Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness

Munjung Kim, Sadamori Kojaku, Yong-Yeol Ahn. Science Advances.

Munjung Kim
Sadamori Kojaku
Yong-Yeol Ahn
j
i
k

We live in the future we once imagined.

Back to the Future Part II (Universal Pictures, 1989): theatrical poster and a still.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Your most memorable technology?

A shift, or a new technology, in your life.

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Your most memorable technology?

A shift, or a new technology, in your life.

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Your most memorable technology?

A shift, or a new technology, in your life.

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Your most memorable technology?

A shift, or a new technology, in your life.

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Your most memorable technology?

A shift, or a new technology, in your life.

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Light bulb
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Light bulb changed human world

more than you’d think

  • 4–6 more hours a day
  • The 24-hour economy
  • Evening entertainment culture

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Anything that is in the world when you’re born is normal and ordinary and is just a natural part of the way the world works.

“The Salmon of Doubt”, Douglas Adams

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Anything that’s invented between when you’re fifteen and thirty-five is new and exciting and revolutionary and you can probably get a career in it.

“The Salmon of Doubt”, Douglas Adams

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Anything invented after you’re thirty-five is against the natural order of things.

“The Salmon of Doubt”, Douglas Adams

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

My age

6y old
12y old
19y old
36y old
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

My age

6y old
12y old
19y old
36y old
Pagers
This was normal
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

My age

6y old
12y old
19y old
36y old
Pagers
This was normal
Wireless phone
Innovative 🤯
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

My age

6y old
12y old
19y old
36y old
Pagers
This was normal
Wireless phone
Innovative 🤯
Smart phone
super cool!
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

My age

6y old
12y old
19y old
36y old
Pagers
This was normal
Wireless phone
Innovative 🤯
Smart phone
super cool!
Smart glass
Goes against
natural order
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Bohr’s model
(1913)
Vegard’s model
(1918)
Schrödinger’s model
(1926)
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

How do we quantify disruptiveness?

Bohr’s model
(1913)
Vegard’s model
(1918)
Schrödinger’s model
(1926)
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Based on citation networks (Funk & Owen-Smith 2017)

developing
disruptive
D=−1
D=1
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
j
i
k
developing
disruptive
D=−1
D=1
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
j
i
k
cite
cite
cite
yes
no
yes
no
yes
citing focal
& its refs
citing
the focal
citing its
refs only
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
j
i
k
cite
cite
cite

D⧫=ni−njni+nj+nkD_{\blacklozenge}=\frac{\textcolor{#B14434}{n_i}-\textcolor{#3959A6}{n_j}}{\textcolor{#B14434}{n_i}+\textcolor{#3959A6}{n_j}+\textcolor{#4d4d4d}{n_k}}

focal
only
focal
+ refs
refs
only
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Large teams develop, small teams disrupt
Wu, Wang & Evans (2019) Nature 566. Park, Leahy & Funk (2023) Nature 613. Lin, Frey & Wu (2023) Nature 623.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Papers are becoming less disruptive over time
Wu, Wang & Evans (2019) Nature 566. Park, Leahy & Funk (2023) Nature 613. Lin, Frey & Wu (2023) Nature 623.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Remote collaboration: fewer breakthrough ideas
Wu, Wang & Evans (2019) Nature 566. Park, Leahy & Funk (2023) Nature 613. Lin, Frey & Wu (2023) Nature 623.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

But the D-index fails

for some well-known disruptive discoveries

Wu, Wang & Evans (2019) Nature 566. Park, Leahy & Funk (2023) Nature 613. Lin, Frey & Wu (2023) Nature 623.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Discovery
1964: Englert, Brout and Higgs predict the boson
Recognition
2013: Nobel Prize in Physics
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Discovery
1964: Englert, Brout and Higgs predict the boson
Recognition
2013: Nobel Prize in Physics
Englert, F.,
& Brout, R.
(1964)
D = 0.15
Top 2.8 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Discovery
1964: Englert, Brout and Higgs predict the boson
Recognition
2013: Nobel Prize in Physics
Englert, F.,
& Brout, R.
(1964)
D = 0.15
Top 2.8 %
Higgs, P.W.
(1964)
D = − 0.27
Bottom 0.1 %
🫠
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

What’s happening?

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
focal + refs
focal only
refs only
Higgs
focal paper
Englert & Brout
D = − 0.27
Bottom 0.1 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
focal + refs
focal only
refs only
✂️
Higgs
focal paper
Englert & Brout
D = − 0.27
Bottom 0.1 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
focal only
focal only
refs only
Higgs
focal paper
Englert & Brout
D = 0.28
Top 1.3 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Why is the D-index so sensitive?

with the citation
one citation cut
D = − 0.27
D = 0.28
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

D-index sorts the citing papers

Does a paper build on the focal paper, the work before it, or both?

build on prior + focal
build on focal
build on prior
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

But papers do not sort so cleanly

Some belong to two groups at once.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

We preserve continuity by abandoning class rounding.

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Simulate the flow
of knowledge
with random walks
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Random
walks
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Random
walks
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

word2vec turns pairs into coordinates

(ancestor, descendant)
word2vec
an information compressor
a coordinate per node
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

How word2vec works

*word2vec has multiple variants. We focus on the skip-gram negative sampling word2vec.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
*word2vec has multiple variants. We focus on the skip-gram negative sampling word2vec.
“Chance favors only the _____ mind.”
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
*word2vec has multiple variants. We focus on the skip-gram negative sampling word2vec.
“Chance favors only the _____ mind.”
“favors”
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
*word2vec has multiple variants. We focus on the skip-gram negative sampling word2vec.
“Chance favors only the _____ mind.”
“favors”
“prepared”
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
*word2vec has multiple variants. We focus on the skip-gram negative sampling word2vec.
“favors”
“prepared”
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
*word2vec has multiple variants. We focus on the skip-gram negative sampling word2vec.
“favors”
“prepared”

qfavor=[0.1−0.2]q_{\text{favor}}=\begin{bmatrix}0.1\\-0.2\end{bmatrix}

N1
N2
query vector
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
*word2vec has multiple variants. We focus on the skip-gram negative sampling word2vec.
“favors”
“prepared”

qfavor=[0.1−0.2]q_{\text{favor}}=\begin{bmatrix}0.1\\-0.2\end{bmatrix}

N1
N2
query vector

kprepare=[0.20.1]k_{\text{prepare}}=\begin{bmatrix}0.2\\0.1\end{bmatrix}

N1
N2
key vector
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

A word has two vectors

“favors”
“favors”
“prepared”
Query
Key
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Trained by negation.

“… favors only
the prepared”
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Trained by negation.

“… favors only
the prepared”
prepared
(key)
favor
(query)
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Trained by negation.

“… favors only
the prepared”
prepared
(key)
favor
(query)
water
(random key)
a randomly
sampled word

r(j)r(j)

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Trained by negation.

“… favors only
the prepared”
prepared
(key)
favor
(query)
water
(random key)
a randomly
sampled word

r(j)r(j)

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
query
key
dot sim
(x)
genuine?
(y)
favor
prepared

qfavor⊤kprepareq_{\text{favor}}^\top k_{\text{prepare}}

Yes (y=1)
favor
water

qfavor⊤kwaterq_{\text{favor}}^\top k_{\text{water}}

No (y=0)
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
query
key
dot sim
(x)
genuine?
(y)
favor
prepared

qfavor⊤kprepareq_{\text{favor}}^\top k_{\text{prepare}}

Yes (y=1)
favor
water

qfavor⊤kwaterq_{\text{favor}}^\top k_{\text{water}}

No (y=0)
Classify by the
logistic regression
train by the log-
likelihood
maximization

σθ(i,j)=11+exp⁡(−qi⊤kj)    θ={qi,ki}i=1N\sigma_\theta(i,j)=\dfrac{1}{1+\exp(-q_i^\top k_j)}\;\;\theta=\{q_i,k_i\}_{i=1}^{N}

max⁡θ∑(i,j)∈D[yi,jlog⁡σθ(i,j)+(1−yi,j)log⁡(1−σθ(i,j))]\max_\theta\sum_{(i,j)\in\mathcal D}\left[y_{i,j}\log\sigma_\theta(i,j)+(1-y_{i,j})\log(1-\sigma_\theta(i,j))\right]

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

word2vec turns pairs into coordinates

(ancestor, descendant)
word2vec
an information compressor
a coordinate per node
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Random
walks
parent → child
grandparent → grandchild
(ancestor, descendant)
Training data
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Random
walks
parent → child
grandparent → grandchild
(ancestor, descendant)
Training data
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Random
walks
parent → child
grandparent → grandchild
(ancestor, descendant)
Training data
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Random
walks
parent → child
grandparent → grandchild
(ancestor, descendant)
Training data
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Random
walks
parent → child
grandparent → grandchild
(ancestor, descendant)
Training data
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
(ancestor, descendant)
Training data
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
(query, key)
Let’s focus on
this paper.
irrelevant to the
focal paper
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
(query, key)
Let’s focus on
this paper.
focal
paper
Paired query & key
get closer.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
(query, key)
Let’s focus on
this paper.
focal
paper
Paired query & key
get closer.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
focal
paper
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
focal
paper
ki
qi
key
vec
query
vec
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
Not mixed
Mixed
ki
qi
focal
paper
Large separation
of
key and query
∼
Discontinuity of citing
and cited papers
ki
qi
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Embedding Disruptiveness Measure (EDM)

Δi:=1−cos⁡(qi,ki)\Delta_i := 1-\cos(q_i,k_i)

How different the
two sides are.
Δ = 1.002
Top 4.3 %
Δ = 1.005
Top 4.1 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Does EDM beat the D-index? 🤔

Tested with APS data

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Conformal analysis

Preserve degrees and time gap.
Shuffle everything else.

original network
random network
Time
Time
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

D-index of milestone works (APS)

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

D-index of milestone works (APS)

Milestone papers with
the bottom-level
D-index value.
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

D-index of milestone works (APS)

Milestone papers with
the bottom-level
D-index value.
Shuffling creates
more high
D-index works 🙈
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
D-index
EDM
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
D-index
EDM
Many milestone
papers have a high
EDM value
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
D-index
EDM
Many milestone
papers have a high
EDM value
Randomization
reduces the EDM-
score for most works
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

EDM aligns better with human judgment

Control
variable
EDM
(proposed)
D-index
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

What does EDM find
that the D-index misses?

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Higgs mechanism (1964)

Englert & Brout
Higgs
D-index
0.15 · Top 2.8 %
− 0.27 · Bottom 0.1 %
EDM
1.002 · Top 4.3 %
1.005 · Top 4.1 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

J/ψ meson (1974)

Richter and Ting cited each other.

Burton Richter and Samuel C. C. Ting
D-index
− 0.11 · Bottom 1 %
− 0.64 · Bottom 0 %
EDM
0.99 · Top 5 %
0.97 · Top 7 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

EDM finds many more simultaneous discoveries

Percentiles of EDM (Δ) and the D-index for each pair of papers
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Simultaneous discoveries sit side by side

Richter & Ting
Their papers sit
very close.
Future vectors of 332,518 APS papers
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

… the pattern of independent multiple discoveries in science is in principle the dominant pattern, rather than a subsidiary one. It is the singletons—discoveries made only once in the history of science—that are the residual cases, requiring special explanation.

“Singletons and Multiples in Scientific Discovery”, Robert Merton

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Summary

M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
The D-index fails on
well-known discoveries
Higgs (1964): D = −0.27, Bottom 0.1 %
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
The D-index fails on
well-known discoveries
Higgs (1964): D = −0.27, Bottom 0.1 %
EDM keeps continuity
A large query-key gap marks a discontinuity
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
The D-index fails on
well-known discoveries
Higgs (1964): D = −0.27, Bottom 0.1 %
EDM keeps continuity
A large query-key gap marks a discontinuity
EDM matches human judgment
Odds ratio 1.23, against 1.03 for the D-index
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
The D-index fails on
well-known discoveries
Higgs (1964): D = −0.27, Bottom 0.1 %
EDM keeps continuity
A large query-key gap marks a discontinuity
EDM matches human judgment
Odds ratio 1.23, against 1.03 for the D-index
EDM finds
simultaneous discoveries
Their papers sit close in the embedding
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

Future work: the same quantification elsewhere

  • Legal documents and patents
  • Mobility networks
  • Other embeddings, such as text
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).
CompleNet 2027
Rochester, NY · March 9–12, 2027
complenet.github.io
Read the paper
Science Advances
12, eadx3420 (2026)
Web: skojaku.github.io
@skojaku.bsky.social
skojaku@binghamton.edu
M. Kim, S. Kojaku, Y.-Y. Ahn. Uncovering simultaneous scientific breakthroughs with a robust measure of disruptiveness. Science Advances 12, eadx3420 (2026).

The paper behind this talk. Ask the room how they would measure that a paper is disruptive.

Opening: the 1989 film imagined 2015. Smart glasses, video calls and flat screens are now ordinary.