Daniel Larsen is an American mathematician known for solving a 1994 conjecture of W. R. Alford, Andrew Granville and Carl Pomerance on the distribution of Carmichael numbers, commonly known as

Bertrand's postulate In number theory, Bertrand's postulate is a theorem stating that for any integer n > 3, there always exists at least one prime number p with :n < p < 2n - 2. A less restrictive formulation is: for every

n > 1

, there is always ...

for Carmichael numbers.

Childhood and education

Larsen was born in 2004 to two Indiana University Bloomington mathematics professors Michael J. Larsen and Ayelet Lindenstrauss (sister of

Elon Lindenstrauss Elon Lindenstrauss ( he, אילון לינדנשטראוס, born August 1, 1970) is an Israeli mathematician, and a winner of the 2010 Fields Medal. Since 2004, he has been a professor at Princeton University. In 2009, he was appointed to Profess ...

) and grew up in Bloomington, Indiana. He had a strong interest in mathematics as a child, inspired by the mathematician background of both his parents. His father hosted a math circle when he was younger that taught math on the weekend to kids in the neighborhood and Larsen attended despite being only four years old. He also had a strong interest in other projects, learning violin at age 5 and piano at age 6, along with practicing solving larger configurations of

Rubik's Cube The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...

s and designing his own coin-sorting robot from

Lego Lego ( , ; stylized as LEGO) is a line of plastic construction toys that are manufactured by The Lego Group, a privately held company based in Billund, Denmark. The company's flagship product, Lego, consists of variously colored interlocking ...

. He competed in the

Scripps National Spelling Bee The Scripps National Spelling Bee (formerly the Scripps Howard National Spelling Bee and commonly called the National Spelling Bee) is an annual spelling bee held in the United States. The bee is run on a not-for-profit basis by The E. W. Scri ...

twice while in middle school, though he never made it to the final round. While attending Bloomington High School South, he became the youngest accepted contributor to ''The New York Times'' crossword puzzle in February 2017 and ended up submitting 11 approved puzzles before his graduation from high school. He applied to and became a finalist in the 2022 Regeneron Science Talent Search for his published research on Carmichael numbers and ultimately won 4th place in the competition, winning $100,000 to pay for his college tuition. In the fall of 2022, he began attending university at the Massachusetts Institute of Technology (MIT).

Career and research

During his teenage years, after watching a documentary about Yitang Zhang, Larsen became interested in number theory and the

twin primes conjecture A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin pr ...

in particular. The subsequent strengthening of Zhang’s method by James Maynard and

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

not long after rekindled his desire to better understand the math involved. He found it too complex at that time, and it wasn't until after reading a paper in February 2021 on Carmichael numbers that he gained insight on the fundamentals of the problem. In November of the same year, Larsen published a paper titled "Bertrand's Postulate for Carmichael Numbers" on the open access repository arXiv that made a more consolidated proof of Maynard and Tao's postulate but involving Carmichael numbers into the twin primes conjecture and attempting to shorten the distance between the numbers per Bertrand's postulate. He concretely showed that for any

and sufficiently large

in terms of

, there will always be at least

Carmichael numbers between

and

He then emailed a copy of the paper to mathematician Andrew Granville and others involved in number theory research. The paper was later published in the journal '' International Mathematics Research Notices''.

References

{{DEFAULTSORT:Larsen, Daniel Living people 21st-century American mathematicians Number theorists Mathematicians from Indiana People from Bloomington, Indiana 2004 births