The Math of Matilda

Gabrielle Birchak/ March 24, 2026/ Contemporary History, Modern History

In 1993, sci­ence his­to­ri­an Mar­garet Rossiter intro­duced the term the Matil­da Effect. Writ­ing in the jour­nal Social Stud­ies of Sci­ence, Rossiter described a recur­ring pat­tern in sci­en­tif­ic his­to­ry where women’s intel­lec­tu­al con­tri­bu­tions were sys­tem­at­i­cal­ly under-rec­og­nized or cred­it­ed to men. She named the effect after nine­teenth-cen­tu­ry suf­frag­ist Matil­da Joslyn Gage, who had already observed that women’s achieve­ments were rou­tine­ly min­i­mized or erased.

Over the years, the Matil­da Effect has often been told as a sto­ry of theft. A woman makes a dis­cov­ery, then a man takes the cred­it, and his­to­ry remem­bers the wrong name.

That sto­ry is not false, but it is incomplete.

Because when we look care­ful­ly at how recog­ni­tion actu­al­ly moves through sci­ence, math­e­mat­ics, and his­tor­i­cal mem­o­ry, some­thing more unset­tling emerges. Most of the time, no one needs to steal any­thing at all.

Instead, small bias­es accu­mu­late, tiny advan­tages com­pound, and insti­tu­tion­al rules qui­et­ly ampli­fy ear­ly recog­ni­tion until his­to­ry itself hard­ens around those outcomes.

The Matil­da Effect is not pri­mar­i­ly about bad actors, it is about sys­tems that behave mathematically.

And once those sys­tems start com­pound­ing, the past becomes very dif­fi­cult to correct.

Why the Theft Nar­ra­tive Falls Short

The theft nar­ra­tive is emo­tion­al­ly sat­is­fy­ing because it offers clar­i­ty. There is a vil­lain, a vic­tim, and a moral res­o­lu­tion. But his­to­ri­ans and soci­ol­o­gists of sci­ence have long warned that this fram­ing obscures how sci­en­tif­ic cred­it actu­al­ly works.

Sci­en­tif­ic recog­ni­tion is not a sin­gle event. It is not grant­ed once, at the moment of dis­cov­ery. It unfolds over time through cita­tions, author­ship order, invi­ta­tions, awards, text­books, and archives.

Mar­garet Rossiter empha­sized that the Matil­da Effect oper­at­ed through sys­tem­at­ic under-recog­ni­tion, not just overt appro­pri­a­tion. In oth­er words, even when no one con­scious­ly took cred­it away from women, the struc­ture of sci­ence still deliv­ered recog­ni­tion unevenly.

This mat­ters because it changes the question.

Instead of ask­ing, “Who stole this idea?” we need to ask, “How did soci­ety enable the move­ment of recognition?”

And that ques­tion leads us direct­ly into mathematics.

Recog­ni­tion as a Cumu­la­tive Advan­tage System

In Soci­ol­o­gy of Sci­ence, the con­cept of cumu­la­tive advan­tage pre­dates the Matil­da Effect. In 1968, soci­ol­o­gist Robert K. Mer­ton described what he called the Matthew Effect, named after a verse in the Gospel of Matthew: “For to every­one who has, more will be given.”

Mer­ton observed that well-known sci­en­tists tend­ed to receive dis­pro­por­tion­ate cred­it, even when their con­tri­bu­tions were sim­i­lar to those of less­er-known col­leagues. As a result, ear­ly recog­ni­tion cre­at­ed future recognition.

This insight has since been for­mal­ized math­e­mat­i­cal­ly through pref­er­en­tial attach­ment mod­els, which describe how net­works grow. These mod­els are used to explain phe­nom­e­na rang­ing from the struc­ture of the inter­net to cita­tion net­works in aca­d­e­m­ic publishing.

Let’s use the con­cept of nodes in this exam­ple. Nodes are con­nec­tion points in a net­work or sys­tem. A node could rep­re­sent a con­nec­tion to a com­put­er, a print­er, a grand­par­ent in a fam­i­ly tree, or that one per­son who knows every­body. And that’s exact­ly where this fits in with the Matthew effect as well as the Matil­da effect. Pref­er­en­tial attach­ment mod­els mean that the nodes with­in that sys­tem already have many oth­er con­nec­tions and are like­ly to receive new ones.

Trans­lat­ed into sci­en­tif­ic cir­cles, papers that are already cit­ed are more like­ly to be cit­ed again. Addi­tion­al­ly, researchers who are already known are more like­ly to be invit­ed, fund­ed, and ref­er­enced. It’s a lot like the social media algo­rithms for social influ­encers where­in ear­ly vis­i­bil­i­ty cre­ates future visibility.

Physi­cist Albert-Lás­zló Barabási, whose work on net­work the­o­ry is foun­da­tion­al, showed that such sys­tems nat­u­ral­ly pro­duce pow­er-law dis­tri­b­u­tions, where a small num­ber of nodes accu­mu­late most of the atten­tion. These out­comes do not require bias to begin. They emerge from the rules of the sys­tem itself.

Now let’s add bias.

If women start with even a slight dis­ad­van­tage in vis­i­bil­i­ty or cred­i­bil­i­ty, pref­er­en­tial attach­ment guar­an­tees that the gap will widen over time.

This is the Matil­da Effect as a math­e­mat­i­cal process. Math­e­mat­i­cal­ly, cumu­la­tive advan­tage is not abstract or metaphor­i­cal. It begins with a sim­ple assump­tion that appears through­out the his­to­ry of math­e­mat­ics: growth depends on what already exists. In pro­por­tion­al growth mod­els, the rate at which some­thing increas­es is tied direct­ly to its cur­rent size, the same log­ic that gov­erns com­pound inter­est and ear­ly pop­u­la­tion equa­tions. When recog­ni­tion fol­lows this rule, even a slight ear­ly dif­fer­ence mat­ters, because the sys­tem ampli­fies what is already present.

Net­work sci­en­tists lat­er for­mal­ized this behav­ior through pref­er­en­tial attach­ment, show­ing that new atten­tion flows toward nodes that already have atten­tion. In cita­tion net­works, this pro­duces pow­er-law dis­tri­b­u­tions, where a small num­ber of names accu­mu­late a dis­pro­por­tion­ate share of recog­ni­tion while most con­tri­bu­tions remain at the mar­gins. Mer­ton described this empir­i­cal­ly as the Matthew Effect, and lat­er sta­tis­ti­cal mod­els made the mech­a­nism explic­it by express­ing recog­ni­tion at each step as a func­tion of pri­or recog­ni­tion plus ran­dom­ness. Even when chance is includ­ed, ear­ly advan­tage dom­i­nates. Once these dynam­ics are in motion, his­to­ry itself becomes sub­ject to sur­vivor­ship bias, because only the work that accu­mu­lat­ed enough recog­ni­tion ear­ly on remains vis­i­ble to be cit­ed, archived, and taught.

The sys­tem is also path depen­dent. Ear­ly recog­ni­tion deci­sions, even if par­tial­ly acci­den­tal, lock in tra­jec­to­ries that are dif­fi­cult to reverse. Fair­ness applied lat­er does not reset the process. In cumu­la­tive sys­tems, ini­tial con­di­tions shape out­comes so strong­ly that inequal­i­ty becomes struc­tur­al, not because any­one intend­ed it, but because the math guar­an­tees it.

And speak­ing of math, I’m going to post the math­e­mat­ics at my web­site at Mathsciencehistory.com for my math nerds. And, while you are there, con­sid­er click­ing on that cof­fee cup and mak­ing a dona­tion through Pay­Pal to Math! Sci­ence! His­to­ry! Because every dona­tion you make keeps us going. It tru­ly does make a dif­fer­ence. Every pen­ny helps pay for addi­tion­al ser­vices such as edit­ing, social media ser­vices, you name it. So that being said, I gen­uine­ly appre­ci­ate every dona­tion that has already come our way. Thank you so much for your support.

Small Bias­es, Large His­tor­i­cal Consequences

One of the most impor­tant fea­tures of cumu­la­tive sys­tems is that small ini­tial dif­fer­ences mat­ter enor­mous­ly.

A five per­cent reduc­tion in cita­tions at the start of a career does not remain five per­cent, it cascades.

A paper that is cit­ed less fre­quent­ly is less like­ly to be read, and a researcher who is read less is invit­ed less often to speak. Few­er talks lead to few­er col­lab­o­ra­tions and few­er col­lab­o­ra­tions lead to few­er high-pro­file publications.

By the time prizes or text­books enter the pic­ture, the diver­gence appears dra­mat­ic. How­ev­er, the cause was incremental.

This is why the Matil­da Effect can­not be fixed sim­ply by “adding women back” lat­er. Once cumu­la­tive advan­tage has reshaped the land­scape, recog­ni­tion is already locked in.

This phe­nom­e­non is vis­i­ble in cita­tion data. Large-scale analy­ses sum­ma­rized by Sci­ence, pub­lished by the Amer­i­can Asso­ci­a­tion for the Advance­ment of Sci­ence, have shown per­sis­tent gen­der cita­tion gaps across mul­ti­ple fields. Women’s papers are cit­ed less often than men’s, even when con­trol­ling for jour­nal pres­tige, sub­field, and pub­li­ca­tion year.

The key point is that cita­tions are not just mark­ers of impact, they are inputs into future recognition.

Bias at the cita­tion lev­el becomes bias every­where else.

Why Peer Review Does Not Neu­tral­ize the System

It is often assumed that peer review acts as a cor­rec­tive mech­a­nism. If papers are eval­u­at­ed anony­mous­ly, the argu­ment goes, then mer­it should prevail.

But peer review does not oper­ate in a vacuum.

A land­mark study pub­lished in Nature in 1997, titled “Sex­ism and Nepo­tism in Peer Review,” exam­ined fel­low­ship eval­u­a­tions and found that women had to be sig­nif­i­cant­ly more pro­duc­tive to receive the same com­pe­tence scores as men. The review­ers were not con­scious­ly dis­crim­i­nat­ing; they were respond­ing to rep­u­ta­tion­al cues.

Lat­er stud­ies repli­cat­ed this effect in hir­ing, grant fund­ing, and rec­om­men­da­tion let­ters. As sum­ma­rized by research reviewed by the Nation­al Acad­e­mies and oth­ers, women were more often described as dili­gent or coop­er­a­tive, while men were described as bril­liant or visionary.

Peer review fil­ters work, but it does not reset rep­u­ta­tion, rather it inher­its the system’s pri­or conditions.

And this mat­ters because cumu­la­tive advan­tage does not only oper­ate down­stream, it shapes who gets eval­u­at­ed favor­ably in the first place.

Invis­i­ble Math­e­mat­i­cal Labor and Non-Cred­itable Work

The Matil­da Effect becomes even more pro­nounced when we look at what kinds of labor gen­er­ate recog­ni­tion.

In math­e­mat­ics and sci­ence, cer­tain activ­i­ties reli­ably pro­duce author­ship and pres­tige such as propos­ing a new the­o­ry, lead­ing a lab, writ­ing the final paper, error check­ing, cal­cu­la­tion, data clean­ing, proof ver­i­fi­ca­tion, repli­ca­tion, and code maintenance.

As his­to­ri­ans of com­put­ing and math­e­mat­ics have shown, women were dis­pro­por­tion­ate­ly con­cen­trat­ed in these roles through­out the twen­ti­eth cen­tu­ry. Human com­put­ers, for exam­ple, per­formed the cal­cu­la­tions that made astro­nom­i­cal and phys­i­cal dis­cov­er­ies pos­si­ble, yet their names rarely appeared on publications.

The his­to­ri­an Marie Hicks, writ­ing about com­put­ing labor, has shown how tech­ni­cal work done by women was often reclas­si­fied as cler­i­cal once it became fem­i­nized, strip­ping it of pres­tige with­out chang­ing its substance.

If you think about this as a sys­tems per­spec­tive, it becomes cru­cial. If a con­tri­bu­tion does not gen­er­ate a node in the recog­ni­tion net­work, it can­not accu­mu­late advan­tage. As a result, it dis­ap­pears mathematically.

Thus, the Matil­da Effect is not only about women being denied cred­it, the Matil­da Effect is about entire cat­e­gories of work being struc­tural­ly unable to receive it.

Archives as Ampli­fiers of Ear­ly Advantage

His­to­ry does not remem­ber every­thing equal­ly, but instead it remem­bers what survives.

Archivists and his­to­ri­ans rely on pub­lished papers, insti­tu­tion­al records, cor­re­spon­dence deemed sig­nif­i­cant, and mate­ri­als that were pre­served, cat­a­logued, and digitized.

Women’s sci­en­tif­ic work was less like­ly to enter these chan­nels. It was more like­ly to appear in let­ters, inter­nal reports, or col­lab­o­ra­tive con­texts that were not pre­served with the same care.

And this cre­ates what his­to­ri­ans call archival bias: what we know about the past is shaped by what was saved.

As schol­ars of archival sci­ence have empha­sized, includ­ing those writ­ing in The Amer­i­can Archivist, archives are not neu­tral con­tain­ers. Archives are prod­ucts of insti­tu­tion­al priorities.

Once again, small bias­es com­pound. What is pre­served is cit­ed, what is cit­ed is taught, what is taught becomes canonical.

The Matil­da Effect per­sists because mem­o­ry itself is cumulative.

Why Recog­ni­tion Arrives Too Late

Anoth­er mod­ern refram­ing of the Matil­da Effect treats it as a lag prob­lem.

In many cas­es, women’s work was even­tu­al­ly val­i­dat­ed, but only after a male author­i­ty endorsed it, or the field shift­ed sys­tem­at­i­cal­ly, or new tools made the con­tri­bu­tion legible.

By the time recog­ni­tion arrived, the oppor­tu­ni­ty for cumu­la­tive advan­tage had passed.

This pat­tern has been dis­cussed by philoso­phers of sci­ence exam­in­ing how legit­i­ma­cy oper­ates. Legit­i­ma­cy often pre­cedes recog­ni­tion, but legit­i­ma­cy itself is social­ly mediated.

The his­to­ri­an Lon­da Schiebinger has argued that women’s ideas were fre­quent­ly dis­missed not because they were wrong, but because they did not fit pre­vail­ing frame­works. When those frame­works changed, the ideas appeared pre­scient. How­ev­er, his­to­ry had already moved on.

Delayed recog­ni­tion is not neu­tral, and in cumu­la­tive sys­tems, tim­ing is everything.

Why Insti­tu­tions Pro­duce These Out­comes Predictably

It is tempt­ing to treat the Matil­da Effect as a cul­tur­al fail­ure. But the deep­er issue is insti­tu­tion­al design. Sci­en­tif­ic insti­tu­tions reward sin­gle author­ship, senior­i­ty, net­work cen­tral­i­ty, and pres­tige mark­ers. How­ev­er, many sci­en­tif­ic insti­tu­tions do not reward main­te­nance, repli­ca­tion, teach­ing, or even col­lab­o­ra­tive depth.

Because women were, and are, his­tor­i­cal­ly steered into the lat­ter cat­e­gories, the sys­tem reli­ably under-cred­it­ed them.

This out­come does not require mali­cious intent. It requires only that insti­tu­tions opti­mize for nar­row sig­nals of success.

Econ­o­mists and soci­ol­o­gists study­ing orga­ni­za­tion­al behav­ior have shown that insti­tu­tions tend to repro­duce their own met­rics, and what they mea­sure becomes what matters.

If recog­ni­tion met­rics are biased, out­comes will be biased, even under con­di­tions of for­mal equality.

What Does This Mean for His­to­ry Right Now?

The most uncom­fort­able impli­ca­tion of this analy­sis is that the Matil­da Effect is not finished.

If recog­ni­tion behaves math­e­mat­i­cal­ly, then future his­to­ri­ans will inher­it the dis­tor­tions we are cre­at­ing today.

Cita­tion gaps doc­u­ment­ed in recent stud­ies pub­lished in Pro­ceed­ings of the Nation­al Acad­e­my of Sci­ences and sum­ma­rized in Sci­ence sug­gest that women’s work con­tin­ues to be under-ref­er­enced. Patent data ana­lyzed by researchers and report­ed in out­lets like STAT show that women are less like­ly to be list­ed as inven­tors, even when they con­tribute to patentable work.

These are not moral fail­ures wait­ing to be cor­rect­ed. Instead, they are tra­jec­to­ries already in motion.

His­to­ry will remem­ber what we amplify.

The Matil­da Effect is often described as a fail­ure of fair­ness. But it is more accu­rate­ly a fail­ure of sys­tems under­scored by lack of fair­ness. There are still sys­tems in place that favor sci­en­tists with the most pop­u­lar name, there are still sys­tems in place that grav­i­tate towards the male sci­en­tist even though he is great­ly unqual­i­fied com­pared to his female coun­ter­part. And, when recog­ni­tion com­pounds, small bias­es do not stay small. Instead, small bias­es become struc­ture, mem­o­ry and history.

Mar­garet Rossiter gave us a name for this pat­tern and math­e­mat­ics explains why it persists.

If we want a dif­fer­ent his­to­ry, we can­not rely on cor­rec­tion alone. Instead, we must pay atten­tion to how cred­it moves, accu­mu­lates, and hard­ens in real time, because the most dan­ger­ous bias­es are not the loud ones. The most treach­er­ous prej­u­dices are the qui­et ones that let math do what math always does.

If the Matil­da Effect were sim­ply a mat­ter of indi­vid­ual wrong­do­ing, it could be solved by bet­ter inten­tions. But because it emerges from cumu­la­tive sys­tems, it requires some­thing more dif­fi­cult: delib­er­ate inter­rup­tion. What do these delib­er­ate inter­rup­tions look like? They can look like sys­tems that ampli­fy gain, which in turn can be redesigned to dis­trib­ute advan­tage. Cita­tion prac­tices can be audit­ed rather than inher­it­ed. Author­ship can be tied to doc­u­ment­ed con­tri­bu­tion rather than posi­tion alone. Addi­tion­al­ly, eval­u­a­tion can rely on struc­tured cri­te­ria instead of rep­u­ta­tion short­cuts. Invi­ta­tions and nom­i­na­tions can be treat­ed as inputs that shape his­to­ry, not neu­tral hon­ors that mere­ly reflect it. Fur­ther­more, archives can pre­serve the labor that sus­tains dis­cov­ery, not only the moments of appar­ent brilliance.

None of these changes require per­fect fair­ness or moral puri­ty. Instead, they require atten­tion at the points where recog­ni­tion enters the sys­tem. The Matil­da Effect per­sists because small dis­tor­tions are allowed to com­pound unchecked. How­ev­er, it dimin­ish­es when those dis­tor­tions are noticed ear­ly, named clear­ly, and cor­rect­ed repeat­ed­ly. His­to­ry does not change all at once. It changes when we stop let­ting math­e­mat­ics run on autopi­lot. It changes when we begin choos­ing, con­scious­ly and col­lec­tive­ly, how cred­it moves through time.

Every lis­ten­er who reads more care­ful­ly, cites more delib­er­ate­ly, and cred­its more pre­cise­ly alters the tra­jec­to­ry of what sur­vives. The future his­to­ry of sci­ence is not writ­ten only by dis­cov­er­ies, but by the choic­es we make about whose work we ampli­fy, remem­ber, and teach. In cumu­la­tive sys­tems, even small acts of recog­ni­tion mat­ter, because they are the ones that compound.

And that is where each of us still has agency, even inside sys­tems that com­pound.
Until next time, carpe diem.

SOURCES:

1. Margaret Rossiter & the Matilda Effect (1993)

Rossiter, M.W. (1993). “The Matthew Matil­da Effect in Sci­ence.” Social Stud­ies of Sci­ence, 23(2), 325–341.

• DOI: https://doi.org/10.1177/030631293023002004
• Free PDF sum­ma­ry via AWIS: https://awis.org/wp-content/uploads/SSS-matilda-effect.pdf

2. Robert K. Merton & the Matthew Effect (1968)

Mer­ton, R.K. (1968). “The Matthew Effect in Sci­ence.” Sci­ence, 159(3810), 56–63.

• DOI: https://doi.org/10.1126/science.159.3810.56
• Link: https://www.science.org/doi/10.1126/science.159.3810.56
• Free PDF: https://garfield.library.upenn.edu/merton/matthew1.pdf

3. Barabási & Preferential Attachment / Power-Law Networks

Barabási, A‑L. & Albert, R. (1999). Scale-free net­works and pref­er­en­tial attachment.

• Overview via Schol­ar­pe­dia (by Barabási): http://www.scholarpedia.org/article/Scale-free_networks
• Wikipedia sum­ma­ry of the Barabási–Albert mod­el: https://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model

4. Wennerås & Wold — Peer Review Sexism Study (1997)

Wen­nerås, C. & Wold, A. (1997). “Nepo­tism and sex­ism in peer-review.” Nature, 387(6631), 341–343.

• DOI: https://doi.org/10.1038/387341a0
• Nature link: https://www.nature.com/articles/387341a0
• PubMed: https://pubmed.ncbi.nlm.nih.gov/9163412/
• Free PDF: https://www.cs.utexas.edu/~mckinley/notes/ww-nature-1997.pdf

5. Marie Hicks — Computing Labor & Reclassification as Clerical

Hicks, M. (2017). Pro­grammed Inequal­i­ty: How Britain Dis­card­ed Women Tech­nol­o­gists and Lost Its Edge in Com­put­ing. MIT Press.

• MIT Press page: https://mitpress.mit.edu/9780262535182/programmed-inequality/
• H‑Net review: https://networks.h‑net.org/node/9782/reviews/3682972/penn-hicks-programmed-inequality-how-britain-discarded-women

6. Londa Schiebinger — Women’s Ideas Dismissed Due to Frameworks

Schiebinger, L. (1989). The Mind Has No Sex? Women in the Ori­gins of Mod­ern Sci­ence. Har­vard Uni­ver­si­ty Press.

• Har­vard Uni­ver­si­ty Press: https://www.hup.harvard.edu/books/9780674576254

Schiebinger, L. (1999). Has Fem­i­nism Changed Sci­ence? Har­vard Uni­ver­si­ty Press.

• Har­vard Uni­ver­si­ty Press: https://www.hup.harvard.edu/books/9780674005440

7. Gender Citation Gap (PNAS & Science)

Huang, J. et al. (2020). “His­tor­i­cal com­par­i­son of gen­der inequal­i­ty in sci­en­tif­ic careers across coun­tries and dis­ci­plines.” PNAS, 117(9).

• Link: https://www.pnas.org/doi/10.1073/pnas.1914221117

Ler­man, K. et al. (2022). “Gen­dered cita­tion pat­terns among the sci­en­tif­ic elite.” PNAS, 119(40).

• Link: https://www.pnas.org/doi/10.1073/pnas.2206070119

Sci­ence/AAAS arti­cle sum­ma­riz­ing the research:

• “Women researchers are cit­ed less than men. Here’s why—and what can be done about it.” Sci­ence, AAAS: https://www.science.org/content/article/women-researchers-cited-less-men-heres-why-what-can-done

8. Women & Patents (STAT News reference)

Kon­ing, R. et al. (2021). Gen­der bias toward men in bio­med­ical patent awards.

• STAT News cov­er­age: https://www.statnews.com/2021/06/17/gender-bias-toward-men-patents-less-biomedical-innovation-women-study/

USPTO “Progress and Poten­tial” reports:

• https://www.uspto.gov/ip-policy/economic-research/publications/reports/progress-potential

9. Archival Bias

The script ref­er­ences gen­er­al schol­ar­ship on archival the­o­ry. The most rel­e­vant jour­nal is The Amer­i­can Archivist, pub­lished by the Soci­ety of Amer­i­can Archivists:

• https://americanarchivist.org/

10. National Academies — Recommendation Letter Language Study

Nation­al Acad­e­mies of Sci­ences, Engi­neer­ing, and Med­i­cine. (2020). Promis­ing Prac­tices for Address­ing the Under­rep­re­sen­ta­tion of Women in Sci­ence, Engi­neer­ing, and Medicine.

• Free PDF: https://nap.nationalacademies.org/catalog/25585