Revisiting Male Allies in Mathematics and Physics Throughout History: Role Models for Men in STEM Education

Ci a ion: Cal o-Iglesias, E.; Epi anio, I. Re isi ing Male Allies in Ma hema ics and Physics Th oughou His o y: Role Models o Men in STEM Educa ion. Educ. Sci. 2024,14, 535. h ps:// doi.o g/10.3390/educsci14050535 Academic Edi o : Ambe Simpson Recei ed: 7 Ap il 2024 Re ised: 12 May 2024 Accep ed: 13 May 2024 Published: 16 May 2024 Copy igh : © 2024 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). educa ion sciences Essay Re isi ing Male Allies in Ma hema ics and Physics Th oughou His o y: Role Models o Men in STEM Educa ion Encina Cal o-Iglesias 1and I ene Epi anio 2,* 1 Depa men o Applied Physics, Uni e si y o San iago de Compos ela, 15782 San iago de Compos ela, Spain; [email p o ec ed] 2Depa men o Ma hema ics-IF, Jaume I Uni e si y, 12071 Cas elló de la Plana, Spain *Co espondence: [email p o ec ed] Abs ac : In he academic wo ld, he e a e also gende inequali ies, which a e especially isible in ce ain masculinized STEM a eas, such as physics and ma hema ics. An essen ial ac o in co ec ing hese inequali ies is he in ol emen o men, who should ac as “allies” in he uni e si y se ing. Likewise, as he li e a u e shows us, we mus o e models wi h gende -incong uen oles o b eak down s e eo ypes and p omo e non- adi ional beha io s. Howe e , o da e, hese ac ions ha e been especially di ec ed owa d women, who gene ally do no hold powe and he e o e ha e less possibil- i y o p omo ing change. Fo he i s ime, his wo k compiles, in a single documen , impo an male physicis s and ma hema icians who ac ed as allies o women h oughou his o y. These examples can be p esen ed o p o ide male e e ences in he eaching o physics and ma hema ics a uni e si y (and high school). Wi h his ini ia i e, we in end o con ibu e o inco po a ing he gende pe spec i e in uni e si y eaching, since, in p ac ice, uni e si y p o esso s a e unawa e o e e ences o al e na i e masculini ies in he academic wo ld. We hope ha his a icle will be he seed o eco e hidden male allies in hese and o he scien i ic ields. This can help b eak down s e eo ypes, and con a y o p e ious ac ions, his wo k is especially di ec ed owa d men. Keywo ds: ma hema ics educa ion; physics educa ion; STEM eaching; ma hema ics his o y; physics his o y; gende equali y; male ad oca es; masculini ies; s e eo ypes MSC: 97C60; 01A70; 97U99; 00A05; 00A79 1. In oduc ion Gende inequali ies pe sis e en in coun ies wi h high a es o gende equali y. Fo example, in ecen yea s, di e en laws ha e been app o ed in Spain ha ha e made i one o he mos ad anced coun ies wi h espec o gende equali y. In ac , acco ding o a epo om he Eu opean Ins i u e o Gende Equali y (EIGE), Spain is he ou h coun y in he Eu opean Union (EU) on he gende equali y index o 2021 [ 1 ]. Bu despi e hese ad ances in equali y policies, he e is s ill a gende wage gap in Spain and low co- esponsibili y, and in ecen mon hs, a wo ying up ick in gende iolence has been obse ed [2]. These p oblems also a ec ins i u ions such as uni e si ies, which could be he engine o change in ou socie y, bu which can ha dly be so i he glass ceiling [ 3 ] and he gende wage gap [ 4 , 5 ] pe sis and si ua ions o sexual ha assmen and gende -based ha assmen occu [ 6 ]. Simila ly, Moss-Racusin e al. [7] e ealed ha scien is s a e biased in hi ing and encou aging men o e women. Sugimo o and La i iè e [8] also e ealed a gap in ci a ions a o ing men-led pape s in mos coun ies, in e ms o bo h i s au ho ship and las au ho ship. This si ua ion a o s e ical seg ega ion ha s ill pe sis s in uni e si ies and public esea ch o ganiza ions. In Spain, he epo Cien í icas en ci as 2023 (Female scien is s in igu es 2023) [ 9 ] shows ha in he ea ly s ages o esea ch ca ee s, women and men a e equally ep esen ed, bu emale alen is p og essi ely being los , un il we ind ha Educ. Sci. 2024,14, 535. h ps://doi.o g/10.3390/educsci14050535 h ps://www.mdpi.com/jou nal/educa ion Educ. Sci. 2024,14, 535 2 o 21 women a e unde - ep esen ed a he highes posi ions, only 25.6% [ 9 ]. This ac con ibu es o a 12.7% pay gap in uni e si ies [ 4 ]. In addi ion, he epo ci ed abo e shows ha women ob ain less unding, e.g., “in 2020, g an s o he implemen a ion o scien i ic esea ch and echnological de elopmen o p oposals gene a ed by women we e a o al amoun o EUR 254.9 million, compa ed o EUR 420.7 million awa ded o p oposals gene a ed by men. The amoun awa ded o women ep esen s 37.7% o he o al amoun , which is much lowe han he pe cen age ob ained by men (62.3%)” [ 9 ] (p. 91). Fu he mo e, Cabe o and Epi anio [10] laid ba e he gende gap in childca e wi h Spanish academic s a . The e was a di e ence o 30 h pe week, on a e age, be ween emale and male academic s a o ca e du ing he pe iod o pa en ing. The e o e, gende oles con inue o be p esen wi h Spanish academic s a , and his con i ms he need o eal changes in ou ins i u ions. Ha ing a legisla i e amewo k ha a o s gende equali y is a g ea ad ance, bu i is no enough. Fo example, a ecen e iew o he s udy plans and eaching guides o he P ima y Educa ion Deg ee highligh s ha “ he Teaching Guides, o he mos pa , use language ha encou ages he in isibili y o women, hey lack coeduca ional compe encies, con en , objec i es and esou ces and ha e an unequal dis ibu ion be ween women and men p esen in he bibliog aphy” [ 11 ] (p. 255). Likewise, he epo Cien í icas en ci as 2023 (Female scien is s in igu es 2023) emphasizes ha “ he in eg a ion o sex/gende analysis in he con en o eaching is one o he un esol ed issues ha has no been achie ed in all uni e si ies, since only wo hi ds o public uni e si ies and hal o p i a e uni e si ies claim o ha e ca ied ou ac ions aimed a p omo ing he inco po a ion o he gende dimension in class ooms in 2022” [ 9 ] (p. 117), and his inac ion is also con i med by he epo Las polí icas de igualdad uni e si a ias (Uni e si y equali y policies) p epa ed by he Spanish Ne wo k o Equali y Uni s o Gende o Uni e si y Excellence [ 12 ] and Epi anio and Cal o-Iglesias [13] , who analyzed he ac ions o gende equali y in scien i ic– echnical a eas in Spanish uni e si ies. To unde s and his low mains eaming o he gende pe spec i e, we mus ake in o accoun ha , in ecen yea s, neolibe al measu es ha e been adop ed in he uni e si y con- ex ha ha e encou aged eache s o p io i ize esea ch o e eaching, bo h o consolida e hei ca ee s and in o de o gain access o a pe manen posi ion [ 14 , 15 ]. These measu es ha e especially a ec ed young women wi h childca e esponsibili ies, because ca ing o amily membe s o s uden s con inues o be a woman’s ask [ 16 ]. Fu he mo e, he da a om he Cien í icas en Ci as epo con i m low male pa icipa ion, a ound 25%, in aining ac ions on gende equali y in uni e si ies and public esea ch o ganiza ions. This gende imbalance in pa icipa ion in equali y aining cou ses is wo ying o wo easons. On he one hand, men con inue o hold powe in hese ins i u ions and monopolize he mos impo an posi ions [ 17 ]. On he o he hand, he e a e highly masculinized a eas such as enginee ing, especially hose ela ed o compu e science [ 18 ], physics, o ma hema ics, whe e i is necessa y o in oduce he gende pe spec i e o end gende biases ha can a ec he de elopmen o echnological p oduc s, as we can see in he de elopmen o AI [ 19 ], o in he de ec ion o diseases ha cos money and e en li es [ 20 ]. By “masculinized a eas” we mean ha hey a e masculinized in e ms o hei pe cep ion and in e ms o hei p ac i ione s. As Gonsal es e al. [21] indica ed, “ he discipline o physics is no only domina ed by men, bu also is laden wi h masculine conno a ions on a symbolical le el, and ha his limi ed and limi ing cons uc ion o physics has made i di icul o many women o ind a place in he discipline”. Le us also ecall ha a ew yea s ago, S umia, a male pa icle physicis , s a ed ha “Physics was in en ed and buil by men, i is no by in i a ion” [22]. The e o e, o ensu e g ea e equali y, we need o inc ease he pa icipa ion o men who ac as allies o eminism wi hin he uni e si y. And i is necessa y o know wha d i es hem o abandon hei p i ileges in o de o a ac mo e men o hese al e na i e masculini ies [ 23 ]. In his pape , we will show he impo ance o p o iding masculine e e ences wi hin he amewo k o new masculini ies o non-hegemonic masculini ies and how we could inco po a e hem in he eaching o subjec s such as physics o ma hema ics. Educ. Sci. 2024,14, 535 3 o 21 To he bes o ou knowledge, his is he i s wo k ha compiles male allies h oughou his o y in hese ields. 1.1. Egali a ian o Al e na i e Masculini ies In e es in egali a ian o al e na i e masculini ies has inc eased in ecen yea s in Spain. And al hough esea ch on his opic is s ill sca ce [ 24 ], al eady, “I is beginning o be conside ed ha , wi hou a change in men, i will no be possible o achie e gende equali y” [ 25 ] (p. 60). Thus, se e al pos g adua e cou ses on masculini ies and equali y ha e been launched, such as he one a Uni e sidad Miguel He nández; con e ences ha e been held; and aining is beginning o be p o ided o eache s and s uden s on his opic. In ac , he Uni e si a Au ònoma de Ba celona has launched he Masculini y Wo kspace, wi h which i aims o p o ide a suppo se ice aimed a men who wan o e hink hei way o ela ing om a non-sexis pe spec i e. These cou ses and hese spaces a e impo an since, as López Ramos and Ci e [23] (p. 292) poin ed ou , “ he change owa ds egali a ian masculini ies equi es a e lec i e and p ac ical e o o he men who pe pe ua e i . An e o ha canno be achie ed wi hou some ype o impulse om he social en i onmen ”. The p omo ion o equali y wi hin he uni e si y en i onmen is essen ial in masculin- ized disciplines such as physics, ma hema ics, and enginee ing o pu an end o he sexis no ms ha s ill pe sis in hese disciplines and ha p e en women om ad ancing. The s udy by Dancy and Hoda i [26] showed us how men in he ield o physics who suppo ed he discou se o equali y in hei usual p ac ices main ained sexis no ms ha in alida ed hose discou ses. And as Sugimo o and La i iè e [8] (p. 1) poin ed ou , gende dispa i ies in science a e seen as a hing o he pas . The same goes o o he ypes o disc imina ion, such as acism [27]. The e o e, people who occupy posi ions o powe in hese disciplines should pa ici- pa e and ge in ol ed in ac ions ha a o equali y, s a ing wi h aining, because oday, we should all know wha he scisso g aph ep esen s in he e olu ion o eaching and esea ch s a . This g aph shows he e olu ion o women and men in hei academic ca ee s. As he ajec o y p og esses, be o e ob aining a doc o a e and up o becoming a esea ch p o esso , he pe cen age o women dec eases and ha o men inc eases. A he beginning, he e a e sligh ly mo e women han men (excep in physics, enginee ing, and compu e science (PECS) a eas), so he wo lines c oss. This is why i is called a scisso g aph. Un o una ely, his is no he case [ 28 ], and we mus assume he consequences o doing no hing, since i we a e no pa o he solu ion, we a e pa o he p oblem. In ac , ecen ly, in Spain, uling 134/2021, o 24 Feb ua y, issued by he con en ious adminis a i e Chambe o he Supe io Cou o Jus ice o he Valencian Communi y [ 29 ], ecognizes ha disc imina ion can occu h ough omission, ha is, by no ac ing when he e is disc imina ion. In ecen yea s, equali y measu es in scien i ic and echnical ields ha e ocused mainly on women and gi ls and, mo e ecen ly, on LGTBIQ+ people, o ge ing ha i is he g oups wi h p i ilege ha can a o change. Wi hou abandoning hese equali y measu es, we need o he measu es ha allow us o inco po a e mo e men because, as bell hooks [30] (p. XVII) s a ed “I is no ue ha men a e unwilling o change. I is ue ha many men a e a aid o change” . And o his, i is necessa y o acili a e he knowledge and isibili y o al e na i e and egali a ian models o men. These models a e no new, and as Bace e [31] (p. 30) highligh ed, “dissidence, also in he male sphe e, has always been p esen , al hough i s di e en exp essions ha e eached ou days wi h di icul y, because he na a i e o he s o ies o dissiden men, as wi h ha o women, i is also biased, condi ioned and impac ed by sexism”. And h oughou his o y he e ha e been men such as Nicolas de Condo ce , Cha les Fou ie , William Thompson, John S ua Mill, Léon Riche , Jin Tianhe and Taha Haddad ha e suppo ed he emancipa ion o women. They de ended women’s physical in eg i y, libe y o mo emen , and in ellec ual, ci il and poli ical equali y. They demanded ha women ha e he igh o lea n, wo k, o e, lo e and be au onomous. [32] (p. X) Educ. Sci. 2024,14, 535 4 o 21 In scien i ic and echnical ields, we can also ind examples o dissiden men who ha e suppo ed hei emale colleagues o disciples a wo k and in li e. And we need o in eg a e hem in o ou explana ions and o e hem as models o ollow, as we will show in he nex sec ion. 1.2. Fai Men, Also in Science? The ision o science and echnology ha con inues o be ansmi ed in he class ooms is posi i is . In gene al, he disas ous consequences ha ce ain disco e ies ha e had, such as hose ha led o he a omic bomb, o he consequences o humani y o his indus ial capi alism ha deple es na u al esou ces and endange s ou su i al on he plane , a e no analyzed. The ac ha women we e e ased om he his o y o science and he scan ecogni ion o hei con ibu ions is no ques ioned ei he . I con inues o be hough ha science is neu al and objec i e, o ge ing ha i is made by people and can he e o e be a ec ed in any way by hei biases. E en hough ex books con inue o ansmi o us an and ocen ic ision o scien i ic knowledge, p og ess has been made, as e lec ed by he la ge numbe o books abou emale scien is s aimed a child en and young people. In he na a i e ha con inues o be sha ed abou science, scien is s con inue o be p esen ed as he oes o he oines, and hei con ibu ions a e a ely ques ioned. No only his, bu we ha e ecen ly seen how he p emie e o he ilm Oppenheime was celeb a ed. Howe e , he e en i depic s should be seen as he bigges ailu e in he his o y o science and echnology due o he des uc ion ha i caused. Fu he mo e, i should lead us o analyze he alliance be ween science and echnology, and enginee ing and wa h oughou his o y. And he ilm igno es he ole o Lise Mei ne , whom he No h Ame ican p ess labeled he mo he o he nuclea bomb, in he disco e y o nuclea ission [ 33 ]. In hese imes o ene gy and clima e c ises, su ounded by wa s, we need o he ypes o s o ies, whe e e hics and human alues, like hose shown by Lise Mei ne who e used o pa icipa e in he Manha an p ojec , help us build a ai e wo ld. This also conce ns he ision o science ha we each in he class oom, whe e we mus ecognize no only scien i ic achie emen s bu also he alue hey ha e had o socie y, including suppo o women in he ield o science. In addi ion, i is necessa y o change he app oach o knowledge and me hodology o Wes e n science o ien ed owa d he dominance o na u e [ 34 ]. We need o do away wi h he masculinis app oach ha ocuses on he use o echnology o o e come his c isis and inco po a e emale and excluded oices, as well as social and gende jus ice conce ns abou he impac o clima e change on women and ulne able popula ions [34]. The his o y o science could be used as a eaching esou ce in his sense “since i allows us o ex ac om i he mos signi ican p oblems ha esea ch had o ace a he ime, in addi ion o o e ing a sample o he con o e sial na u e o scien i ic esea ch, which is he esul o he wo k o nume ous people, mos ly men, and igno ing he con ibu ions o women scien is s” [ 35 ] (p. 22). Thus, einse ing women in o scien i ic his o y and e- claiming hei knowledge and ha o o he adi ionally excluded g oups will con ibu e o ending he sexism, and ocen ism, and colonialism ha s ill pe mea e scien i ic knowledge. We would like o emphasize ha we ind i e y in e es ing o use his o ical en ichmen as a p oposal o decolonize he cu iculum [ 36 ]. Bu ou p oposal is ocused on cha ac e s o he XIX and XX cen u ies ha buil he physics and ma hema ics ha we mainly each in uni e si y cou ses on physics and ma hema ics. Since Enheduanna (2300 BCE), who is conside ed he i s emale au ho and also he i s emale scien is in his o y, he e ha e been many women who ha e con ibu ed o he ad ancemen o science, mos ly women om he uppe classes o belonging o amilies o scien is s, as is he case o many as onome s. As Sugimo o and La i iè e [8] (p. 17) said, Be o e he wen ie h cen u y, science was associa ed wi h ama eu ism, which allowed weal hy women and hose who ma ied scien is s o pa icipa e in sci- en i ic ac i i ies. Beginning in he 1870s, women inc eased hei membe ship in scien i ic o ganiza ions and began ob aining employmen in museums and obse - a o ies. By he end o he nine een h cen u y, howe e , science began a p ocess o Educ. Sci. 2024,14, 535 5 o 21 p o essionaliza ion ha se ed o dec ease women’s access o schola ship. When science became codi ied as a p o essional—and he e o e masculine—domain, women we e u he isola ed om pa icipa ion. Un il ecen ly, we did no know hei names, bu oday, hanks o books such as Hypa ia’s He i age by Alic [37] , which has inspi ed many o he s, we a e al eady eco e ing hem. And in addi ion o eco e ing hei names and hei legacy, we should also ecognize he men who suppo ed hem, such as Py hago as (490 BCE), known as “ he philosophe iend o women”, and Gös a Mi ag-Le le (1846–1927), a de ende o women’s access o academic posi ions ha hey we e p ohibi ed om holding. We need ole models o men who do no app op ia e he disco e ies o hei emale colleagues and who ecognize hei wo h, as Pie e Cu ie did when he claimed he Nobel P ize o Ma ie Cu ie, as well as men who help and ecognize emale alen , such as William He schel and F ied ich Pockels, who helped hei sis e s Ca oline He schel (1750–1848) and Agnes Pockels (1862–1935) de elop hei scien i ic alen . Al hough i is ue ha in he case o W. He schel and o he s, his suppo could be in e p e ed as ha ing been p o ided o his own bene i , as Donald [38] (p. 21) ema ked, “Ca oline He schel was able o be an ou lie , o midable al hough he con ibu ions we e, by i ue o he ci cles which she was able o pene a e h ough he b o he ”. Simila ly, we wan male p o esso s who alue he abili ies o hei emale s uden s, such as Ka l Weie s aß (1815–1897) and Max Planck (1858–1947) wi h So ia Ko alé skaya (1850–1891) and Lise Mei ne (1878–1968), espec i ely, al hough nei he o hem we e, in p inciple, a o able o he admission o women o uni e si ies, and Geo ge Gamow (194–1968), who made i possible o Ve a Rubin (1928–2016) o ca y ou he hesis. Mo eo e , i is impo an ha , in ou p esen a ions, ou i ual class ooms, and ou eachings, when making hese women scien is s isible, we highligh he alue o he male allies who helped hem de elop hei alen . Because i is no ai ha women, “as Glo ia S einem would say, (...) om he momen we en e kinde ga en un il we inish he doc o a e, (...) we dedica e ou sel es i elessly o s udying ou own absence” [ 39 ] (p. 19), o ha men do no ha e equal mi o s in which o look a hemsel es. We ag ee wi h Gonsal es e al. [40] on he u ili y o s o y-based me hodologies o explo ing he di e en pa hs ollowed o s ay and belong in physics. In seconda y school, i is impo an o o e o he s o ies abou science [ 41 ] ha can a ac mo e women o mino ized g oups [ 42 ] o his discipline who do no iden i y wi h his supe masculini y ha seems o domina e physics and o he STEM a eas. 2. Male Allies in Ma hema ics and Physics A na a i e e iew is conside ed. Unlike sys ema ic e iews ha a e guided by p ocedu es such as PRISMA (P e e ed Repo ing I ems o Sys ema ic Re iews and Me a- Analyses), he e a e no es ablished p ocedu es o na a i e e iews. We ollow he guide- lines o na a i e e iews sugges ed by Sukhe a [43] , which a e as ollows: (1) a ionale o a na a i e e iew; (2) cla i y o bounda ies, scope, and de ini ions; (3) jus i ica ion o inclusion and exclusion c i e ia; (4) e lexi i y and a sa u a ion/su iciency s a emen ; and (5) de ails on analysis and in e p e a ion. Rega ding he i s poin , we chose a na a i e e iew because his opic is unde - esea ched, which is a si ua ion whe e a na a i e e iew is use ul o educa o s [ 43 ]. We compiled e idence om mul iple sou ces in o one accessi- ble and usable documen . Some o hose sou ces a e “neu al”, i.e., hey limi hemsel es o s a ing ce ain ac s. Howe e , we conside ed a gende egali a ianism poin o iew (poin 5). The e o e, his is also a c i ical e iew om he gende equali y pe spec i e. As ega ds poin (4), na a i e e iews do no aim o be inclusi e o all li e a u e abou he opic. The e o e, o he sake o b e i y, we p io i ized including mo e scien is s using a limi ed numbe o e e ences pe scien is han including many e e ences o ew scien is s. Conce ning poin s 2 and 3, hey a e speci ied as ollows. In his sec ion, we will e iew male physicis s and ma hema icians who ac ed as allies o he emale physics and ma hema ics (poin 3) who usually appea in he syllabi o undamen al physics and ma hema ics subjec s in Spain (poin 2), no only in physics and Educ. Sci. 2024,14, 535 6 o 21 ma hema ics deg ees, bu also in mos science and enginee ing deg ees; so, hey would se e o STEM deg ees in gene al. We will also poin ou he male ma hema icians and physicis s who no only we e no allies bu also ac ually ac ed agains hem in o de o be especially ca e ul and no use hem as e e ences (poin 3). In addi ion o STEM deg ees, ma hema ics, and especially s a is ics, is augh in deg ees in he ields o heal h and social sciences. Consequen ly, he scope o applica ion is no es ic ed only o STEM (poin 2). 2.1. Ma hema ics and S a is ics Fi s ly, we will use some espec ed igu es ha appea in a basic s a is ics subjec as a common h ead, combining his wi h he in oduc ion o espec ed igu es in o he a eas o ma hema ics. 2.1.1. Desc ip i e S a is ics In he ield o desc ip i e s a is ics, Flo ence Nigh ingale (1820–1910) [ 44 ] is a no able name as she was a pionee in using s a is ical g aphs o achie e changes in he s a egies o au ho i ies [ 45 ]. She had James Joseph Syl es e (1814–1897) as a u o , known among o he hings o his con ibu ions in he ield o ma ices. Syl es e was a iend o ano he illus ious ma hema ician, A hu Cayley (1821–1895), who suppo ed uni e si y educa ion o women. In he ea ly days o Gi on College, Camb idge’s i s women’s college, Cayley assis ed in eaching. Addi ionally, he was chai man o he council o Newnham College, Camb idge’s second women’s college. Cha lo e Angas Sco ’s (1858–1931) [ 46 ] hesis was di ec ed by Cayley, who ecommended ha she mo e o B yn Maw College (USA) so she could wo k he e. In his way, Sco was able o supe ise he doc o a es o a leas eigh emale ma hema icians, many o whom s udied wi h Felix Klein (1849–1925) a he Uni e si y o Gö ingen. Among Flo ence Nigh ingale’s allies, wi h whom she wo ked and co esponded ex ensi ely, a e he s a is icians William Fa (1807–1883) and Lambe Adolphe Que ele (1796–1874), ecognized as one o he a he s o mode n s a is ics. Toge he wi h F ancis Gal on (1822–1911) (a s a is ician ecognized o a ious con ibu ions, such as s anda d de ia ion, coining he e ms pe cen ile and co ela ion), he collabo a ed o c ea e a new Chai o S a is ics a Ox o d, wi hou success. Howe e , we mus be cau ious wi h bo h Gal on and o he amous s a is icians such as Ka l Pea son (1857–1936) and Ronald Fishe (1890–1962), who had deep ies o eugenics and acial and class p ejudices, and no use hem as e e ences, i.e., no be conside ed exempla s o be emula ed. Ins ead, hei his o y can be shown o e lec on he ole o s a is ics in he wo ld [ 47 ], i.e., b inging hese igu es up in he class oom could be use ul. This ecommenda ion conce ns no only hese pa icula s a is icians; we mus be wa y mo e b oadly, and we ad ise no o be blindly suppo i e o a pa icula scien is . Gal on’s beha io was also sexis . He c ea ed a “beau y map” o he women o G ea B i ain based on he sec e obse a ion o women om di e en egions, whom he a ed on a scale as a ac i e, indi e en , o epulsi e, indica ing his opinions on a piece o pape in he shape o a c oss. His cousin, Cha les Da win (1809–1882), de ended he in e io i y o women o men. The ollowing is an ex ac om a le e he w o e o Lady Ca oline Kenna d (1827–1907), a leading igu e in he eminis mo emen o he ime: I ce ainly hink ha women hough gene ally supe io o men [in] mo al quali ies a e in e io in ellec ually; and he e seems o me o be a g ea di icul y om he laws o inhe i ance, (i I unde s and hese laws co ec ly) in hei becoming he in ellec ual equals o man. [48] (p. 14). No only did Da win conside women in e io , bu he also added ha women should no aspi e o a li e ou side he home, since ha would be de imen al o he happiness o child en and homes [48]. Educ. Sci. 2024,14, 535 7 o 21 2.1.2. P obabili y Con inuing wi h he concep s ha appea in basic s a is ics subjec s, in he ield o p obabili y, Bo elian algeb a is shown, in hono o Emile Bo el (1871–1956). Bo el suppo ed he wo k o his wi e Ma gue i e Appell (1883–1969), known as Camille Ma bo, a enowned F ench eminis w i e , and hey bo h ounded he scien i ic and li e a y magazine Re ue du Mois. In 1911, he and Ma bo hos ed Ma ie Cu ie (1867–1934) in hei home when Cu ie, hen a widow, was a acked o he a ai wi h Paul Lange in (1872–1946) (de ails can be ound in he physics sec ion), despi e p essu e om he F ench go e nmen o no accep he . Bo el and Lange in we e ac i e in he de ense o human igh s. Bo el p oposed a law o gua an ee he ep esen a ion o women in municipal councils [ 49 ]. His social commi men also led him o be a membe o he F ench Resis ance du ing Wo ld Wa II. Mo e han a hund ed yea s ea lie , ano he ma hema ician, Nicolas de Condo ce (1743–1794), had been e y ac i e in de ending women’s igh s, being in a o o he emale o e, which was no achie ed in F ance un il 1945. In Bo el’s academic amily, we ind ano he ally, his hesis supe iso , he illus ious Jean Gas on Da boux (1842–1917), who was in ol ed in ounding he École no male supé ieu e de jeunes illes in 1880. Howe e , his academic g andson, Lau en Schwa z (1915–2002), winne o a Field Medal in 1950, al hough poli ically ac i e (he was a T o skyis and an i-colonialis , signing he Mani es o o he 121 on he Alge ian Wa , o which his igh o each was suspended om 1961 o 1963) [ 50 ], did no ac i ely suppo his wi e, ma hema ician Ma ie-Hélène Schwa z (1913–2013), daugh e o ma hema ician Paul Lé y (1886–1971), wi h no ma hema ical exchanges ound be ween he couple [51]. Lé y was supe ised by Jacques Salomon Hadama d (1865–1963) and Vi o Vol e a (1860–1940). Vol e a was ano he dis inguished ma hema ician, ac i ely engaged in an i- ascism. He was one o 12 p o esso s ou o 1250 who e used o ake he obliga o y oa h o loyal y o he ascis go e nmen o Beni o Mussolini in 1931. Consequen ly, he was expelled om his posi ion a he uni e si y and om his membe ship o I alian scien i ic academies, li ing ab oad o much o he nex ew yea s and only e u ning o Rome jus be o e his dea h in 1940. Vol e a was an ally. In 1906, he p oposed he ounding o he Socie à I aliana pe il P og esso delle Scienze (SIPS), a whose inaugu al cong ess he was elec ed p esiden and whose inno a i e s a u es made i possible o women scien is s o join he socie y. Vol e a suppo ed his emale disciples, helping hem o pu sue ca ee s, in con as o he hinking held by some men acco ding o which women could no each he high sphe es o ma hema ics [ 52 ]. Vol e a wo ked wi h he ollowing emale ma hema icians: Co nelia Fab i (1869–1915), Elena F eda (1890–1978) and he sis e Eleono a F eda, Giudi a G aziani (18??–?), Cesi a O landi (1881–?), Pie ina Quin ili (~1880–?), Emma Sciole e (1886–?), and Gina Zanoni (~1890–?). Con inuing wi h p obabili y, ano he ele an name is Pa nu y Chebyshe (1821–1894), who go he illus ious So ia Ko alé skaya (1850–1891) o be named an hono a y membe o he Sain Pe e sbu g Academy o Sciences [ 53 ]. Howe e , among Ko alé skaya’s allies, we also ind enowned physicis s and ma hema icians om o he a eas o ma hema ics apa om p obabili y, such as he amous physicis Gus a Ki chho (1824–1887), who allowed he o a end his classes. A special men ion should be made o he amous ma hema ician, Ka l Weie s aß (1815–1897), conside ed he a he o mode n analysis, who was he men o . Since she was no allowed o a end classes, Weie s aß u o ed he , gi ing he p i a e lessons o ee o ou yea s. Weie s aß made use o one o his o me s uden s, he ma hema ician Laza us Fuchs (1833–1902) a he Uni e si y o Gö ingen, and h ough him and wi h a g ea deal o e o , in 1874, he managed o ha e Ko alé skaya awa ded a doc o a e wi hou an o al exam, based only on he wo k she submi ed. Ano he o Ko alé skaya’s g ea allies was Gös a Mi ag-Le le (1846–1927), who ga e he a posi ion as a p o esso a S ockholm Uni e si y in 1883, al hough he i s yea was wi hou any sala y (he s uden s paid he ), and she was appoin ed p o esso o li e in 1889. Educ. Sci. 2024,14, 535 8 o 21 2.1.3. P obabili y Dis ibu ions In p obabili y dis ibu ions, many names o illus ious ma hema icians appea , some allies and o he s no , as will be explained, pi o ing a ound he eminen ma hema ician Sophie Ge main (1776–1831). Sophie Ge main was a sel - augh ma hema ician since she was no allowed o access o mal aining [ 54 ]. The École Poly echnique, ounded in 1794, did no admi women un il 1972, a he end o he 20 h cen u y. The e o e, Ge main ob ained he no es o he amous ma hema ician Joseph Louis Lag ange (1736–1813) h ough a amily iend, An oine-Augus e Le Blanc, and submi ed he wo k unde his name. When Lag ange, who admi ed he wo k, me he , he encou aged he o con inue, in i ing he o he ma hema ical ga he ings ha he o ganized [ 55 ]. Ano he no able ma hema ician and ally was Ad ien-Ma ie Legend e (1752–1833), wi h whom Ge main collabo a ed on an equal oo ing. Bap is e Joseph Fou ie (1768–1830) was also an ally. A e being elec ed Pe manen Sec e a y o he Academy o Sciences, Fou ie allowed he o a end sessions, being he i s woman who was no he wi e o an academic o do so. Among Ge main’s allies, Ka l F ied ich Gauss (1777–1855) s ands ou : he p o usely p aised Ge main’s alen , poin ing ou he p ejudices and obs acles she su e ed o being a woman, bu as Mackinnon (1990) highligh ed, i is no jus he ex bu also he ma hema ics included in he le e s ha indica e ha Gauss dedica ed ime o he . Gauss’s public commi men o Ge main is also shown in he pos humous g an ing o he i le o hono a y doc o by he Uni e si y o Gö ingen in 1831 due o he p essu e he had o exe , since Gauss’s eques had al eady been ejec ed in 1830. Among hose who should no be included as e e ence igu es a e Pie e Simon Laplace (1749–1827) and his p o égé Siméon Denis Poisson (1781–1840). Laplace o ganized a compe i ion on he ma hema ical heo y o elas ic su aces, hinking ha he p ize could go o Poisson, whom he also included on he ju y (in his case, he e we e no only no obs acles bu also “gi s”). A e h ee anonymous a emp s by Ge main and some une hical maneu e s by Poisson, he Ex ao dina y P ize o Ma hema ical Sciences o he Pa is Academy o Sciences wen o Ge main. Poisson, who we emembe was also on he ju y, was p esen ed wi h he p ize wi h he equa ion p e iously in oduced by Ge main bu using alse ma hema ical simpli ica ions. Poisson publicly igno ed Ge main and was also unwilling o discuss ma hema ics wi h he . Poisson’s esponse o a le e om Ge main, in which she asked o his opinion on a se ies o ma hema ical easonings, consis ed simply o sending he his epo , which symbolizes his con emp o Ge main. 2.1.4. Ma hema icians om he Uni e si y o Gö ingen The Uni e si y o Gö ingen has been men ioned p e iously. One o i s p o esso s, he dis inguished ma hema ician Felix Klein (1849–1925), could be conside ed he a che ype o an ally, as he was one o he main ad oca es o women being able o s udy ma hema ics. This ole as an ally was ans e ed o many o his s uden s, who became he i s male ma hema icians o supe ise doc o al heses by emale ma hema icians a hei espec i e uni e si ies [ 56 ]. A Gö ingen, women we e able o a end he classes o Klein and o he ecognized ma hema icians, such as Da id Hilbe (1862–1943), Ca l Runge (1856–1927), and He mann Minkowski (1864–1909) [ 57 ]. Klein changed his usual class g ee ing om “Gen lemen!” o “Lis ene s!” o be mo e inclusi e, and i he e e go con used, he would ec i y i wi h a smile [58] (p. 192). Le us e iew some o he ac ions ca ied ou by Klein in a o o women in ma h- ema ics. In 1891, he Ku a o o he Uni e si y o Gö ingen denied he eques o wo emale ma hema icians o a end Klein’s classes. To ge a ound his e usal, in 1893, a he eques o Ma y F ances Wins on (1869–1959) h ough he eache s Hein ich Maschke (1853–1908) and Oska Bolza (1857–1942), Klein a oided he Ku a o and communica ed on se e al occasions wi h he P ussian Minis e o Educa ion, who was mo e open o women s udying. The minis e app o ed he applica ions (in six days) o ma hema ician G ace Chisholm Wins on (1868–1944) and physicis Ma ga e Eliza Mal by (1860–1944). A e ha , he Ku a o esigned. In la e yea s, Klein again asked he minis e o pe mission Educ. Sci. 2024,14, 535 9 o 21 o o he emale ma hema icians, such as Annie Louise MacKinnon (1868–1940) and Isabel Maddison (1869–1950). In 1895, he e we e nine emale ma hema icians a Gö ingen, who o med wha could be conside ed he i s “associa ion” o emale ma hema icians. Da id Hilbe a i ed a Gö ingen in 1895 and was also a de ende o women’s igh s o s udy. He supe ised he doc o al heses o six emale ma hema icians, h ee o whom came om he Bes uzhe Cou ses in Sain Pe e sbu g, he main ins i u ion o highe educa ion o women in Russia and whose eache s included he amous chemis Dmi i Mendelee (1834–1907), who abandoned his posi ion a he uni e si y in de ense o he s uden s. One o hem was Ve a Lebede a (1880–1970), who was able o become a p o esso a he Uni e si y o Ia s , i in Romania, a he same ime as he husband, he ma hema ician Alexande Mylle (1879–1965), which would no ha e been possible elsewhe e a ha ime. Klein a gued in Pa liamen and o he ins i u ions ha women we e jus as capable as men and highligh ed he obs acles hey aced. In 1908, P ussia enac ed new laws allowing he o icial en ollmen o women in uni e si ies and he es ablishmen o new seconda y schools o gi ls. The educa ional e o m, known as he Klein Re o m, led o an inc ease in emale s uden s and he opening o p o essional oppo uni ies o women: hus, one o Klein’s daugh e s was p incipal o a seconda y school o gi ls eaching ma hema ics and physics, while ano he daugh e o Runge was an indus ial ma hema ician a OSRAM and Tele unke. Howe e , laws con inued o exclude women om uni e si y eaching posi ions in P ussia un il 1920. In 1915, he illus ious ma hema ician Emmy Noe he (1882–1935) was endo sed in he Habili a ion, a equi emen o eaching, by Hilbe , Klein, Runge, and Cons an in Ca a héodo y (1873–1950), among o he s [ 59 , 60 ]. Hilbe was especially in ol ed, a guing o hose who opposed ha “I do no see ha he sex o he candida e is an a gumen agains he admission. We a e a uni e si y, no a ba hhouse” [ 61 ] (p. 126). Howe e , i was no un il 1919 ha Noe he ob ained he Habili a ion, a e Klein con ac ed he Minis e o Cul u e again. Ne e heless, Noe he ’s posi ions a he uni e si y we e e y p eca ious, and she was ne e able o ob ain a p o esso ship in P ussia. In 1923, he amous ma hema ician Richa d Cou an (1888–1972) managed, h ough adminis a i e sub e uge, o pay Noe he , e en i modes ly. In 1930, he enowned ma hema ician He mann Weyl (1885–1955) ied o imp o e Noe he ’s employmen si ua ion h ough he Minis y, wi hou success. Many sexis commen s ha e been p ese ed in ela ion o Noe he , abou he physique o clo hing, which is no he case wi h male scien is s. Fo example, Edwa d James McShane (1904–1989) made he ollowing sexis ema k o Albe Tucke (1905–1995): “You know how you can ell a penguin om Emmy Noe he ? A penguin doesn’ ha e a b ie case” [ 62 ] (PMC6-8). Tucke ound such a “desc ip ion” o Noe he i ing [ 62 ]. Allies mus in e ene in hese kinds o si ua ions. 2.1.5. O he Ma hema icians as Allies Ano he amous ma hema ician who suppo ed emale ma hema icians wi h his co - dial ea men was He mann Schwa z (1843–1921). In 1872, a Eidgenössische Technis- che Hochschule Zü ich, Schwa z had he ma hema ician Eliza e a Fedo o na Li ino a (1845–1919) as a s uden (she was he only woman a he ins i u ion). Schwa z u o ed he in some cases a his house, and he also in i ed he o ha e ea o spend an e ening wi h his amily [63] . Li ino a’s doc o al hesis was supe ised in 1879 by ano he amous ma hema ician, Ludwig Schlä li (1814–1895). La e , Schwa z had he illus ious Hilda Hudson (1881–1965) as a s uden a he Uni e si y o Be lin. Hudson was he i s emale ma hema ician o pa icipa e (Lau a Pisa i had p e iously been in i ed, bu agically died in 1908, be o e he cong ess) in an In e na ional Cong ess o Ma hema icians (ICM) in 1912. She ea ned he O de o he B i ish Empi e [64]. Examples o an i-disc imina o y ac ions by a ious male ma hema icians o scien- is s/ echnologis s in de ense o women o some emale ma hema ician a e summa ized as ollows. (a) The eminen John S ua Mill (1806–1873) asked he memo able ma he- Educ. Sci. 2024,14, 535 16 o 21 addi ion, o al e na i ely, hey need eache s, iends, colleagues o pa ne s who suppo hem as equals. In o he wo ds, women need o be admi ed in o ha selec ci cle ha he ounde s o he Royal Socie y called he “in isible college”. ...I you a e no accep ed in o ha college o ne wo k—which is always pe sonal, ins i u ional, and poli ical a he same ime—i is impossible o make science and/o ha e a place in i s his o y. As Go oni sugges ed, o suppo equal oppo uni ies in science and ma hema ics, we ha e o begin by s eng hening he image o science as cul u e and, secondly, “ o wo k much mo e on boys and men han on gi ls and women” [ 115 ] (p. 311). And his is wha we in ended in his wo k, o e ie e posi i e e e ences ha we can show o ou s uden s, among which we could also include physicis s Tomas B age [ 116 ], p o esso o physics and expe in gende equi y and equal oppo uni ies, and Paolo Gio dano, he au ho o Tasmania [117], a no el whe e sexism in physics is also discussed. 3. Conclusions Th oughou his pape , he impo ance o suppo and denuncia ion om he g oup wi h powe , he p i ileged g oup, in his case, whi e he e osexual men [ 118 ], in elimina ing obs acles o emale physicis s and ma hema icians was demons a ed. Likewise, he signi icance o co- esponsibili y was e ealed, om which we a e s ill a away oday wi hin he academic wo ld [ 10 ]. Examples o male allies we e also shown, including no able physicis s and ma hema icians who can be used in classes as coun e -s e eo ypical gende ole models, ha is, wi h gende -incong uen oles, in o de o b eak down s e eo ypes and p omo e non- adi ional beha io s [ 119 ], especially in men in STEM subjec s. Howe e , i is ad isable o ha e models o close allies, especially among eaching s a . Un o una ely, gende s e eo ypes a e s ill in o ce in science and a e ansmi ed e en in p ima y ma hema ics ex books [ 120 ]. To change his si ua ion, he in ol emen o he scien i ic communi y is necessa y, especially hose who hold powe and he e o e ha e a mo e in luen ial oice and g ea e s eng h o oppose disc imina ion [ 26 ]. Fu he mo e, he messenge is key, as he e a e men who a e no willing o lis en o he message o gende equali y i i comes om women bu who a e willing o lis en o i i ano he man is he messenge [ 121 ]. The e o e, i is impo an o p omo e spaces and mee ings whe e con e sa ions can be held abou he inequali y p esen in he scien i ic communi y, bo h o gene a e empa hy and inc ease awa eness and o lea n abou he successes o o he de ende s o equali y [ 122 ]. These mee ings would also se e o keep allies engaged, since hey mus belie e ha hei e o s a e impo an [ 123 ], which is why in some uni e si ies, he e a e p og ams such as Ad oca es and Allies a No h Dako a S a e Uni e si y [ 124 ]. No e ha becoming an ally is a li elong p ocess, wi h i e a i e cycles o unde s andings and ac ion [ 125 ]. We also wan o highligh ha he pe cep ions be ween men and women on he suppo needed o achie e equali y a e di e en ; men belie e ha hey a e g ea allies in he wo kplace, while women disag ee [ 126 ]. Consequen ly, as indica ed by he Associa ion o Women in Science, i is ad isable o a good ally o lis en o women [ 127 ]. Mo e ecommenda ions o men a e a ailable in [ 128 , 129 ], which highligh he impo ance o he ac i e pa icipa ion o (cis-whi e) men as allies in changing he cu en cul u e, in bo h day- o-day se ings and he big pic u e. Some ac s o allyship commen ed in his pape we e suppo i e o many women, bu o he s we e suppo i e o jus one woman, who pe haps was seen as an “excep ion” o gene alized s e eo ypes. The e o e, we mus be cau ious so ha male s uden s do no hink ha indi idualized ac ions a e enough, o ha hey a e doing enough by helping he women in hei immedia e o bi , a he han ocusing on ins i u ional change. Al hough we ocused on uni e si ies, ou con ibu ion can also be implemen ed in high schools. No e ha using he his o y o science p o ides a iche con ex o lea n no only science bu also he in e ac ions be ween socie y and science and scien is s [130]. Rega ding how o inco po a e his o ical igu es oge he wi h ac ual and close ole models in ma hema ics and physics, di e en ways can be conside ed. Fo example, we Educ. Sci. 2024,14, 535 17 o 21 can in oduce he biog aphy o he igu e who is an expe in each ield be o e wo king in ha ield, as p oposed by Figuei as e al. [58] , o use Wikipedia asks [ 131 ]. Mo e p oposals a e explained by Epi anio e al. [132] , such as using quo es o he igu es a he beginning o a uni o ini ia e a sho discussion, o include hem in p oblems, o in es iga e di e en igu es as asks o o use gami ica ion, such as h ough digi al escape ooms [ 133 ]. Fo esou ces abou emale ma hema icians and physicis s, you can see [ 134 , 135 ], espec i ely. As many male igu es appea in hese disciplines h ough laws, ules, heo ems, esul s, e c., we hink i is ecommendable o include mo e women and o he mino ized g oups han male allies o balancing. Ne e heless, including he con ibu ions o women and o he mino ized g oups oge he wi h male allies should no be an isola ed ac nei he in e ms o ime (i should no cons i u e he ac ion o a single isola ed day) no as a unique ac ion, i.e., ou eaching should ake in o accoun di e si y in all ace s, such as class oom managemen , con en s, e alua ion, e c. The guides o mains eaming gende in uni e si y eaching in physics [ 135 ] and ma hema ics [ 134 ] con ain ecommenda ions on hose aspec s. As u u e wo k, he impac o p esen ing hese male allies as e e ences in uni e si y class ooms could be analyzed. This wo k cons i u ed he i s bu essen ial s ep, which is he compila ion o allies in physics and ma hema ics since hey a e unknown o he as majo i y o eache s in hese ields. This was demons a ed by he esul o a su ey ca ied ou among uni e si y p o esso s in hese ields du ing a aining cou se on eaching wi h a gende pe spec i e in ma hema ics a Jaume I Uni e si y in Janua y 2024, in which he pa icipan s we e unable o p o ide any names. I should be no ed ha he compila ion ca ied ou he e is no exhaus i e, bu i was in ended as a s a ing poin o eco e ing hidden male allies in hese and o he scien i ic ields. Au ho Con ibu ions: All au ho s con ibu ed equally o his wo k. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Funding: This esea ch was unded by Uni e si a Jaume I g an numbe TRANSUJI/2023/6. Ins i u ional Re iew Boa d S a emen : No applicable. In o med Consen S a emen : No applicable. Da a A ailabili y S a emen : No new da a we e c ea ed o analyzed in his s udy. Da a sha ing is no applicable o his a icle. Con lic s o In e es : The au ho s decla e no con lic s o in e es . 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