,” J. Am. Math. Soc. 4 : 1 (January 1991), pp. 1–​23. MR 1080648 Zbl 0725.​11027 article

[82]B. Mazur and J. Tate: “The \( p \)-ad­ic sigma func­tion,” Duke Math. J. 62 : 3 (1991), pp. 663–​688. MR 1104813 Zbl 0735.​14020 article

[83]B. Mazur: “Num­ber the­ory as gad­fly,” Am. Math. Mon. 98 : 7 (August–September 1991), pp. 593–​610. This evolved from the present­a­tion with the same title which was pub­lished in Num­ber the­ory: Pro­ceed­ings of a sym­posi­um (1990). MR 1121312 Zbl 0764.​11021 article

[84]F. Gouvêa and B. Mazur: “Fam­il­ies of mod­u­lar ei­gen­forms,” Math. Com­put. 58 : 198 (April 1992), pp. 793–​805. MR 1122070 Zbl 0773.​11030 article

[85]B. Mazur: “The to­po­logy of ra­tion­al points,” Exp. Math. 1 : 1 (1992), pp. 35–​45. MR 1181085 Zbl 0784.​14012 article

[86]F. Q. Gouvêa and B. Mazur: “On the char­ac­ter­ist­ic power series of the \( U \) op­er­at­or,” Ann. Inst. Four­i­er 43 : 2 (1993), pp. 301–​312. MR 1220270 Zbl 0779.​11022 article

[87]B. Mazur: “On the pas­sage from loc­al to glob­al in num­ber the­ory,” Bull. Am. Math. Soc., New Ser. 29 : 1 (July 1993), pp. 14–​50. MR 1202293 Zbl 0813.​14016 article

[88]B. Mazur: Galois de­form­a­tions and Hecke curves, 1993. Har­vard course notes, Fall 1993. misc

[89]B. Mazur: “On mono­dromy in­vari­ants oc­cur­ring in glob­al arith­met­ic, and Fon­taine’s the­ory,” pp. 1–​20 in \( p \)-ad­ic mono­dromy and the Birch and Swin­ner­ton-Dyer con­jec­ture (Bo­ston, MA, 12–16 Au­gust 1991). Edi­ted by B. Mazur and G. Stevens. Con­tem­por­ary Math­em­at­ics 165. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1994. MR 1279599 Zbl 0846.​11039 incollection

[90]\( p \)-ad­ic mono­dromy and the Birch and Swin­ner­ton-Dyer con­jec­ture (Bo­ston, MA, 12–16 Au­gust 1991). Edi­ted by B. Mazur and G. Stevens. Con­tem­por­ary Math­em­at­ics 165. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1994. MR 1279598 Zbl 0794.​00016 book

[91]B. Mazur: “Ques­tions of de­cid­ab­il­ity and un­de­cid­ab­il­ity in num­ber the­ory,” J. Symb. Log. 59 : 2 (June 1994), pp. 353–​371. In memory of Dav­id Lachter­man. MR 1276620 Zbl 0814.​11059 article

[92]E. M. Fried­lander and B. Mazur: “Cor­res­pond­ence ho­mo­morph­isms for sin­gu­lar vari­et­ies,” Ann. Inst. Four­i­er 44 : 3 (1994), pp. 703–​727. MR 1303882 Zbl 0811.​14007 article

[93]E. M. Fried­lander and B. Mazur: Fil­tra­tions on the ho­mo­logy of al­geb­ra­ic vari­et­ies. Mem­oirs of the Amer­ic­an Math­em­at­ic­al So­ci­ety 529. July 1994. With an ap­pendix by Daniel Quil­len. MR 1211371 Zbl 0841.​14019 book

[94]J.-M. Fon­taine and B. Mazur: “Geo­met­ric Galois rep­res­ent­a­tions,” pp. 41–​78 in El­lipt­ic curves, mod­u­lar forms, & Fer­mat’s last the­or­em (Hong Kong, 18–21 Decem­ber 1993). Edi­ted by J. Coates and S.-T. Yau. Series in Num­ber The­ory 1. In­ter­na­tion­al Press (Somerville, MA), 1995. MR 1363495 Zbl 0839.​14011 incollection

[95]B. Mazur: Fer­mat’s last the­or­em, 1995. 60 minute video­cas­sette. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI). A lec­ture presen­ted in Van­couver, BC, 15 Au­gust 1993. MR 1419093 Zbl 0974.​11500 misc

[96]F. Q. Gouvêa and B. Mazur: “Search­ing for \( p \)-ad­ic ei­gen­func­tions,” Math. Res. Lett. 2 : 5 (1995), pp. 515–​536. To A. O. L. Atkin, on his re­tire­ment. MR 1359960 Zbl 0851.​11031 article

[97]L. Ca­pora­so, J. Har­ris, and B. Mazur: “How many ra­tion­al points can a curve have?,” pp. 13–​31 in The mod­uli space of curves (Texel Is­land, Neth­er­lands, April 1994). Edi­ted by R. H. Dijk­graaf, C. Faber, and G. B. M. van der Geer. Pro­gress in Math­em­at­ics 129. Birkhäuser (Bo­ston, MA), 1995. MR 1363052 Zbl 0862.​14012 incollection

[98]B. Mazur: “Spec­u­la­tions about the to­po­logy of ra­tion­al points: An up-date,” pp. 165–​182 in Columbia Uni­versity num­ber the­ory sem­in­ar (New York, 1992). As­térisque 228. 1995. MR 1330932 Zbl 0851.​14009 incollection

[99]S. Kami­enny and B. Mazur: “Ra­tion­al tor­sion of prime or­der in el­lipt­ic curves over num­ber fields,” pp. 81–​100 in Columbia Uni­versity num­ber the­ory sem­in­ar (New York, 1992). As­térisque 228. So­ciété Math­ématique de France (Par­is), 1995. With an ap­pendix by A. Gran­ville. MR 1330929 Zbl 0846.​14012 incollection

[100]D. Ab­ramovich: “Form­al fi­nite­ness and the tor­sion con­jec­ture on el­lipt­ic curves: A foot­note to a pa­per: ‘Ra­tion­al tor­sion of prime or­der in el­lipt­ic curves over num­ber fields’ by S. Kami­enny and B. Mazur,” pp. 3, 5–​17 in Columbia Uni­versity Num­ber The­ory Sem­in­ar (New York, 1992). Astérisque 228. 1995. MR 1330925

[101]B. Mazur: Ques­tions about num­ber. Lec­ture notes, Har­vard Uni­versity. An ex­pos­it­ory lec­ture on the ABC con­jec­ture, writ­ten for a volume en­titled New Dir­ec­tions in Math­em­at­ics. techreport

[102]B. Mazur: “An ‘in­fin­ite fern’ in the uni­ver­sal de­form­a­tion space of Galois rep­res­ent­a­tions,” pp. 155–​193 in Journées arith­métiques [Arith­met­ic days] (Bar­celona, Ju­ly 1995), published as Col­lect. Math. 48 : 1–​2. Spring­er (Ber­lin), 1997. In memory of R. H. Bing. MR 1464022 Zbl 0865.​11046 incollection

[103]B. Mazur: “An in­tro­duc­tion to the de­form­a­tion the­ory of Galois rep­res­ent­a­tions,” pp. 243–​311 in Mod­u­lar forms and Fer­mat’s last the­or­em (Bo­ston, MA, 9–18 Au­gust 1995). Edi­ted by G. Cor­nell, J. H. Sil­ver­man, and G. Stevens. Spring­er (New York), 1997. MR 1638481 Zbl 0901.​11015 incollection

[104]El­lipt­ic curves and mod­u­lar forms: Pa­pers from the NAS Col­loqui­um (Wash­ing­ton, DC, 15–17 March 1996), published as Proc. Natl. Acad. Sci. USA 94 : 21. Issue edi­ted by B. Mazur and K. Ru­bin. Na­tion­al Academy of Sci­ences (Wash­ing­ton, DC), 1997. MR 1491966 Zbl 0882.​00034 booklet

[105]B. Mazur: “Con­jec­ture,” pp. 197–​210 in Proof and pro­gress in math­em­at­ics (Bo­ston, MA, 1996), published as Syn­these 111 : 2. Spring­er (Dordrecht), 1997. MR 1465271 Zbl 1052.​00513 incollection

[106]D. Eis­en­bud and B. Mazur: “Evol­u­tions, sym­bol­ic squares, and Fit­ting ideals,” J. Reine An­gew. Math. 488 (1997), pp. 189–​201. MR 1465370 Zbl 0912.​13010 ArXiv alg-​geom/​9511008 article

[107]L. Ca­pora­so, J. Har­ris, and B. Mazur: “Uni­form­ity of ra­tion­al points,” J. Am. Math. Soc. 10 : 1 (January 1997), pp. 1–​35. MR 1325796 Zbl 0872.​14017 article

[108]B. Mazur: “Book re­view: Alice Fulton, ‘Sen­su­al math’,” Har­vard Re­view 12 (1997), pp. 170–​172. article

[109]J. Har­ris, B. Mazur, and R. Pand­hari­pande: “Hy­per­sur­faces of low de­gree,” Duke Math. J. 95 : 1 (1998), pp. 125–​160. MR 1646558 Zbl 0991.​14018 article

[110]B. Mazur: “Open prob­lems re­gard­ing ra­tion­al points on curves and vari­et­ies,” pp. 239–​265 in Galois rep­res­ent­a­tions in arith­met­ic al­geb­ra­ic geo­metry (Durham, UK, 9–18 Ju­ly 1996). Edi­ted by A. J. Scholl and R. L. Taylor. Lon­don Math­em­at­ic­al So­ci­ety Lec­ture Note Series 254. Cam­bridge Uni­versity Press, 1998. MR 1696485 Zbl 0943.​14009 incollection

[111]F. Q. Gouvêa and B. Mazur: “On the dens­ity of mod­u­lar rep­res­ent­a­tions,” pp. 127–​142 in Com­pu­ta­tion­al per­spect­ives on num­ber the­ory: Pro­ceed­ings of a con­fer­ence in hon­or of A. O. L. Atkin (Chica­go, Septem­ber 1995). Edi­ted by D. A. Buell and J. T. Teitel­baum. AMS/IP Stud­ies in Ad­vanced Math­em­at­ics 7. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1998. MR 1486834 Zbl 1134.​11324 incollection

[112]R. Cole­man and B. Mazur: “The ei­gen­curve,” pp. 1–​113 in Galois rep­res­ent­a­tions in arith­met­ic al­geb­ra­ic geo­metry (Durham, UK, 9–18 Ju­ly 1996). Edi­ted by A. J. Scholl and R. L. Taylor. Lon­don Math­em­at­ic­al So­ci­ety Lec­ture Note Series 254. Cam­bridge Uni­versity Press, 1998. MR 1696469 Zbl 0932.​11030 incollection

[113]B. Mazur: “Book re­view: Rochelle Owens, ‘New and se­lec­ted poems, 1961–1996’,” Har­vard Re­view 14 (1998), pp. 135–​137. article

[114]B. Mazur: “Book re­view: Martha Ronk, ‘Eye­t­rouble’,” Har­vard Re­view 15 (1998), pp. 171–​173. article

[115]Cur­rent de­vel­op­ments in math­em­at­ics, 1997 (Cam­bridge, MA, 1997). Edi­ted by R. Bott, A. Jaffe, D. Jer­is­on, G. Lusztig, I. Sing­er, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 1999. MR 1698851 Zbl 0927.​00019 book

[116]Cur­rent de­vel­op­ments in math­em­at­ics, 1998 (Cam­bridge, MA, 1998). Edi­ted by B. Mazur, W. Schmid, S.-T. Yau, D. Jer­is­on, I. M. Sing­er, and D. Stroock. In­ter­na­tion­al Press (Somerville, MA), 1999. MR 1772320 Zbl 0963.​00022 book

[117]Cur­rent de­vel­op­ments in math­em­at­ics, 1999 (Cam­bridge, MA, 1999). Edi­ted by B. Mazur, W. Schmid, S.-T. Yau, D. Jer­is­on, I. M. Sing­er, and D. Stroock. In­ter­na­tion­al Press (Somerville, MA), 1999. MR 1990245 Zbl 1051.​00008 book

[118]B. Mazur: “Visu­al­iz­ing ele­ments of or­der three in the Sha­far­ev­ich–Tate group,” Asi­an J. Math. 3 : 1 (March 1999), pp. 221–​232. MR 1701928 Zbl 0958.​11043 article

[119]B. Mazur: “Open prob­lems in num­ber the­ory,” pp. 199–​203 in Cur­rent de­vel­op­ments in math­em­at­ics, 1997 (Som­merville, MA). Edi­ted by R. Bott, A. Jaffe, D. Jer­is­on, G. Lusztig, I. Sing­er, and S.-T. Yau. In­ter­na­tion­al Press, 1999. MR 1700300 incollection

[120]B. Mazur: “Book re­view: Kurt Brown (ed.), ‘Verse & uni­verse: Poems about sci­ence and math­em­at­ics’,” Har­vard Re­view 16 (1999), pp. 141–​146. article

[121]Math­em­at­ics: Fron­ti­ers and per­spect­ives. Edi­ted by V. Arnold, M. Atiyah, P. Lax, and B. Mazur. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2000. MR 1754762 Zbl 1047.​00015 book

[122]2000 Steele Prizes,” No­tices Am. Math. Soc. 47 : 4 (April 2000), pp. 477–​480. MR 1745621 Zbl 1040.​01503 article

[123]B. Mazur: “Abeli­an vari­et­ies and the Mor­dell–Lang con­jec­ture,” pp. 199–​227 in Mod­el the­ory, al­gebra, and geo­metry. Edi­ted by D. Haskell, A. Pil­lay, and C. Stein­horn. Math­em­at­ic­al Sci­ences Re­search In­sti­tute Pub­lic­a­tions 39. Cam­bridge Uni­versity Press, 2000. MR 1773708 Zbl 0990.​14006 incollection

[124]B. Mazur: “The theme of \( p \)-ad­ic vari­ation,” pp. 433–​459 in Math­em­at­ics: Fron­ti­ers and per­spect­ives. Edi­ted by V. Arnold, M. Atiyah, P. Lax, and B. Mazur. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2000. MR 1754790 Zbl 0959.​14008 incollection

[125]J. E. Cre­mona and B. Mazur: “Visu­al­iz­ing ele­ments in the Sha­far­ev­ich–Tate group,” Exp. Math. 9 : 1 (2000), pp. 13–​28. To Bry­an Birch. MR 1758797 Zbl 0972.​11049 article

[126]B. Mazur: “Ques­tions about powers of num­bers,” No­tices Am. Math. Soc. 47 : 2 (2000), pp. 195–​202. MR 1740351 Zbl 1041.​11065 article

[127]D. Kazh­dan, B. Mazur, and C.-G. Schmidt: “Re­l­at­ive mod­u­lar sym­bols and Rankin–Sel­berg con­vo­lu­tions,” J. Reine An­gew. Math. 519 (2000), pp. 97–​141. MR 1739728 Zbl 0941.​11020 article

[128]Cur­rent de­vel­op­ments in math­em­at­ics, 2001 (Cam­bridge, MA, 2001). Edi­ted by A. J. de Jong, D. Jer­is­on, G. Lusztig, B. Mazur, W. Schmid, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2001. MR 1971375 Zbl 1013.​00015 book

[129]Cur­rent de­vel­op­ments in math­em­at­ics, 2000 (Cam­bridge, MA, 2000). Edi­ted by B. Mazur, W. Schmid, S.-T. Yau, A. J. de Jong, D. Jer­is­on, and G. Lusztig. In­ter­na­tion­al Press (Somerville, MA), 2001. MR MR1882532 Zbl 0990.​00013 book

[130]B. Mazur: “Qu’est-ce qu’un prob­leme? Une hy­po­these? Une con­jec­ture?” [What is a prob­lem? A hy­po­thes­is? A con­jec­ture?], La Recher­che 32 : 346 (2001), pp. 18. article

[131]B. Mazur: “Book re­view: Laure-Anne Bos­se­laar, ‘Urb­an nature: Poems about wild­life in the city’,” Har­vard Re­view 16 (2001), pp. 141–​144. article

[132]B. Mazur: “Open wide,” Har­vard Re­view 14 (2001), pp. 67. A poem. article

[133]B. Mazur: “LIBR,” Har­vard Re­view 20 (2001), pp. 24–​25. A poem. article

[134]B. Mazur and K. Ru­bin: “El­lipt­ic curves and class field the­ory,” pp. 185–​195 in Pro­ceed­ings of the In­ter­na­tion­al Con­gress of Math­em­aticians (Beijing, 20–28 Au­gust 2002), vol. 2: In­vited lec­tures. Edi­ted by L. Tat­si­en, C. Zhijie, X. Mi, and Z. Chun­li­an. High­er Edu­ca­tion Press (Beijing), 2002. MR 1957032 Zbl 1036.​11023 ArXiv math/​0304235 incollection

[135]F. La Nave and B. Mazur: “Read­ing Bombelli,” Math. In­tell. 24 : 1 (2002), pp. 12–​21. MR 1889932 Zbl 1023.​01005 article

[136]Cur­rent de­vel­op­ments in math­em­at­ics, 2003. Edi­ted by B. Mazur, W. Schmid, S.-T. Yau, A. J. de Jong, D. Jer­is­on, and G. Lusztig. In­ter­na­tion­al Press (Somerville, MA), 2003. MR 2132322 Zbl 1090.​00008 book

[137]B. Mazur and K. Ru­bin: “Study­ing the growth of Mor­dell–Weil,” Doc. Math. Extra volume (2003), pp. 585–​607. To Kazuya Kato, with ad­mir­a­tion. MR 2046609 Zbl 1142.​11339 article

[138]Cur­rent de­vel­op­ments in math­em­at­ics, 2002 (Cam­bridge, MA, 15–17 Novem­ber 2002). Edi­ted by D. Jer­is­on, G. Lusztig, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2003. Pro­ceed­ings of a sem­in­ar in hon­or of Wil­fried Schmid and George Lusztig. MR 2051781 Zbl 1033.​00012 book

[139]B. Mazur: Ima­gin­ing num­bers (par­tic­u­larly the square root of minus fif­teen). Far­rar, Straus and Giroux (New York), 2003. MR 1950850 Zbl 1049.​00502 book

[140]B. Mazur: His­tory of math­em­at­ics as a tool. Lec­ture notes, Har­vard Uni­versity, 2003. Lec­ture notes for sem­in­ar or­gan­ized by An­thony Liu and Lu­cia Mocz. techreport

[141]P. Di­ac­onis: “The prob­lem of think­ing too much,” Bull. Am. Acad. Arts Sci. 56 : 3 (2003), pp. 26–​38. With an in­tro­duc­tion by Barry Mazur. article

[142]B. Mazur: “Math and art without the fil­ters,” LA Times (May 18 2003). article

[143]B. Mazur: “Plus symétrique que la sphère” [More sym­met­ric than the sphere], Pour la Sci­ence. Dossier 41 (October–December 2003), pp. 78–​85. article

[144]T. Graber, J. Har­ris, B. Mazur, and J. Starr: “Arith­met­ic ques­tions re­lated to ra­tion­ally con­nec­ted vari­et­ies,” pp. 531–​542 in The leg­acy of Niels Hen­rik Abel: The Abel bi­cen­ten­ni­al (Oslo, 3–8 June 2002). Edi­ted by O. A. Laud­al and R. Piene. Spring­er (Ber­lin), 2004. MR 2077583 Zbl 1071.​14053 incollection

[145]T. Graber, J. Har­ris, B. Mazur, and J. Starr: “Jumps in Mor­dell–Weil rank and arith­met­ic sur­jectiv­ity,” pp. 141–​147 in Arith­met­ic of high­er-di­men­sion­al al­geb­ra­ic vari­et­ies (Pa­lo Alto, CA, 11–20 Decem­ber 2002). Edi­ted by B. Poon­en and Y. Tschinkel. Pro­gress in Math­em­at­ics 226. Birkhäuser (Bo­ston, MA), 2004. MR 2029867 Zbl 1075.​14021 incollection

[146]B. Mazur: “What is … a motive?,” No­tices Am. Math. Soc. 51 : 10 (2004), pp. 1214–​1216. MR 2104916 Zbl 1054.​14511 article

[147]B. Mazur and K. Ru­bin: “Kolyva­gin sys­tems,” Mem. Am. Math. Soc. 168 : 799 (2004), pp. viii+96. Avail­able open access here. MR 2031496 Zbl 1055.​11041 article

[148]B. Mazur: “Per­turb­a­tions, de­form­a­tions, and vari­ations (and ‘near-misses’) in geo­metry, phys­ics, and num­ber the­ory,” Bull. Am. Math. Soc., New Ser. 41 : 3 (2004), pp. 307–​336. In memory of René Thom. MR 2058289 Zbl 1057.​11033 article

[149]B. Mazur and K. Ru­bin: “In­tro­duc­tion to Kolyva­gin sys­tems,” pp. 207–​221 in Stark’s con­jec­tures: Re­cent work and new dir­ec­tions (Bal­timore, MD, 5–9 Au­gust 2002). Edi­ted by D. Burns, C. Popes­cu, J. Sands, and D. So­lomon. Con­tem­por­ary Math­em­at­ics 358. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2004. Avail­able open access here. MR 2088718 Zbl 1081.​11069 incollection

[150]B. Mazur and K. Ru­bin: “Pair­ings in the arith­met­ic of el­lipt­ic curves,” pp. 151–​163 in Mod­u­lar curves and abeli­an vari­et­ies (Bar­celona, 15–18 Ju­ly 2002). Edi­ted by J. Cre­mona, J.-C. Lario, J. Quer, and K. Ribet. Pro­gress in Math­em­at­ics 224. Birkhäuser (Basel), 2004. Avail­able open access here. MR 2058649 Zbl 1071.​11028 incollection

[151]B. Mazur: “On the ab­sence of time in math­em­at­ics,” Learn. Math. 24 : 3 (November 2004), pp. 18–​20. article

[152]A. Agashe and W. Stein: “Vis­ible evid­ence for the Birch and Swin­ner­ton-Dyer con­jec­ture for mod­u­lar abeli­an vari­et­ies of ana­lyt­ic rank zero,” Math. Com­put. 74 : 249 (2005), pp. 455–​484. With an ap­pendix by J. Cre­mona and B. Mazur. MR 2085902 Zbl 1084.​11033 article

[153]B. Mazur and K. Ru­bin: “Find­ing large Selmer groups,” J. Dif­fer. Geom. 70 : 1 (2005), pp. 1–​22. Avail­able open access here. MR 2192059 Zbl 1211.​11068 article

[154]T. Graber, J. Har­ris, B. Mazur, and J. Starr: “Ra­tion­al con­nectiv­ity and sec­tions of fam­il­ies over curves,” Ann. Sci. Éc. Norm. Supér. (4) 38 : 5 (September–October 2005), pp. 671–​692. MR 2195256 Zbl 1092.​14062 article

[155]B. Mazur and K. Ru­bin: “Or­gan­iz­ing the arith­met­ic of el­lipt­ic curves,” Adv. Math. 198 : 2 (2005), pp. 504–​546. MR 2183387 Zbl 1122.​11038 article

[156]B. Mazur: “Pour­quoi les nombres premi­ers?” [Why the prime num­bers?], Les Dossiers de la Recher­che 20 (August–October 2005), pp. 20–​24. article

[157]B. Mazur and P. Pes­ic: “On math­em­at­ics, ima­gin­a­tion & the beauty of num­bers,” Daedalus 134 : 2 (2005), pp. 124–​130. article

[158]A. Ash and R. Gross: Fear­less sym­metry: Ex­pos­ing the hid­den pat­terns of num­bers. Prin­ceton Uni­versity Press, 2006. With a fore­word by Barry Mazur. MR 2229945 Zbl 1111.​11001 book

[159]Cur­rent de­vel­op­ments in math­em­at­ics, 2004 (Cam­bridge, MA, 2005). Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2006. MR 2459295 Zbl 1161.​00012 book

[160]B. Mazur, W. Stein, and J. Tate: “Com­pu­ta­tion of \( p \)-ad­ic heights and log con­ver­gence,” pp. 577–​614 in John H. Coates’ six­tieth birth­day, published as Doc. Math. Ex­tra volume. Deutsche Math­em­atiker-Ver­ein­i­gung (Biele­feld), 2006. MR 2290599 Zbl 1135.​11034 incollection

[161]Cur­rent de­vel­op­ments in math­em­at­ics, 2004. Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2006. MR 2459289

[162]B. Mazur: A “Ba­sic No­tions” lec­ture about sign in­tu­itions. Lec­ture notes, Har­vard Uni­versity, February 2006. Based on joint work with Karl Ru­bin. Notes to Ba­sic No­tions Sem­in­ar talk, giv­en 6 Feb­ru­ary 2006. techreport

[163]B. Mazur: “Math­em­at­ics: Con­trolling our er­rors,” Nature 443 : 7107 (7 September 2006), pp. 38–​40. article

[164]B. Mazur: “About the cov­er: Di­o­phantus’s ‘Arith­met­ica’,” Bull. Amer. Math. Soc., New Ser. 43 : 3 (July 2006), pp. 399–​401. article

[165]B. Bek­temirov, B. Mazur, W. Stein, and M. Watkins: “Av­er­age ranks of el­lipt­ic curves: Ten­sion between data and con­jec­ture,” Bull. Am. Math. Soc., New Ser. 44 : 2 (April 2007), pp. 233–​254. MR 2291676 Zbl 1190.​11032 article

[166]B. Mazur, K. Ru­bin, and A. Sil­ver­berg: “Twist­ing com­mut­at­ive al­geb­ra­ic groups,” J. Al­gebra 314 : 1 (August 2007), pp. 419–​438. MR 2331769 Zbl 1128.​14034 ArXiv math/​0609066 article

[167]B. Mazur and K. Ru­bin: “Find­ing large Selmer rank via an arith­met­ic the­ory of loc­al con­stants,” Ann. Math. (2) 166 : 2 (2007), pp. 579–​612. MR 2373150 Zbl 1219.​11084 ArXiv math/​0512085 article

[168]B. Mazur and K. Ru­bin: Growth of Selmer rank in nona­beli­an ex­ten­sions of num­ber fields. Pre­print, 2007. ArXiv 0703363 techreport

[169]T. Dantzig: Num­ber: The lan­guage of sci­ence, 4th re­prin­ted edition. Edi­ted by J. Mazur. Plume (New York), 2007. With a new fore­word by Barry Mazur. book

[170]B. Mazur: Ru­min­a­tions on my very minor run­ning in­jury, 2007. A po­et­ic re­sponse to Rumi’s “Un­marked boxes”. misc

[171]L. R. Lieber: The edu­ca­tion of T. C. Mits: What mod­ern math­em­at­ics means to you, re­print edition. Paul Dry Books (Phil­adelphia), 2007. With a fore­word by Barry Mazur. book

[172]L. R. Lieber: In­finty: Bey­ond the bey­ond the bey­ond, 2nd edition. Edi­ted by B. Mazur. Paul Dry Books (Phil­adelphia), 2007. Ed­ited and with a new fore­word by Barry Mazur. book

[173]B. Mazur: “When is one thing equal to some oth­er thing?,” pp. 221–​241 in Proof and oth­er di­lem­mas: Math­em­at­ics and philo­sophy. Edi­ted by B. Gold and R. A. Si­mons. Spec­trum. Math­em­at­ic­al As­so­ci­ation of Amer­ica (Wash­ing­ton, DC), 2008. In memory of Saun­ders Mac Lane. MR 2452082 incollection

[174]B. Mazur and K. Ru­bin: “Growth of Selmer rank in nona­beli­an ex­ten­sions of num­ber fields,” Duke Math. J. 143 : 3 (2008), pp. 437–​461. MR 2423759 Zbl 1151.​11023 article

[175]Cur­rent de­vel­op­ments in math­em­at­ics, 2006 (Cam­bridge, MA, 2006). Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2008. MR 2459303 Zbl 1149.​00018 book

[176]B. Mazur: “Find­ing mean­ing in er­ror terms,” Bull. Am. Math. Soc., New Ser. 45 : 2 (April 2008), pp. 185–​228. In memory of Serge Lang. MR 2383303 Zbl 1229.​11001 article

[177]B. Mazur: “Math­em­at­ic­al Pla­ton­ism and its op­pos­ites,” Eur. Math. Soc. Newsl. 68 (2008), pp. 19–​21. Zbl 1154.​00310 article

[178]B. Mazur: “Al­geb­ra­ic num­bers,” pp. 315–​332 in The Prin­ceton com­pan­ion for math­em­at­ics. Edi­ted by T. Gowers, J. Bar­row-Green, and I. Lead­er. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2008. Sec­tion IV.1. incollection

[179]B. Mazur: “How did Theaetetus prove his the­or­em?,” pp. 227–​250 in The en­vi­sioned life: Es­says in hon­or of Eva Brann. Edi­ted by P. Kalkavage and E. Salem. Paul Dry Books (Phil­adelphia), 2008. incollection

[180]E. Galv­in: Do the math. Tu­pelo Press (North Adams, MA), 2008. With a fore­word by Barry Mazur. book

[181]B. Mazur: Some notes about ima­gin­a­tion and math­em­at­ics re­lated to a con­ver­sa­tion with Eva Brann. Lec­ture notes, Har­vard Uni­versity, 2008. A con­ver­sa­tion with Eva Brann. techreport

[182]F. Calegari and B. Mazur: “Nearly or­din­ary Galois de­form­a­tions over ar­bit­rary num­ber fields,” J. Inst. Math. Jussieu 8 : 1 (January 2009), pp. 99–​177. MR 2461903 Zbl 1211.​11065 ArXiv 0708.​2451 article

[183]Cur­rent de­vel­op­ments in math­em­at­ics, 2008 (Cam­bridge, MA, 2008). Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2009. MR 2555925 Zbl 1173.​00021 book

[184]Cur­rent de­vel­op­ments in math­em­at­ics, 2007 (Cam­bridge, MA, 2007). Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. Somerville, MA: In­ter­na­tion­al Press, 2009. MR 2531714 Zbl 1166.​00310 book

[185]B. Mazur: Arith­met­ic and some of its as­pir­a­tions. Lec­ture notes, Har­vard Uni­versity, May 2009. Brief talk giv­en to the “Friends of the Har­vard Math­em­at­ics De­part­ment” on 5 May 2009. techreport

[186]B. Mazur: What should a pro­fes­sion­al math­em­atician know?. Technical report, Har­vard Uni­versity, 2009. An es­say writ­ten in re­sponse to a ques­tion posed by Phil Dav­is and Dav­id Mum­ford. techreport

[187]B. Mazur: The lan­guage of ex­plan­a­tion. Lec­ture notes, Har­vard Uni­versity, November 2009. An es­say writ­ten for the Uni­versity of Utah Sym­posi­um in Sci­ence and Lit­er­at­ure (Novem­ber, 2009) and in an­ti­cip­a­tion of a pan­el dis­cus­sion on Math­em­at­ics, Lan­guage, and Ima­gin­a­tion. techreport

[188]B. Mazur: Prob­lems con­nnect­ing lo­gic and num­ber the­ory. Lec­ture notes, Har­vard Uni­versity, May 2009. Notes for a pan­el on Num­ber The­ory and Lo­gic, at the MAMLS@Har­vard con­fer­ence, 9 May 2009. techreport

[189]B. Mazur: On time (in math­em­at­ics and lit­er­at­ure). Lec­ture notes, Har­vard Uni­versity, March 2009. Notes for a talk giv­en at a con­fer­ence in com­par­at­ive lit­er­at­ure, Har­vard, March 2009. techreport

[190]P. D. Lax, F. Hirzebruch, B. Mazur, L. Con­lon, E. B. Curtis, H. M. Ed­wards, J. Huebschmann, and H. Shul­man: “Raoul Bott as we knew him,” pp. 43–​49 in A cel­eb­ra­tion of the math­em­at­ic­al leg­acy of Raoul Bott (Mon­tréal, QC, 9–13 June 2008). Edi­ted by P. R. Ko­ti­uga. CRM Pro­ceed­ings & Lec­ture Notes 50. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 2010. MR 2648884 Zbl 1195.​01029 incollection

[191]Cur­rent de­vel­op­ments in math­em­at­ics, 2009 (Cam­bridge, MA, Novem­ber 2009). Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2010. MR 2757356 Zbl 1205.​00075 book

[192]B. Mazur and K. Ru­bin: “Ranks of twists of el­lipt­ic curves and Hil­bert’s tenth prob­lem,” In­vent. Math. 181 : 3 (September 2010), pp. 541–​575. MR 2660452 Zbl 1227.​11075 ArXiv 0904.​3709 article

[193]B. Mazur, B. Gross, and D. Mum­ford: “An­drew Gleason, 4 Novem­ber 1921–17 Oc­to­ber 2008,” Proc. Am. Phil. Soc. 154 : 4 (December 2010), pp. 471–​476. A slightly ex­pan­ded ver­sion of the ob­it­u­ary pub­lished in the Har­vard Uni­versity Gaz­ette (1 April 2010). article

[194]B. Mazur: Hil­bert’s tenth prob­lem and el­lipt­ic curves. Lec­ture notes, Har­vard Uni­versity, February 2010. “Ba­sic No­tions” talk giv­en on 1 Feb­ru­ary 2010. techreport

[195]B. Mazur: Ranks of twists of el­lipt­ic curves. Lec­ture notes, Har­vard Uni­versity, February 2010. Num­ber The­ory Sem­in­ar lec­ture on 3 Feb­ru­ary 2010. techreport

[196]B. Mazur, B. Gross, and D. Mum­ford: “An­drew Mat­tei Gleason,” Har­vard Gaz­ette (1 April 2010). A slightly ex­pan­ded ver­sion of this ob­it­u­ary was pub­lished in Proc. Am. Phil. Soc. 154:4 (2010). article

[197]B. Mazur: “How can we con­struct abeli­an Galois ex­ten­sions of ba­sic num­ber fields?,” Bull. Am. Math. Soc., New Ser. 48 : 2 (2011), pp. 155–​209. MR 2774089 Zbl 1228.​11163 article

[198]B. Mazur and K. Ru­bin: “Re­fined class num­ber for­mu­las and Kolyva­gin sys­tems,” Com­pos. Math. 147 : 1 (2011), pp. 56–​74. MR 2771126 Zbl 1225.​11144 ArXiv 0909.​3916 article

[199]B. Mazur: Dis­par­ity in the stat­ist­ics for quad­rat­ic twist fam­il­ies. Lec­ture notes, Har­vard Uni­versity, April 2011. Based on joint work with Zev Klags­brun and Karl Ru­bin. Notes for the 13 April 2011 work­shop of the pro­gram “Arith­met­ic Stat­ist­ics” at MSRI. techreport

[200]B. Mazur: El­lipt­ic curves, their com­pan­ions, and their stat­ist­ics. Lec­ture notes, Har­vard Uni­versity, 2011. Lec­ture notes for a joint MSRI-UC Berke­ley col­loqui­um for gradu­ate stu­dents en­titled “El­lipt­ic curves, their com­pan­ions, and their stat­ist­ics” giv­en in the winter of 2011 in con­junc­tion with the MSRI pro­gram “Arith­met­ic Stat­ist­ics.”. techreport

[201]B. Mazur: What is the sur­face area of a hedge­hog?. Lec­ture notes, Har­vard Uni­versity, September 2011. Lec­ture notes for a Stein­er Lec­ture giv­en at St. Johns Col­lege, An­na­pol­is, MD, 30 Septem­ber 2011. techreport

[202]Cur­rent de­vel­op­ments in math­em­at­ics, 2010 (Cam­bridge, MA, 2010). Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2011. MR 2906369 Zbl 1245.​00031 book

[203]B. Mazur: Math­em­at­ics and story, 20 April 2012. Guest con­tri­bu­tion to lit­er­ary web­site ber­frois. misc

[204]Cur­rent de­vel­op­ments in math­em­at­ics, 2011 (Cam­bridge, MA, Novem­ber 2011). Edi­ted by D. Jer­is­on, B. Mazur, T. Mrowka, W. Schmid, R. Stan­ley, and S.-T. Yau. In­ter­na­tion­al Press (Somerville, MA), 2012. Zbl 1256.​00015 book

[205]J. Hoff­man: “Q&A: The maths ra­con­teur,” Nature 483 : 7390 (22 March 2012), pp. 405. An in­ter­view with Mazur con­nec­ted to the pub­lic­a­tion of his book Circles dis­turbed (2012). article

[206]B. Mazur and K. Ru­bin: Selmer com­pan­ion curves. Pre­print, March 2012. ArXiv 1203.​0620 techreport

[207]B. Mazur: Primes, knots and Po. Lec­ture notes, Har­vard Uni­versity, July 2012. techreport

[208]B. Mazur: “About Her­mann Weyl’s ‘Rami­fic­a­tions, old and new, of the ei­gen­value prob­lem’,” Bull. Am. Math. Soc., New Ser. 49 : 2 (2012), pp. 325–​326. MR 2888169 Zbl 1236.​01013 article

[209]B. Mazur: Is it plaus­ible?. Lec­ture notes, Har­vard Uni­versity, January 2012. Lec­ture notes for the joint AMS-MAA con­fer­ence, 5 Janu­ary 2012. techreport

[210]B. Mazur: El­lipt­ic curves and their stat­ist­ics. Lec­ture notes, Har­vard Uni­versity, February 2012. Notes for a sem­in­ar giv­en 28 Feb­ru­ary 2012. techreport

[211]Circles dis­turbed: The in­ter­play of math­em­at­ics and nar­rat­ive. Edi­ted by A. Dox­i­adis and B. Mazur. Prin­ceton Uni­versity Press, 2012. MR 2906079 Zbl 1237.​00022 book

[212]B. Mazur: “Vis­ions, dreams, and math­em­at­ics,” pp. 183–​210 in Circles dis­turbed: The in­ter­play of math­em­at­ics and nar­rat­ive. Edi­ted by A. Dox­i­adis and B. Mazur. Prin­ceton Uni­versity Press, 2012. An in­ter­view with Mazur con­nec­ted to the pub­lic­a­tion of this book was pub­lished in Nature 483:7390 (2012). MR 2918069 incollection

[213]B. Mazur: A brief in­tro­duc­tion to the work of Haruzo Hida. Lec­ture notes, Har­vard Uni­versity, June 2012. Lec­ture notes for the con­fer­ence in cel­eb­ra­tion of the 60th birth­day of Haruzo Hida, UCLA, 18–23 June 2012. techreport

[214]B. Mazur and K. Ru­bin: Re­fined class num­ber for­mu­las for \( \mathbb{G}_m \). Pre­print, December 2013. ArXiv 1312.​4053 techreport

[215]J. B. Fried­lander, H. Iwaniec, B. Mazur, and K. Ru­bin: “The spin of prime ideals,” In­vent. Math. 193 : 3 (September 2013), pp. 697–​749. MR 3091978 Zbl pre06222256 article

[216]B. Mazur: Some com­ments on el­lipt­ic curves over gen­er­al num­ber fields and Brill–No­eth­er mod­u­lar vari­et­ies. Un­pub­lished lec­ture notes, Har­vard Uni­versity, 2013. Notes for a lec­ture giv­en at the Que­bec/Maine Num­ber The­ory Con­fer­ence, 2013. techreport

[217]Z. Klags­brun, B. Mazur, and K. Ru­bin: “Dis­par­ity in Selmer ranks of quad­rat­ic twists of el­lipt­ic curves,” Ann. Math. (2) 178 : 1 (2013), pp. 287–​320. MR 3043582 Zbl pre06190561 article

[218]B. Mazur: Arith­met­ic stat­ist­ics: El­lipt­ic curves and oth­er things. Un­pub­lished lec­ture notes, Har­vard Uni­versity, 2013. Notes for the Er­dős Me­mori­al Lec­ture, Temple Uni­versity, 12 Oc­to­ber 2013. techreport

[219]B. Mazur and K. Ru­bin: Con­trolling Selmer groups in the high­er core rank case. Pre­print, December 2013. ArXiv 1312.​4052 techreport