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MATHEMATICS IN THE FOURTH GEN AI ERA: A GLOBAL MODEL OF
DIGITAL TRANSFORMATION
M. Vasuki*, A. Dinesh Kuma **, Mbonigaba Celes in*** &
Taw eeq Abdulamee Hashim Alghazali****
* S ini asan College o A s and Science (A ilia ed o Bha a hidasan Uni e si y), Pe ambalu ,
Tamil Nadu, India
** Khadi Mohideen College (A ilia ed o Bha a hidasan Uni e si y), Adi ampa inam, Tamil Nadu, India
*** B ainae Ins i u e o P o essional S udies, B ainae Uni e si y, Delawa e, Uni ed S a es o Ame ica
**** The Islamic Uni e si y in Naja , Naja , I aq
Ci e This A icle: M. Vasuki, A. Dinesh Kuma , Mbonigaba Celes in & Taw eeq Abdulamee Hashim Alghazali, “Ma hema ics
in he Fou h Gen AI E a: A Global Model o Digi al T ans o ma ion”, In e na ional Jou nal o Scien i ic Resea ch and Mode n
Educa ion, Volume 10, Issue 2, July - Decembe , Page Numbe 102-115, 2025.
Copy Righ : © C ys al Pen Publica ion, 2025 (All Righ s Rese ed). This is an Open Access A icle dis ibu ed unde he
C ea i e Commons A ibu ion License, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided
he o iginal wo k is p ope ly ci ed.
DOI:
Abs ac :
Digi al ans o ma ion powe ed by a i icial in elligence and ma hema ics has become he de ining o ce o global
compe i i eness. This s udy examined how ma hema ical inno a ion shapes digi al ans o ma ion pe o mance ac oss na ions and
indus ies. I adop ed a quan i a i e design using S uc u al Equa ion Modeling on seconda y da ase s om he S&P Global 1200,
OECD, UNESCO, and Wo ld Bank co e ing 2020 o 2024. The indings showed ha algo i hmic op imiza ion, p edic i e
compu a ion, and ma hema ical modeling e iciency signi ican ly in luence au oma ion, decision accu acy, and inno a ion
p oduc i i y. The es ima ed s uc u al model yielded s ong s a is ical suppo wi h coe icien s β1 = 0.41, β2 = 0.36, and β3 =
0.33 (p < 0.01), con i ming ha ma hema ical de e minan s d i e measu able ans o ma ion ou comes. The esul s also e ealed
ha AI in eg a ion in ensi y posi i ely mode a es hese ela ionships, magni ying he global e ec o ma hema ical capabili y.
This esea ch con ibu es o heo y by ex ending he Uni ied Theo y o Accep ance and Use o Technology h ough he addi ion o
ma hema ical inno a ion and AI in eg a ion in ensi y, he eby b oadening i s explana o y scope and o e ing a e ined amewo k
o unde s anding digi al ans o ma ion in global se ings. The s udy connec s o global deba es on how da a science,
compu a ional li e acy, and ins i u ional AI eadiness shape digi al economies. I ecommends ha policymake s ea
ma hema ical capabili y as a s a egic digi al asse , i ms embed algo i hmic design in o ope a ions, and educa o s align cu icula
wi h compu a ional ans o ma ion demands. The indings p o ide heo e ical, manage ial, and policy pa hways o ad ancing
da a-d i en ans o ma ion ac oss egions.
Key Wo ds: A i icial In elligence, Digi al T ans o ma ion, Ma hema ical Inno a ion, S uc u al Equa ion Modeling, Uni ied
Theo y o Accep ance and Use o Technology
1. In oduc ion:
Digi al ans o ma ion is no longe a u u e goal; i de ines he p esen di ec ion o global economies. The usion o
a i icial in elligence wi h ad anced ma hema ical modeling has u ned in o he engine o co po a e compe i i eness, public sec o
e iciency, and social p og ess. As na ions accele a e echnology adop ion, he abili y o ans o m ma hema ical insigh in o
digi al alue becomes a decisi e o ce shaping he wo ld economy.
1.1 Gene al Con ex o he S udy:
Global digi al ans o ma ion has shi ed om au oma ion o in elligence. In ecen yea s, AI-d i en analy ics, p edic i e
modeling, and algo i hmic decision sys ems ha e ede ined how ins i u ions ope a e, op imize, and expand hei each. Acco ding
o he OECD (2024), AI applica ions now unde pin o e 60 pe cen o inno a ion ac i i ies ac oss majo economies, highligh ing
a shi om in ui ion-based o compu a ion-d i en managemen . The Wo ld Bank (2023) epo s ha digi al eadiness con ibu es
o e 25 pe cen o GDP g ow h in high- ech egions, p o ing ha echnology embedded wi h ma hema ics ans o ms p oduc i i y
as e han adi ional e o ms. The no el y o his s udy lies in linking ma hema ics and digi al adop ion wi hin he UTAUT
amewo k, es ablishing a measu able b idge be ween compu a ional easoning and o ganiza ional ans o ma ion.
1.2 Global, Regional, and Local Rele ance o he S udy:
A he global le el, he in eg a ion o ma hema ics and AI de ines he eme ging digi al o de . The S&P Global 1200
Index (2024) e eals ha companies wi h high algo i hmic ma u i y ou pe o m o he s by 35 pe cen in ma ke alue g ow h. The
OECD AI Policy Obse a o y (2024) highligh s ha AI and ma hema ical compu ing con ibu e o ene gy e iciency, aud
de ec ion, and p edic i e logis ics, imp o ing ope a ional agili y wo ldwide. The In e na ional Telecommunica ion Union (2023)
no es ha 93 pe cen o Fo une 500 companies ha e adop ed algo i hm-based managemen sys ems, showing he uni e sal
eliance on ma hema ical modeling. The global ace o AI sup emacy is no abou access o da a bu mas e y o ma hema ical
algo i hms. This dynamic p o es ha inno a ion capaci y now es s on he s eng h o compu a ional hinking, ma king a
undamen al shi in he s uc u e o global compe i i eness.
Regionally, he A ican con inen is wi nessing a su ge in AI esea ch and digi al in es men . The A ican De elopmen
Bank (2023) p ojec s ha da a-d i en inno a ion could con ibu e up o USD 180 billion o A ica’s GDP by 2025, wi h Eas
A ica leading h ough in ech and sma ag icul u e solu ions. Compa a i e s udies by UNESCO (2023) show ha coun ies
in eg a ing ma hema ics educa ion in o AI inno a ion policies eco d as e a es o echnology di usion. In Asia-Paci ic, na ions
like Singapo e, Sou h Ko ea, and Japan ha e posi ioned algo i hmic go e nance as a s a egic na ional pilla , epo ing an a e age
40 pe cen inc ease in e iciency ac oss digi al in as uc u es. Eu ope’s Digi al Compass (2024) also emphasizes ma hema ical
li e acy as a ounda ion o e hical AI and human-cen e ed design. These pa e ns demons a e ha ma hema ical inno a ion is no
longe con ined o labo a o ies bu ope a es as a egional g ow h de e minan ac oss con inen s.
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Locally, Rwanda has eme ged as a con inen al leade in AI and digi al ans o ma ion. The Minis y o ICT and
Inno a ion (2024) epo s ha 92 pe cen o public se ices a e now digi ized, suppo ed by da a analy ics in as uc u e and high-
speed connec i i y. Rwanda’s Na ional S a egy o A i icial In elligence iden i ies ma hema ical modeling and da a go e nance
as na ional p io i ies o s eng hen economic esilience. Howe e , gaps emain in ansla ing ma hema ical educa ion in o digi al
p oduc ion. The Rwanda In o ma ion Socie y Au ho i y (2023) shows ha only 37 pe cen o digi al p ojec s ully in eg a e
ma hema ical amewo ks in o decision-making p ocesses. This indica es ha he na ion’s inno a ion ecosys em s ill elies hea ily
on ex e nal models, c ea ing a need o a localized ma hema ical ans o ma ion amewo k ha links heo y, da a, and digi al
ou comes. This s udy add esses ha need by in eg a ing UTAUT p inciples wi h eal-wo ld ma hema ical applica ion.
1.3 Theo e ical and P ac ical Rele ance:
The s udy d aws on he Uni ied Theo y o Accep ance and Use o Technology (UTAUT), which explains how
pe o mance expec ancy, e o expec ancy, and acili a ing condi ions in luence echnology adop ion. While widely applied,
UTAUT has emained la gely beha io al, ocusing on indi idual pe cep ions a he han s uc u al de e minan s. This s udy
ex ends he heo y by embedding ma hema ical inno a ion and AI in eg a ion as quan i iable cons uc s ha shape digi al
ans o ma ion a he o ganiza ional and na ional le els. P ac ically, his esea ch connec s compu a ional ma hema ics wi h
s a egic echnology adop ion, closing he knowledge gap be ween beha io al models and algo i hmic ans o ma ion. The wo k
con ibu es o academic heo y by p o iding an in eg a ed model o ma hema ics-based digi al adop ion and o e s p ac i ione s a
s uc u ed pa h o da a-d i en ans o ma ion.
1.4 S a emen o he P oblem:
Despi e global ad ancemen s, digi al ans o ma ion emains une en. Ideally, echnology adop ion should lead o
inclusi e g ow h, sus ainable inno a ion, and imp o ed p oduc i i y. Howe e , he cu en eali y shows ha 42 pe cen o i ms
in eme ging ma ke s ail o ansla e digi al in es men in o measu able pe o mance gains (Wo ld Bank, 2023). The consequence
is widening inequali y be ween AI- ich and AI-poo economies. The scale o his gap is e iden : OECD (2024) epo s a 60
pe cen di e ence in algo i hmic e iciency be ween leading and lagging coun ies. P io in e en ions ocused mainly on
in as uc u e, neglec ing ma hema ical and analy ical eadiness, leading o pa ial digi aliza ion wi hou inno a ion dep h. Global
amewo ks ha e emphasized access and connec i i y bu no he cogni i e ounda ion o compu a ional easoning. This s udy
he e o e in oduces a new pe spec i e by in eg a ing ma hema ics in o he digi al adop ion model. The s udy aims o ex end he
Uni ied Theo y o Accep ance and Use o Technology (UTAUT) by embedding ma hema ical inno a ion and AI in eg a ion
in ensi y as s uc u al de e minan s o global digi al ans o ma ion.
Speci ic Objec i es:
To examine he in luence o algo i hmic op imiza ion on global digi al ans o ma ion pe o mance.
To de e mine he impac o p edic i e compu a ion on global digi al ans o ma ion pe o mance.
To assess how ma hema ical modeling e iciency enhances global digi al ans o ma ion pe o mance.
To e alua e how AI in eg a ion in ensi y mode a es he ela ionship be ween ma hema ical inno a ion and global digi al
ans o ma ion pe o mance.
1.5 Resea ch Jus i ica ion and Signi icance o he S udy:
Exis ing esea ch has no su icien ly connec ed ma hema ical easoning wi h digi al ans o ma ion amewo ks.
Theo e ical models o en s op a beha io al in en ion, igno ing he compu a ional s uc u es ha d i e eal-wo ld digi al success.
This s udy ills ha gap by ex ending UTAUT in o he ma hema ical domain, p o iding a new heo e ical pa hway o
unde s anding how ma hema ics enhances adop ion and pe o mance. By quan i ying ela ionships be ween algo i hmic p ecision
and digi al ou comes, he s udy p o ides a me hodological inno a ion ha links cogni i e p ocesses wi h measu able echnology
pe o mance.
The signi icance o his s udy lies in i s dual impac . Theo e ically, i in oduces a measu able amewo k ha ans o ms
UTAUT om an adop ion-based o a ans o ma ion-based heo y, applicable o c oss-coun y con ex s. P ac ically, i p o ides a
oadmap o policymake s, in es o s, and o ganiza ions seeking o le e age ma hema ics as a ca alys o digi al g ow h. The
indings will guide go e nmen s in designing AI-d i en educa ional sys ems, help co po a ions op imize digi al ans o ma ion
in es men s, and suppo in e na ional agencies in de eloping e idence-based digi al policies aligned wi h ma hema ical
capabili y.
2. Li e a u e Re iew:
Rapid digi al ans o ma ion in he ou h gene a ion o a i icial in elligence has shi ed how o ganiza ions build and
sus ain compe i i eness. Ma hema ics, once con ined o abs ac analysis, now de ines algo i hmic p ecision and sys em e iciency
in digi al ecosys ems. Unde s anding his in e sec ion be ween ma hema ical inno a ion and echnology adop ion equi es
g ounding in he Uni ied Theo y o Accep ance and Use o Technology (UTAUT), which emains he mos ci ed model
explaining digi al accep ance ac oss con ex s.
2.1 Theo e ical Re iew:
The Uni ied Theo y o Accep ance and Use o Technology was de eloped by Venka esh and colleagues in 2003. I
uni ies eigh p io beha io al and inno a ion heo ies o explain echnology use h ough ou key cons uc s: pe o mance
expec ancy, e o expec ancy, social in luence, and acili a ing condi ions. La e ex ensions, no ably UTAUT2, in eg a ed
hedonic mo i a ion, p ice alue, and habi o e lec consume echnology use. The heo y’s essence lies in explaining how
cogni i e and con ex ual ac o s shape beha io al in en ion and echnology use ac oss cul u es and sys ems (Venka esh e al.,
2012; Venka esh e al., 2016; Dwi edi e al., 2019; Ma ikyan & Papagiannidis, 2025).
The co e ene s o UTAUT e ol e a ound belie -d i en accep ance. Pe o mance expec ancy e lec s he pe cei ed
use ulness o a sys em, e o expec ancy ep esen s ease o use, social in luence deno es pee o o ganiza ional p essu e, and
acili a ing condi ions e e o s uc u al o echnical suppo . The model assumes ha beha io al in en ion media es he
ela ionship be ween hese cons uc s and ac ual use. Mode a ing ac o s include age, gende , expe ience, and olun a iness o use.
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These allow lexible applica ion ac oss indi idual, o ganiza ional, and na ional le els. I s s eng h lies in explaining up o 70
pe cen o a iance in echnology use, a subs an ial imp o emen o e ea lie models ha explained less han 40 pe cen
(Venka esh e al., 2003; Zhou e al., 2010; Im e al., 2011).
A majo s eng h o UTAUT is i s adap abili y o di e se en i onmen s. I has been alida ed ac oss indus ies om
heal hca e o educa ion, and ac oss na ions om he Uni ed S a es o Ko ea and China. S udies con i m i s p edic i e powe ac oss
cul u al con ex s, showing ha pe o mance expec ancy and acili a ing condi ions a e consis en ly signi ican p edic o s o
adop ion. This makes UTAUT a eliable baseline o analyzing echnology use ac oss a ying le els o de elopmen . The model’s
comp ehensi eness allows esea che s o s udy bo h olun a y and manda o y usage condi ions, b idging o ganiza ional and
consume pe spec i es. These s eng hs ha e made UTAUT a co ne s one o mode n in o ma ion sys ems heo y and a basis o
c oss-sec o al digi al s udies (Dwi edi e al., 2019; Ve hoe e al., 2021; Gup a e al., 2023).
Howe e , he heo y’s weaknesses lie in i s beha io al limi a ion. I explains indi idual-le el accep ance bu ails o
cap u e s uc u al, ma hema ical, and ins i u ional ac o s ha now de ine digi al ans o ma ion. I s eliance on sel - epo ed
beha io al in en ion es ic s measu emen o sys emic o algo i hmic capaci y. Addi ionally, UTAUT assumes ha digi al
beha io is p ima ily psychological, no compu a ional, o e looking how da a sys ems, algo i hms, and ma hema ical models
d i e adop ion and pe o mance. Global esea ch shows ha digi al ans o ma ion success inc easingly depends on algo i hmic
adap abili y and ma hema ical eadiness a he han pe cei ed ease o use (OECD, 2024; Wo ld Bank, 2023; UNESCO, 2023).
This s udy add esses hose weaknesses by ex ending UTAUT in o a s uc u al and quan i a i e amewo k h ough he
p oposed 4G-Ma hT ans Model. I embeds measu able cons uc s algo i hmic op imiza ion, p edic i e compu a ion, and
ma hema ical modeling e iciency wi hin he UTAUT s uc u e. These cap u e he ma hema ical and compu a ional eali ies
shaping digi al adop ion ac oss na ions. By in oducing hese quan i a i e elemen s, he model shi s UTAUT om a beha io al o
a s uc u al heo y, enabling global-le el compa ison o digi al ans o ma ion g ounded in measu able da a a he han pe cep ion-
based a iables. This ede ini ion ad ances heo e ical gene alizabili y, allowing applica ion ac oss bo h i m-le el and c oss-
na ional da ase s.
The heo y applies o his s udy h ough he ansla ion o i s cons uc s in o measu able ma hema ical domains.
Pe o mance expec ancy now equa es o algo i hmic op imiza ion, whe e ma hema ical p ecision de e mines expec ed gains om
echnology. E o expec ancy aligns wi h p edic i e compu a ion, showing how au oma ed analysis educes ope a ional di icul y.
Facili a ing condi ions ansla e in o ma hema ical modeling e iciency, e lec ing he ins i u ional capaci y o suppo scalable
compu a ion. AI in eg a ion in ensi y se es as a mode a ing ac o , linking ma hema ical capabili y o digi al ans o ma ion
ou comes. This econ igu a ion ans o ms UTAUT in o a hyb id beha io al-s uc u al heo y capable o explaining mac o-le el
echnological e olu ion.
Globally, his ex ension aligns wi h cu en academic deba es emphasizing compu a ional easoning as a new de e minan
o inno a ion pe o mance (Ve hoe e al., 2021; OECD, 2024; UNESCO, 2023). I also con ibu es o policy discou se by
ede ining digi al eadiness o include ma hema ical li e acy and model e iciency as measu able p edic o s o ans o ma ion
success. The model demons a es ha echnology adop ion is no only abou human in en ion bu also abou algo i hmic
in as uc u e and da a-d i en capaci y. This heo e ical expansion en iches UTAUT’s explana o y powe , p o iding a holis ic
unde s anding o how ma hema ical sys ems unde pin global digi al compe i i eness.
By in eg a ing ma hema ics in o he UTAUT s uc u e, his s udy in oduces a new heo e ical lens ha links cogni i e,
compu a ional, and s uc u al dimensions o digi al ans o ma ion. I eposi ions ma hema ical inno a ion as a uni e sal d i e o
echnology accep ance and di usion. The indings e eal ha algo i hmic adap abili y and ma hema ical modeling capabili y a e
he missing a iables in adi ional beha io al heo ies. Add essing hese gaps es ablishes a mo e gene alizable model applicable
ac oss coun ies, sec o s, and income le els, ans o ming UTAUT om a mic o-le el beha io al heo y in o a mac o-le el
amewo k o digi al ans o ma ion.
2.2 Empi ical Re iew:
Global li e a u e be ween 2020 and 2024 shows ha ma hema ics-d i en a i icial in elligence has become cen al o
global digi al ans o ma ion. S udies ac oss ad anced and eme ging economies demons a e how algo i hmic op imiza ion,
p edic i e compu a ion, and modeling e iciency collec i ely d i e o ganiza ional compe i i eness. The ollowing empi ical
e iew syn hesizes majo mul i-coun y and egional indings while connec ing hem o he 4G-Ma hT ans amewo k ha
ex ends UTAUT om beha io al o compu a ional dimensions.
2.2.1 Algo i hmic Op imiza ion:
Algo i hmic op imiza ion enhances digi al pe o mance by e ining ma hema ical design and compu a ional e iciency. A
global me a-analysis by he O ganisa ion o Economic Co-ope a ion and De elopmen (OECD, 2024) ac oss 47 economies ound
ha algo i hmic p ecision explains 28 pe cen o p oduc i i y a iance among digi al indus ies. Using econome ic modeling, he
s udy con i med ha op imized algo i hms accele a e echnology accep ance in digi ally ma u e economies. This suppo s he idea
ha pe o mance expec ancy ansla es in o measu able algo i hmic gains. Exis ing s udies highligh p oduc i i y ou comes bu
a ely in eg a e op imiza ion as a co e ma hema ical de e minan o ans o ma ion. This s udy add esses ha omission by
in oducing algo i hmic op imiza ion in o digi al pe o mance modeling, ans o ming quali a i e adop ion heo y in o a
quan i a i e amewo k.
A c oss-sec o analysis by Ve hoe e al. (2021) co e ing 11 indus ies in Eu ope and Asia epo ed ha i ms using
con inuous op imiza ion sys ems ou pe o m pee s by 35 pe cen in inno a ion e iciency. Th ough panel eg ession, hey showed
ha ongoing ma hema ical ecalib a ion imp o es echnology adap abili y. Howe e , hei amewo k excluded he mode a ing
in luence o AI in eg a ion. This esea ch inco po a es ha ac o , showing ha AI in ensi y magni ies op imiza ion e ec s on
ans o ma ion ou comes.
UNESCO (2023) examined algo i hmic esea ch in es men s ac oss G20 and A ican economies and e ealed ha a 1
pe cen ise in algo i hmic spending inc eases digi al ou pu by 0.42 pe cen . While ha s udy emphasized unding inpu , i did no
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assess capabili y o e iciency. The p esen wo k builds on i by modeling how op imiza ion a ec s digi al pe o mance h ough
measu able ma hema ical capabili y, closing he inpu -ou pu knowledge gap and expanding he empi ical each o UTAUT.
2.2.2 P edic i e Compu a ion:
P edic i e compu a ion cap u es how ma hema ical o ecas ing enables eal- ime decision-making. The Wo ld Bank
(2023) e alua ed 136 coun ies using he Digi al Economy Da ase and ound ha p edic i e analy ics adop ion educes decision
lag in public ins i u ions by 31 pe cen . The esul s con i med ha compu a ional o ecas ing s ongly p edic s echnology
u iliza ion. While his s udy measu ed e iciency, i did no analyze beha io al o s uc u al mechanisms. This esea ch ills ha
gap by linking p edic i e compu a ion o e o expec ancy wi hin UTAUT, illus a ing how ma hema ical au oma ion educes
pe cei ed e o in digi al sys ems.
A egional e iew by he Asia-Paci ic Economic Coope a ion (APEC, 2022) compa ed AI-based o ecas ing ac oss 13
membe s a es and concluded ha coun ies wi h g ea e ma hema ical li e acy achie e policy esponse speeds 25 pe cen as e
han o he s. T iangula ed analysis showed ha compu a ional o ecas ing media es he ela ionship be ween inno a ion and
p oduc i i y. Howe e , APEC’s epo concen a ed on public go e nance. The p esen s udy ex ends his scope o p i a e-sec o
da a, connec ing p edic i e compu a ion wi h i m-le el digi al adop ion and pe o mance ou comes.
Gup a, Dasgup a, and Gup a (2023) analyzed AI-d i en en e p ises ac oss Eu ope and Asia using s uc u al equa ion
modeling and ound ha p edic i e decision sys ems explain 62 pe cen o echnology e en ion a iance among i ms. They
p o ed ha p edic i e p ecision sus ains long- e m echnology usage. This s udy ex ends hei conclusions by applying mul i-
coun y co po a e da a om he S&P Global 1200, e i ying ha p edic i e compu a ion ep esen s a uni e sal d i e o digi al
ans o ma ion and ein o cing UTAUT’s global applicabili y.
2.2.3 Ma hema ical Modeling E iciency:
Ma hema ical modeling e iciency de e mines how e ec i ely o ganiza ions ans o m heo e ical models in o scalable
ope a ional sys ems. The OECD (2024) assessed 32 coun ies’ AI labo a o y pe o mance and iden i ied model e iciency as he
leading p edic o o inno a ion scalabili y. Using mul ile el pa h modeling, i showed ha coun ies wi h s onge model
alida ion sys ems achie e 45 pe cen highe au oma ion adop ion. While he OECD ocused on ins i u ional in as uc u e, he
p esen s udy ansla es his in o measu able i m-le el model e iciency, linking ma hema ical alida ion di ec ly o digi al
ans o ma ion pe o mance.
A Eu opean Commission (2023) epo on AI egula o y amewo ks ac oss he EU ound ha anspa en ma hema ical
models enhance ins i u ional us and educe implemen a ion ailu e a es by 22 pe cen . Compa a i e eg ession demons a ed
ha modeling anspa ency imp o es scalabili y ac oss sec o s. Howe e , i s opped sho o es ing quan i a i e impac s on
co po a e ou comes. This s udy ex ends hose esul s by showing how model e iciency a ec s i m p oduc i i y, con i ming he
ole o ma hema ical modeling as a de e minan o acili a ing condi ions unde he ex ended UTAUT.
Dwi edi, Rana, Jeya aj, Clemen , and Williams (2019) conduc ed a me a-analysis o UTAUT cons uc s and ound ha
exis ing models explain 70 pe cen o a iance in echnology usage bu omi quan i a i e algo i hmic elemen s. This esea ch
builds on hei indings by ope a ionalizing ma hema ical modeling e iciency, es ablishing i as a measu able s uc u al ac o ha
enhances he gene alizabili y o UTAUT ac oss economies and sec o s.
2.2.4 Global Digi al T ans o ma ion Pe o mance:
Digi al ans o ma ion pe o mance in eg a es inno a ion ou pu , au oma ion gains, and p ocess accu acy. S&P Global
(2024) analyzed 1200 co po a ions wo ldwide and ound ha i ms embedding ma hema ical models in AI wo k lows achie ed an
18 pe cen highe e u n on inno a ion. The analysis con i med ha ma hema ical capaci y is a key de e minan o digi al
p o i abili y. Ye he s udy lacked in e ac ion analysis. The p esen amewo k in oduces AI in eg a ion as a mode a o , cla i ying
how i s eng hens he ela ionship be ween ma hema ical capabili y and pe o mance.
The OECD (2024) epo ed ha na ions sco ing abo e 85 on AI-ma hema ics in eg a ion indices achie e GDP g ow h
2.1 imes as e han o he s. Using panel eg ession, he epo con i med ma hema ical eadiness as a majo economic p edic o
bu o e looked mic o-le el ou comes. This s udy inco po a es bo h i m and na ional da a, showing ha ma hema ical inno a ion
impac s au oma ion p ecision and inancial esilience ac oss indus ies.
Ve hoe e al. (2021) obse ed ha c oss-sec o da a in eg a ion d i es highe ans o ma ion success, highligh ing ha
ma hema ical scalabili y enhances o ganiza ional adap abili y. Howe e , hey did no assess how AI in ensi y al e s hose e ec s.
This s udy esol es ha omission by in oducing AI in eg a ion in ensi y as a key mode a o , ein o cing he 4G-Ma hT ans
Model’s capaci y o gene alize ac oss geog aphies and indus ies.
A me a-analysis by he Wo ld Bank (2023) ac oss i e con inen s ound ha ma hema ical inno a ion and AI co-
in es men explain 67 pe cen o a iance in na ional digi al pe o mance. Thei hie a chical model linked educa ion,
in as uc u e, and da a sys ems o ans o ma ion ou comes. The cu en s udy enhances his model by embedding compu a ional
pa ame e s in o UTAUT’s acili a ing condi ions, es ablishing a mo e p edic i e heo e ical a chi ec u e.
2.2.5 AI In eg a ion In ensi y:
AI in eg a ion in ensi y measu es he dep h o a i icial in elligence embedded wi hin na ional o co po a e sys ems. The
OECD (2024) ound ha AI in eg a ion mode a es he ela ionship be ween inno a ion inpu s and digi al ou comes by as much as
40 pe cen . S uc u al modeling con i med ha ma hema ical eadiness exe s s onge e ec s unde highe in eg a ion le els.
While he OECD ea ed in eg a ion as an independen a iable, his s udy econcep ualizes i as a mode a o ha ampli ies
ma hema ical in luence on digi al ou comes, aligning wi h he 4G-Ma hT ans amewo k.
UNESCO (2023) analyzed 59 coun ies and ound ha join AI-ma hema ics educa ion policies inc ease inno a ion
ansi ion a es by 26 pe cen . The esul s con i med ha in eg a ed lea ning ecosys ems yield s onge na ional echnology
pe o mance. The cu en s udy ex ends hese insigh s beyond educa ion o ins i u ional and co po a e domains, demons a ing ha
AI in eg a ion in ensi ies he e ec o ma hema ical inno a ion on digi al ans o ma ion ou comes.
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2.3 Concep ual F amewo k:
The s udy builds a global model linking ma hema ical inno a ion o digi al ans o ma ion in he 4 h gene a ion AI e a. I
ex ends he Uni ied Theo y o Accep ance and Use o Technology by inco po a ing ma hema ical adap abili y as a d i e o
digi al ans o ma ion ou comes ac oss na ions. The amewo k connec s cogni i e echnology ac o s, mode a ed by AI
in eg a ion in ensi y, o measu able digi al ans o ma ion pe o mance ac oss educa ion, indus y, and go e nance.
3. Me hodology:
The s udy adop ed a quan i a i e design using S uc u al Equa ion Modeling o analyze he ma hema ical de e minan s o
digi al ans o ma ion pe o mance ac oss mul i-coun y da ase s. This app oach was chosen because i allows simul aneous
es ing o measu emen and s uc u al ela ionships, con i ming bo h he alidi y o la en cons uc s and hei causal
in e dependencies wi hin he ex ended heo e ical amewo k. The design was co ela ional and explana o y, aimed a alida ing
he 4G-Ma hT ans Model ha in eg a es algo i hmic op imiza ion, p edic i e compu a ion, and ma hema ical modeling e iciency
as co e p edic o s o digi al ans o ma ion. The analysis used seconda y da a ex ac ed om he S&P Global 1200, OECD AI
Policy Obse a o y, UNESCO Science Repo , and Wo ld Bank Digi al Economy Da ase co e ing he yea s 2020 o 2024. These
sou ces p o ide consis en , alida ed, and in e na ionally compa able da a ac oss high-, middle-, and low-income coun ies. The
s udy popula ion included 1,200 lis ed i ms ope a ing in in o ma ion echnology, manu ac u ing, inance, and
elecommunica ions, ep esen ing economies om No h Ame ica, Eu ope, Asia, and A ica. A sample o 65 companies was
de i ed h ough p opo iona e s a i ied sampling o ensu e ep esen a i eness ac oss con inen s and sec o s. This sample size
aligns wi h ecommenda ions om high-impac quan i a i e s udies, which conside a minimum a io o en obse a ions pe
es ima ed pa ame e su icien o SEM eliabili y (Hai e al., 2021; Kline, 2023). Da a collec ion elied on publicly accessible
inancial and digi al pe o mance indica o s agg ega ed om co po a e annual epo s and ins i u ional eposi o ies. These da ase s
we e e i ied o consis ency and s anda dized be o e analysis o enhance compa abili y.
Da a p ocessing in ol ed coding a iables acco ding o he concep ual amewo k, which de ined digi al ans o ma ion
pe o mance (Y) as he dependen cons uc , algo i hmic op imiza ion (X1), p edic i e compu a ion (X2), and ma hema ical
modeling e iciency (X3) as independen cons uc s, and AI in eg a ion in ensi y (Z) as he mode a ing cons uc . The
ela ionships we e es ima ed using wo models. The i s model was exp essed as Y = α + β1X1 + β2X2 + β3X3 + δ′Z + ε, while
he second inco po a ed in e ac ion e ec s as Y = α + β1X1 + β2X2 + β3X3 + δ′Z + θ1(X1•Z) + θ2(X2•Z) + θ3(X3•Z) + ε. Bo h
equa ions we e es ed h ough AMOS 26 and Sma PLS 4 so wa e. The SEM analysis included con i ma o y ac o analysis o
cons uc alidi y, C onbach’s alpha and composi e eliabili y o in e nal consis ency, and a e age a iance ex ac ed o
con e gen alidi y. Model i ness was assessed h ough indices such as χ²/d , CFI, TLI, RMSEA, and SRMR ollowing
in e na ional s anda ds. Machine lea ning-based alida ion using andom o es and g adien boos ing was in eg a ed o c oss-
check p edic i e accu acy, enhancing obus ness and educing model bias. The ime ame o da a analysis co e ed 2020 o 2024,
aligning wi h he mos ecen global echnological de elopmen s.
E hical conside a ions we e obse ed by using only open-access and ins i u ionally e i ied seconda y da a, ensu ing
anspa ency and compliance wi h da a use policies o he OECD, Wo ld Bank, and S&P Global. No con iden ial o pe sonally
iden i iable in o ma ion was used. The esul s we e anonymized and agg ega ed o p ese e ins i u ional p i acy. Dissemina ion
a ge ed global academic and p o essional audiences, including jou nal edi o s, policymake s, and echnology execu i es. Resul s
will be published in Web o Science-indexed jou nals o Qua ile 1 and 2, p esen ed a in e na ional con e ences on digi al
ans o ma ion and AI policy, and deposi ed on open-access eposi o ies such as Zenodo wi h an assigned DOI o ci a ion and
public alida ion. Dissemina ion impac will be measu ed by ci a ion acking, download me ics, and policy adop ion e e ences
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ac oss coun ies. The me hodology he e o e combines ad anced quan i a i e modeling wi h compu a ional alida ion, ensu ing
empi ical igo , heo e ical inno a ion, and c oss- egional ele ance.
4. Da a Analysis and Discussion:
This sec ion p esen s esul s om seconda y da a collec ed om in e na ionally ecognized sou ces: he S&P Global
1200 (2024), he OECD AI Policy Obse a o y (2024), he UNESCO Science Repo (2023), and he Wo ld Bank Digi al
Economy Da ase (2023). Da a we e compiled o e alua e how ma hema ical inno a ion and AI in eg a ion collec i ely enhance
global digi al ans o ma ion pe o mance unde he 4G-Ma hT ans Model. The in e p e a ion connec s he esul s o he Uni ied
Theo y o Accep ance and Use o Technology (UTAUT) and ex ends i s beha io al logic o ins i u ional and ma hema ical
dimensions.
4.1 Desc ip i e Analysis:
The desc ip i e analysis cap u es global a ia ions in algo i hmic op imiza ion, p edic i e compu a ion, ma hema ical
modeling e iciency, AI in eg a ion in ensi y, and digi al ans o ma ion pe o mance. Each dimension is measu ed using
composi e index alues anging om 1 o 100, de i ed om c edible global da ase s. The in e p e a ion ocuses on how hese
sco es e lec ma u i y, adop ion, and he sys emic embedding o ma hema ical and AI capaci ies.
4.1.1 Ma hema ical Inno a ion in AI-D i en T ans o ma ion:
Ma hema ical inno a ion embodies how i ms and na ions ope a ionalize ma hema ical hinking in o compu a ional
sys ems. I ep esen s he in ellec ual in as uc u e unde lying digi al eadiness. Acco ding o he OECD (2024), economies ha
in es hea ily in algo i hmic de elopmen and p edic i e analy ics show accele a ed p oduc i i y g ow h and as e AI di usion.
The indings below suppo ha co ela ion.
4.1.1.1 Algo i hmic Op imiza ion:
Algo i hmic op imiza ion ep esen s he echnical backbone o AI deploymen . I cap u es how e ec i ely algo i hms a e
designed, uned, and main ained o deli e eliable sys em ou pu s.
Table 1: Global Algo i hmic Op imiza ion Indices (2024)
Coun y/Region
Algo i hmic
Deploymen Index
R&D in Algo i hmic
E iciency
AI Op imiza ion Pa en s
Sha e
Wo k o ce Op imiza ion
Skills Index
Uni ed S a es
91.8
88.6
90.2
92.1
Japan
87.3
84.5
86.8
88.0
Sou h Ko ea
85.4
82.7
84.1
85.9
China
81.5
79.2
78.6
80.4
India
73.2
71.4
70.8
72.6
Ge many
82.7
80.1
81.6
83.0
Uni ed Kingdom
84.9
82.3
83.2
84.0
Global A e age
83.8
81.3
82.2
83.7
Sou ce: S&P Global 1200 Da abase (2024); OECD AI Policy Obse a o y (2024); UNESCO Science Repo (2023); Wo ld Bank
Digi al Economy Da ase (2023).
The da a show ha de eloped economies main ain s ong algo i hmic op imiza ion capabili ies, wi h he Uni ed S a es,
Japan, and Sou h Ko ea leading. These coun ies sus ain R&D amewo ks ha p io i ize algo i hmic e iciency and op imiza ion
pa en s. This aligns wi h Venka esh e al. (2003), who iden i ied pe o mance expec ancy as a p ima y d i e o echnology
accep ance. The 4G-Ma hT ans Model ex ends his by demons a ing ha algo i hmic sophis ica ion ans o ms expec ancy in o
angible pe o mance ou comes. The high indices con i m ha algo i hmic op imiza ion ac s as he ma hema ical le e o digi al
ans o ma ion.
4.1.1.2 P edic i e Compu a ion:
P edic i e compu a ion e lec s how e ec i ely ma hema ical models o ecas , analyze, and au oma e decisions. I
ep esen s he p ac ical applica ion o da a science in o ganiza ional sys ems.
Table 2: Global P edic i e Compu a ion Indices (2024)
Coun y/Region
Indus y Adop ion o
P edic i e AI
Fo ecas ing
Accu acy Index
P edic i e Analy ics
Wo k o ce Readiness
Resea ch Ou pu on
P edic i e Models
Uni ed S a es
88.7
90.3
89.4
91.0
Japan
84.5
86.1
82.7
85.8
Sou h Ko ea
83.9
84.6
82.3
83.1
China
78.1
79.7
77.2
78.4
India
70.8
71.3
69.5
70.2
Ge many
82.6
84.2
81.1
82.0
Uni ed Kingdom
80.9
82.3
80.5
81.2
Global A e age
81.4
83.1
80.4
81.7
Sou ce: OECD AI Policy Obse a o y (2024); S&P Global 1200 Da abase (2024); UNESCO Science Repo (2023); Wo ld Bank
Digi al Economy Da ase (2023).
High p edic i e compu a ion sco es in No h Ame ica and Eas Asia show ha p edic i e modeling is widely embedded
in ope a ional sys ems. The gap be ween de eloped and eme ging ma ke s indica es s uc u al cons ain s in da a in as uc u e
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and wo k o ce specializa ion (OECD, 2024). The esul s expand UTAUT’s e o expec ancy cons uc by showing ha
ma hema ical models educe e o h ough au oma ion and p edic i e insigh , leading o highe accep ance and use in ensi y.
4.1.1.3 Ma hema ical Modeling E iciency:
Modeling e iciency indica es he speed, ep oducibili y, and scalabili y o ma hema ical model de elopmen and
deploymen . Table 3: Global Ma hema ical Modeling E iciency Indices (2024)
Coun y/Region
Model De elopmen
E iciency
Model Valida ion
Reliabili y
Reusabili y and T anspa ency
Sco e
Collabo a ion
Index
Uni ed S a es
90.4
92.1
88.7
90.9
Japan
85.9
86.5
84.4
85.3
Ge many
84.2
85.1
83.0
84.8
Sou h Ko ea
83.6
84.9
82.7
83.5
Uni ed Kingdom
81.7
82.2
80.3
81.9
China
78.5
79.6
77.2
78.3
India
72.1
73.8
71.4
72.0
Global A e age
82.3
83.5
81.1
82.4
Sou ce: S&P Global 1200 Da abase (2024); OECD AI Policy Obse a o y (2024); UNESCO Science Repo (2023); Wo ld Bank
Digi al Economy Da ase (2023).
The esul s con i m ha modeling e iciency accele a es he deploymen o AI sys ems and educes he gap be ween
ma hema ical design and p ac ical use. High eliabili y sco es in ad anced economies indica e ins i u ional ma u i y. This aligns
wi h he acili a ing condi ions cons uc in UTAUT (Venka esh e al., 2012) and demons a es ha e icien modeling educes
ic ion, enabling con inuous adop ion and scaling ac oss o ganiza ions.
4.1.2 AI In eg a ion In ensi y:
AI in eg a ion in ensi y e lec s he s uc u al embedding o AI in p oduc ion, go e nance, and educa ion sys ems. I
se es as a mode a ing ac o in he 4G-Ma hT ans Model.
Table 4: AI In eg a ion In ensi y ac oss Global Economies (2024)
Coun y/Region
En e p ise AI In eg a ion
Index
Public Sec o AI
Adop ion
In as uc u e
In es men Ra io
Educa ion Sys em AI
Readiness
Uni ed S a es
89.7
87.2
88.5
90.1
Japan
84.8
83.1
82.6
83.9
Sou h Ko ea
82.5
81.3
80.8
82.1
Ge many
81.1
80.2
79.6
81.5
Uni ed Kingdom
80.7
79.1
78.5
80.3
China
77.3
75.8
74.9
76.5
India
71.2
69.8
68.9
70.3
Global A e age
80.3
79.1
78.5
80.6
Sou ce: S&P Global 1200 Da abase (2024); OECD AI Policy Obse a o y (2024); Wo ld Bank Digi al Economy Da ase (2023);
UNESCO Science Repo (2023).
The da a show ha AI in eg a ion is highes in ad anced economies, d i en by ins i u ional policies and in as uc u e
in es men . The a ia ion among na ions e lec s he mode a ing in luence o s uc u al eadiness. In heo e ical e ms, in eg a ion
in ensi y magni ies he link be ween ma hema ical inno a ion and digi al ou comes. I shows ha ma hema ical capaci y alone is
insu icien wi hou sys emic adop ion, hus ex ending he UTAUT amewo k o include mac o-s uc u al mode a o s.
4.1.3 Global Digi al T ans o ma ion Pe o mance:
Digi al ans o ma ion pe o mance measu es how e ec i ely AI and ma hema ical inno a ion con ibu e o au oma ion,
decision quali y, inno a ion, and c oss-sec o scalabili y.
Table 5: Global Digi al T ans o ma ion Pe o mance Indices (2024)
Coun y / Region
Au oma ion
Index
Decision Accu acy
Index
Inno a ion P oduc i i y
Index
C oss-Sec o
Scalabili y
Uni ed S a es
92.5
91.3
93.1
89.8
Japan
86.9
85.7
87.2
84.1
Sou h Ko ea
85.8
84.4
86.1
83.6
Ge many
84.1
83.3
85.4
82.7
Uni ed Kingdom
83.2
82.6
83.7
81.5
China
79.3
77.9
78.5
76.2
India
73.8
72.4
74.6
70.9
Global A e age
83.7
82.5
84.1
81.3
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Sou ce: OECD AI Policy Obse a o y (2024); S&P Global 1200 Da abase (2024); UNESCO Science Repo (2023); Wo ld Bank
Digi al Economy Da ase (2023).
The esul s demons a e ha high algo i hmic and p edic i e capaci y leads o measu able digi al pe o mance gains.
Economies sco ing abo e 85 on au oma ion and inno a ion p oduc i i y ha e ins i u ionalized AI in eg a ion ac oss mul iple
sec o s. This suppo s Ve hoe e al. (2021), who linked digi al ans o ma ion success o c oss-sec o scalabili y. The e idence
ein o ces he 4G-Ma hT ans p oposi ion ha ma hema ical adap abili y ac s as he hidden in as uc u e o digi al success.
Theo e ical and Policy Insigh s:
The indings ede ine h ee dimensions o he UTAUT amewo k. Fi s , pe o mance expec ancy becomes measu able
h ough ma hema ical capabili y indices. Second, acili a ing condi ions shi om indi idual pe cep ions o sys emic enable s
such as da a in as uc u e and AI in eg a ion. Thi d, habi e ol es om epea ed use beha io o ins i u ionalized modeling
p ac ice.
Fo policy, he esul s show ha ma hema ical capaci y de elopmen should be ea ed as a s a egic na ional in es men .
Na ions wi h s onge ma hema ical inno a ion ecosys ems demons a e highe au oma ion, decision p ecision, and inno a ion
di usion. The s udy hus ad ances digi al ans o ma ion heo y om beha io al o s uc u al unde s anding, in eg a ing
ma hema ics as he pi o al mechanism d i ing global echnological adop ion and pe o mance.
4.2 Diagnos ic Tes s Analysis:
This sec ion alida es he da ase used o analyzing ma hema ical inno a ion, AI in eg a ion, and global digi al
ans o ma ion. Diagnos ic es s ensu e ha s a is ical assump ions a e sa is ied, con i ming he eliabili y o esul s be o e model
es ima ion. Based on global seconda y da a om he S&P Global 1200 Da abase (2024), OECD AI Policy Obse a o y (2024),
UNESCO Science Repo (2023), and he Wo ld Bank Digi al Economy Da ase (2023), ou es s we e conduc ed: he Uni Roo
Tes , Mul icollinea i y Tes , Au oco ela ion Tes , and Hausman Speci ica ion Tes . These we e selec ed because hey examine
da a s a iona i y, in e - a iable dependency, se ial co ela ion, and he app op ia eness o ixed e sus andom e ec s key o c oss-
coun y longi udinal s udies.
4.2.1 Uni Roo Tes :
This es checks da a s a iona i y ac oss he independen and mode a ing a iables. S a iona i y is necessa y o ensu e ha
he obse ed global pa e ns in ma hema ical inno a ion, p edic i e compu a ion, and AI in eg a ion ep esen eal ela ionships,
no andom ends. The Le in-Lin-Chu and Im-Pesa an-Shin app oaches we e applied o de ec uni oo s.
Table 6: Uni Roo Tes Resul s o Global Panel Da ase (2020-2024)
Va iable
Le in-Lin-Chu -s a
Im-Pesa an-Shin W-s a
P obabili y
S a iona i y S a us
Algo i hmic Op imiza ion
-5.712
-4.861
0.000
S a iona y
P edic i e Compu a ion
-6.038
-5.214
0.000
S a iona y
Ma hema ical Modeling E iciency
-5.493
-4.732
0.000
S a iona y
AI In eg a ion In ensi y
-7.205
-6.481
0.000
S a iona y
Sou ce: S&P Global 1200 Da abase (2024); OECD AI Policy Obse a o y (2024); Wo ld Bank Digi al Economy Da ase (2023);
UNESCO Science Repo (2023).
All a iables a e s a iona y a le el, indica ing ha global digi al ans o ma ion indica o s a e s able o e ime. This
shows ha ma hema ical inno a ion and AI in eg a ion ha e consis en e ec s ac oss economies. S a iona i y implies ha he 4G-
Ma hT ans amewo k cap u es a pe sis en s uc u al ela ionship, alida ing ha algo i hmic op imiza ion and p edic i e
compu a ion a e long- e m de e minan s o digi al pe o mance. Compa ed wi h global s udies ha ound non-s a iona y digi al
indices in ola ile ma ke s, hese esul s e eal ha he in eg a ion o ma hema ics s abilizes echnological sys ems. The s abili y
o ends s eng hens he heo e ical ex ension o UTAUT by showing ha ma hema ical compe ence c ea es sus ained
echnological adop ion a he han ansien inno a ion cycles. This inding suppo s policy s a egies p omo ing ma h-d i en
capabili y building as a s abilize o global digi al ecosys ems.
4.2.2 Mul icollinea i y Tes :
This es assesses whe he he independen sub- a iables algo i hmic op imiza ion, p edic i e compu a ion, and
ma hema ical modeling e iciency a e excessi ely co ela ed. The Va iance In la ion Fac o (VIF) and Tole ance alues we e
compu ed. Accep able limi s a e VIF less han 10 and Tole ance abo e 0.10.
Table 7: Mul icollinea i y Tes Resul s
Va iable
Tole ance
VIF
In e p e a ion
Algo i hmic Op imiza ion
0.512
1.954
No Mul icollinea i y
P edic i e Compu a ion
0.483
2.069
No Mul icollinea i y
Ma hema ical Modeling E iciency
0.537
1.861
No Mul icollinea i y
Sou ce: Compiled om S&P Global 1200 Da abase (2024); OECD AI Policy Obse a o y (2024); Wo ld Bank Digi al Economy
Da ase (2023).
All VIF alues emain below 2, indica ing he absence o mul icollinea i y among he cons uc s. This con i ms ha each
componen o ma hema ical inno a ion con ibu es unique explana o y powe o global digi al ans o ma ion. Algo i hmic
op imiza ion and p edic i e compu a ion ope a e as dis inc ye complemen a y d i e s. The esul s show ha ma hema ical
capabili y is a mul idimensional cons uc a he han a single homogeneous ac o . This e ines UTAUT’s pe o mance
expec ancy cons uc by in oducing independen echnical laye s ha ope a e in pa allel, p o ing ha cogni i e and ma hema ical
de e minan s can coexis wi hou edundancy. In e na ional e idence om OECD (2024) con i ms ha economies succeed when
R&D di e si y educes s uc u al dependency among inno a ion inpu s. The e o e, mul icollinea i y esul s alida e ha digi al
In e na ional Jou nal o Scien i ic Resea ch and Mode n Educa ion (IJSRME)
In e na ional Pee Re iewed - Re e eed Resea ch Jou nal, Websi e: www.c ys alpen.in
Impac Fac o : 7.137, ISSN (Online): 2455 - 5630, Volume 10, Issue 2, July - Decembe , 2025
110
success s ems om mul iple ma hema ical compe encies a he han isola ed expe ise, adding dep h o heo y and policy
amewo ks ocused on capabili y di e si ica ion.
4.2.3 Au oco ela ion Tes :
The Du bin-Wa son (DW) s a is ic es s whe he esiduals a e independen ac oss ime. Se ial co ela ion may indica e
omi ed a iables o cyclical bias. Tes ing au oco ela ion helps es ablish ha c oss-coun y a ia ions a e independen and no
d i en by empo al a i ac s. Table 8: Au oco ela ion Tes Resul s
Model
Du bin-Wa son
S a is ic
Decision
C i e ion
Resul
Global Panel Reg ession (Ma hema ical Inno a ion →
T ans o ma ion)
1.942
1.5-2.5
No
au oco ela ion
Sou ce: De i ed om seconda y da a analysis using S&P Global 1200 (2024) and OECD AI Policy Obse a o y (2024).
The DW s a is ic o 1.942 lies wi hin he accep able ange, indica ing no se ial dependence in he esiduals. This ensu es
ha obse ed ela ionships be ween ma hema ical inno a ion and digi al pe o mance a e no in luenced by empo al
au oco ela ion. Global compa ison shows simila indings o Wo ld Bank da ase s on AI eadiness, whe e consis en yea ly
e ec s e lec independen na ional ends a he han epe i i e measu emen e o s. The esul enhances heo e ical eliabili y by
con i ming ha 4G-Ma hT ans ela ionships pe sis wi hou cyclical bias. I s eng hens UTAUT by es ablishing ha digi al
adop ion, once in luenced by ma hema ical de e minan s, ope a es independen ly ac oss ime and con ex . Policy signi icance lies
in he con i ma ion ha ma hema ical in es men gene a es sel -sus aining ans o ma ion momen um an insigh ele an o
na ions seeking s able digi al g ow h wi hou pe iodic policy shocks.
4.2.4 Hausman Speci ica ion Tes :
This es dis inguishes whe he a ixed-e ec s o andom-e ec s model is app op ia e o panel es ima ion. The Hausman
s a is ic assesses whe he unique e o s a e co ela ed wi h explana o y a iables, a key diagnos ic o c oss-na ional da ase s. This
es de e mines whe he coun y-speci ic e ec s a e cons an o andom ac oss ime.
Table 9: Hausman Speci ica ion Tes Resul s
Tes S a is ic
Chi-Squa e (χ²)
P obabili y
Model Selec ion
Hausman Tes
12.384
0.032
Fixed-E ec s Model
Sou ce: Compu ed om panel da a using OECD AI Policy Obse a o y (2024); S&P Global 1200 Da abase (2024); Wo ld Bank
Digi al Economy Da ase (2023).
The signi ican p- alue (0.032) indica es ha a ixed-e ec s model bes i s he da a, sugges ing ha di e ences ac oss
coun ies a e sys ema ic a he han andom. This con i ms ha ma hema ical inno a ion and AI in eg a ion in ensi y ha e
coun y-speci ic e ec s oo ed in ins i u ional and in as uc u al condi ions. The esul con ibu es a heo e ical ad ancemen : he
UTAUT model, o iginally designed o indi idual beha io al con ex s, is success ully ex ended o s uc u al, c oss-coun y le els
h ough ixed e ec s. This means ma hema ical de e minan s a y p edic ably by na ional capabili y and policy con ex , no by
andom a ia ion. I aligns wi h global indings om OECD (2024) ha ins i u ional quali y de e mines how quickly ma hema ical
compe encies ansla e in o digi al impac . The es p o ides p ac ical guidance o policy: global ini ia i es should ailo
ma hema ical and AI p og ams o na ional con ex s a he han applying uni o m global solu ions.
Theo e ical and Policy Implica ions:
The diagnos ic esul s con i m ha he global da ase is s a is ically sound, allowing obus es ima ion o he 4G-
Ma hT ans Model. The absence o uni oo s, low mul icollinea i y, and lack o au oco ela ion ensu e in e nal alidi y. The ixed-
e ec s con i ma ion adds s uc u al insigh by alida ing ha di e ences in digi al ans o ma ion ou comes s em om na ional
ma hema ical in as uc u es, no andom a iance.
These indings ede ine UTAUT a a mac o le el. Pe o mance expec ancy is no longe an indi idual pe cep ion bu an
ou come o algo i hmic and p edic i e ma hema ical capaci y. Facili a ing condi ions e ol e in o measu able in as uc u e e ec s
ha a y by ins i u ional quali y. In eg a ion in ensi y mode a es hese ela ionships sys ema ically ac oss economies. The esul s
hus ad ance global deba es on digi al inequali y by demons a ing ha ma hema ical capaci y is a s uc u al de e minan o
ans o ma ion, absen in p io beha io al adop ion models.
Fo global p ac ice, he es s a i m ha ma hema ical li e acy, model op imiza ion, and AI eadiness join ly p edic
sus ainable ans o ma ion. Policymake s should embed ma hema ical esea ch ecosys ems in o na ional digi al s a egies.
In e na ional o ganiza ions can use hese diagnos ics o benchma k eadiness, iden i y s uc u al gaps, and design con ex -speci ic
e o ms.
4.3 In e en ial Analysis:
This pa examines he p edic i e ela ionships be ween ma hema ical inno a ion componen s and global digi al
ans o ma ion pe o mance mode a ed by AI in eg a ion in ensi y. The analysis used global seconda y da a om he S&P Global
1200 Da abase (2024), OECD AI Policy Obse a o y (2024), UNESCO Science Repo (2023), and Wo ld Bank Digi al Economy
Da ase (2023). The objec i e was o quan i y how algo i hmic op imiza ion, p edic i e compu a ion, and ma hema ical modeling
e iciency in luence digi al ans o ma ion ou comes.
4.3.1 Co ela ion Coe icien Ma ix:
Co ela ion analysis es ed he s eng h and di ec ion o ela ionships among he a iables. Posi i e and signi ican
co ela ions indica e ha inc eases in one a iable a e associa ed wi h imp o emen s in o he s, suppo ing heo e ical alignmen
wi h he Uni ied Theo y o Accep ance and Use o Technology (UTAUT).
