Researchers / independent engineers · Science/Research · milestone at age 18 ·Professionally distinctive
Selected age-relative milestone · age 18
At age 17, proved Bertrand's postulate for Carmichael numbers, resolving a 1994 conjecture of Alford, Granville, and Pomerance, while still a high school student.
Larsen grew up in Bloomington, Indiana with both parents serving as mathematics professors at Indiana University. His father hosted a math circle that Larsen attended from age four. After watching a documentary about Yitang Zhang, he became interested in number theory and, after roughly 300 hours of work, proved a result about Carmichael numbers that had eluded mathematicians for decades.
Born 2003 in Bloomington, Indiana; both parents are mathematicians at Indiana University (mother Ayelet Lindenstrauss, father Michael Larsen). Started designing crossword puzzles in middle school and became the youngest NYT crossword constructor at age 13.
Current position (2026)
Undergraduate student at MIT studying mathematics; Regeneron Science Talent Search 4th place winner (2022); Morgan Prize Honorable Mention (2026).
Where the conditions came from
Three sources, read side by side
Each is placed on a −1 to 3 scale from documented evidence, and the three are never added together. A combined total would rank Daniel Larsen against other people. Held apart, they explain why this path ran differently from another one—which is the only comparison this project supports.
The marble itself
What they brought
+3Tailwind
-10+1+2+3
What capability, drive, or early skill is documented in the person rather than their surroundings?
Attended math circle from age 4. Asked philosophical questions about infinity at 3. Youngest NYT crossword publisher at 13. Proved Bertrand's postulate for Carmichael numbers at 17, resolving a 1994 conjecture. Regeneron STS 4th place. Prodigy-level ability.
Where it was dropped
What they were handed
+3Tailwind
-10+1+2+3
What money, family standing, network, or permission was already in place before the work began?
Both parents are mathematics professors at Indiana University. Mother is the sister of Fields Medalist Elon Lindenstrauss. Father hosted a math circle that Daniel attended from age 4. Rare, trajectory-changing family-domain immersion.
The shape of the track
What surrounded them
+2Tailwind
-10+1+2+3
What place, timing, institution, or peer group made the next step available?
Father's math circle from age 4. Indiana University academic environment. MIT for undergraduate. Grew up immersed in an academic mathematical household with direct access to elite mathematicians.
A −1 is a documented headwind, not a missing value; a 0 means the sources record nothing notable either way. Annotation confidence: High. These are analyst readings of what the sources record, not measurements of merit, talent, or effort. The twenty-two scored dimensions remain available inside the deeper research detail.
What moved through the conditions
Perseverance and luck stay visible—not scored.
Documented perseveranceNot documented in the reviewed biographical summaries.
Silence in a biography is not evidence that perseverance was absent.
Luck and unobserved varianceNo discrete luck event is documented in the reviewed biographical summaries.
A successful-only archive cannot recover all encounters, avoided setbacks, or alternative outcomes.
Open the legacy 22-field research annotation
How this path compounded
01 Starting advantages
8/24 starting-position score
Strongest documented signals: Parent / family domain, Family financial platform, Elite institution pipeline.
Describes the starting position, not what the person later made of it.
Cohort percentile: 74
02 Built or converted leverage
12/25 multiplying-capacity score
Strongest observed levers: Domain proximity, Started serious reps before 20, Prior reps.
Measures what was present, not whether it was inherited, earned, self-built, external, or mixed.
Cohort percentile: 37
03 Compounding trajectory
6 documented steps
The timeline below shows the sequence of work and transitions around the selected early milestone. It is evidence of a path, not proof that every step was necessary.
Milestone at age 18
04 Observed career standing
T4 · Specialist-known
Notable, but primarily known within a niche. The tier summarizes documented career recognition through the data cutoff—not Daniel Larsen's worth or future potential.
Each non-zero lever gets a best-supported origin, evidence signals, and confidence. Unresolved is the honest default when the biography cannot distinguish self-built, advantage-enabled, earned, external, or mixed.
Started serious reps before 201/1
Advantage-enabledmedium confidence
One or more documented starting advantages plausibly enabled this lever.
Parent / family domain (2/2)Rare early tools (1/2)Dedicated mentor / coach (1/2)Elite institution pipeline (1/2)
Domain proximity2/2
Advantage-enabledmedium confidence
One or more documented starting advantages plausibly enabled this lever.
Direct domain exposure (1/2)Parent / family domain (2/2)Elite institution pipeline (1/2)
Prior reps2/3
Advantage-enabledmedium confidence
One or more documented starting advantages plausibly enabled this lever.
Parent / family domain (2/2)Rare early tools (1/2)Dedicated mentor / coach (1/2)Elite institution pipeline (1/2)
Scarce skill depth2/3
Advantage-enabledmedium confidence
One or more documented starting advantages plausibly enabled this lever.
Parent / family domain (2/2)Rare early tools (1/2)Dedicated mentor / coach (1/2)Elite institution pipeline (1/2)
Concentration intensity2/3
Advantage-enabledmedium confidence
One or more documented starting advantages plausibly enabled this lever.
Family financial platform (1/2)Dedicated mentor / coach (1/2)
Capital safety1/2
Advantage-enabledmedium confidence
One or more documented starting advantages plausibly enabled this lever.
Family financial platform (1/2)Elite institution pipeline (1/2)
Elite ecosystem network1/3
Advantage-enabledmedium confidence
One or more documented starting advantages plausibly enabled this lever.
Parent / family domain (2/2)Elite institution pipeline (1/2)
Structural wave / timing1/3
Externalmedium confidence
A structural wave is external to the person, even when their position improved access to it.
No decisive linked signal
This is a bounded inference from the current annotations—not a claim about private effort, merit, or the percentage of Daniel Larsen's outcome attributable to any origin.
Luck is not a leftover score.
Structural luck, Encounter luck, Event luck, Outcome variance can change every arrow in the path. This successful-only dataset cannot observe the near-identical paths that did not break through, so luck stays visible and unscored.
Within Researchers / independent engineers, Daniel Larsen's starting-advantage total is at the 74th percentile. Separately, their built or converted leverage total is at the 37th percentile. Other T4 profiles average 5.9 / 24 starting advantage and 10.4 / 25 leverage. Similar scores appear in other tiers, so these figures describe positioning—not a cause.
Trajectory
2017 · age 14
Youngest NYT crossword constructor
Became the youngest accepted contributor to The New York Times crossword puzzle in February 2017 at age 13, ultimately submitting 11 approved puzzles.
2021 · age 18
Proved Bertrand's postulate for Carmichael numbers
Published a paper on arXiv in November 2021 proving Bertrand's postulate for Carmichael numbers, resolving a 1994 conjecture of Alford, Granville, and Pomerance, while still a high school student.
2022 · age 19
Regeneron Science Talent Search 4th place
Became a finalist in the 2022 Regeneron Science Talent Search for his Carmichael numbers research, winning 4th place and $100,000 for college tuition.
2022 · age 19
Enrolled at MIT
Began undergraduate studies in mathematics at the Massachusetts Institute of Technology in the fall of 2022.
2023 · age 20
Paper published in IMRN
His paper 'Bertrand's Postulate for Carmichael Numbers' was published in the International Mathematics Research Notices journal.
2026 · age 23
Morgan Prize Honorable Mention
Received an Honorable Mention for the 2026 Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student.
Primary leverage engine
Technical depth
Scarce technical / intellectual depth
Secondary engine
Family domain transfer
Built/converted leverage
12 / 25
evidence: High
Built or converted leverage
Multiplying capacity documented later in the path. Measures what was present, not whether it was inherited, earned, self-built, external, or mixed.
Started serious reps before 20
1/1
Prior reps
2/3
Scarce skill depth
2/3
Native distribution
0/3
Elite ecosystem network
1/3
Complementary team
0/2
Structural wave / timing
1/3
Concentration intensity
2/3
Capital safety
1/2
Domain proximity
2/2
Starting-advantage scores (0–2 each)
Access or conditions documented near the beginning of the path. Zero means "no clear evidence in reviewed sources," not "advantage was absent."
Family financial platform
1/2
Parent / family domain
2/2
Inherited audience / network
0/2
Elite institution pipeline
1/2
Frontier geography
0/2
Rare early tools
1/2
Dedicated mentor / coach
1/2
Exceptional peer / cofounder
0/2
Early online platform
0/2
Direct domain exposure
1/2
Prodigy / innate ability
1/2
Adversity / constraint catalyst
0/2
Family context
Born to Indiana University Bloomington mathematics professors Michael J. Larsen and Ayelet Lindenstrauss; grew up in Bloomington, Indiana in an academic household.
Parent / family domain
Both parents are mathematics professors at Indiana University; his mother Ayelet Lindenstrauss is the sister of Fields Medalist Elon Lindenstrauss; father hosted a math circle for neighborhood children that Larsen attended from age four.
Archetype & tags
Family-domain apprenticeshipparents mathematiciansmath circle from age 4academic householdIndiana Universityself-studyYitang Zhang inspiration
Evidence summary
Larsen's both parents are mathematics professors at Indiana University, providing an exceptionally strong family-domain advantage. His father hosted a math circle that Larsen attended from age four, and his mother is the sister of Fields Medalist Elon Lindenstrauss. He grew up immersed in an academic mathematical household, which gave him direct domain exposure and early mentorship. After watching a documentary about Yitang Zhang, he spent roughly 300 hours proving a result about Carmichael numbers that had eluded mathematicians since 1994, while still in high school.