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{{Short description|American mathematician}}
{{Use American English|date=November 2022}}
{{Use mdy dates|date=November 2022}}

{{Infobox person
| name = Daniel Larsen
| image =
| birth_place = Indiana, United States
| known_for = Work on [[Carmichael numbers]]
}}

'''Daniel Larsen''' is an American mathematician known for solving<ref name="Quanta" /> a 1994 conjecture of [[W. R. (Red) Alford|W. R. Alford]], [[Andrew Granville]] and [[Carl Pomerance]] on the distribution of [[Carmichael numbers]], commonly known as [[Bertrand's postulate]] for Carmichael numbers.<ref name="Alford-1994">{{cite journal |author=W. R. Alford |author2=Andrew Granville |author3-link=Carl Pomerance |author3=Carl Pomerance |title=There are Infinitely Many Carmichael Numbers |journal=[[Annals of Mathematics]] |volume=140 |year=1994 |issue=3 |pages=703–722 |doi=10.2307/2118576 |url=http://www.math.dartmouth.edu/~carlp/PDF/paper95.pdf |archive-url=https://web.archive.org/web/20050304203448/http://math.dartmouth.edu/~carlp/PDF/paper95.pdf |archive-date=2005-03-04 |url-status=live|jstor=2118576 |author2-link=Andrew Granville |author-link=W. R. (Red) Alford }}</ref>

==Childhood and education==
Larsen was born in 2004 to [[Indiana University Bloomington]] mathematics professors [[Michael J. Larsen]] and Ayelet Lindenstrauss (sister of [[Elon Lindenstrauss]]), 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.<ref name="Quanta"/> 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]]s and designing his own coin-sorting robot from [[Lego]]. He competed in the [[Scripps National Spelling Bee]] twice while in middle school, though he never made it to the final round.<ref name="Wright">{{cite news |last=Wright |first=Lili |date=August 28, 2022 |title=The Ups And Downs Of Daniel Larsen |url=https://www.indianapolismonthly.com/longform/the-ups-and-downs-of-daniel-larsen |work=[[Indianapolis Monthly]] |access-date=October 15, 2022}}</ref>

While attending [[Bloomington High School South]], he became the youngest accepted contributor to [[The New York Times crossword puzzle|''The New York Times'' crossword puzzle]] in February 2017<ref>{{Cite web |title=Indiana 7th grader becomes crossword puzzle creator |url=https://apnews.com/article/90e1ee72b6d1400db1a754b7a27f8370 |access-date=2022-12-18 |website=AP NEWS |language=en}}</ref> and ended up submitting 11 approved puzzles before his graduation from high school.<ref>{{cite news |last=Shortz |first=Will |date=February 14, 2017 |title=The Youngest Crossword Constructor in New York Times History |url=https://www.nytimes.com/2017/02/14/insider/the-youngest-crossword-constructor-in-new-york-times-history.html |work=[[The New York Times]] |access-date=October 15, 2022}}</ref><ref name="Amien">{{cite news |last=Amien |first=Deb |date=March 3, 2022 |title=60 Seconds With Daniel Larsen |url=https://www.nytimes.com/2022/03/03/crosswords/60-seconds-with-daniel-larsen.html |work=[[The New York Times]] |access-date=October 15, 2022}}</ref> 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,<ref>{{cite news |last=Stephenson |first=Christine |date=March 23, 2022 |title=How an Indiana high school student learned about himself through a mathematical discovery |url=https://www.heraldtimesonline.com/story/news/education/2022/03/23/daniel-larsen-crypto-bloomington-high-school-math-student-cryptography/7076997001/ |work=[[The Herald-Times]] |access-date=October 15, 2022}}</ref><ref name="Wright"/> winning $100,000 to pay for his college tuition.<ref>{{Cite web |date=2022-03-23 |title=High School South student Daniel Larsen wins 100k for math project |url=https://darik.news/massachusetts/high-school-south-student-daniel-larsen-wins-100k-for-math-project/543228.html |access-date=2022-12-18 |website=Massachusetts News |language=en-US}}</ref> In the fall of 2022, he began attending university at the [[Massachusetts Institute of Technology]] (MIT).<ref name="Quanta">{{cite news |last=Cepelewicz |first=Jordana |date=October 13, 2022 |title=Teenager Solves Stubborn Riddle About Prime Number Look-Alikes |url=https://www.quantamagazine.org/teenager-solves-stubborn-riddle-about-prime-number-look-alikes-20221013/ |work=[[Quanta Magazine]] |access-date=October 15, 2022}}</ref>

==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]] in particular. The subsequent strengthening of Zhang’s method by [[James Maynard (mathematician)|James Maynard]] and [[Terence Tao]] 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.<ref name="Quanta"/> In November of the same year, Larsen published a paper titled "Bertrand's Postulate for Carmichael Numbers"<ref>{{cite arXiv |last1=Larsen |first1=Daniel |date=November 5, 2021 |title=Bertrand's Postulate for Carmichael Numbers |class=math.NT |eprint=2111.06963}}</ref> 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 <math>{\displaystyle \delta >0}</math> and sufficiently large <math>{\displaystyle x}</math> in terms of <math>{\displaystyle \delta }</math>, there will always be at least <math>{\displaystyle \exp {\left({\frac {\log {x}}{(\log \log {x})^{2+\delta }}}\right)}}</math> Carmichael numbers between <math>{\displaystyle x}</math> and <math>{\displaystyle x+{\frac {x}{(\log {x})^{\frac {1}{2+\delta }}}}.}</math>

He then emailed a copy of the paper to mathematician [[Andrew Granville]] and others involved in number theory research.<ref name="Quanta"/> The paper was later published in the journal ''[[International Mathematics Research Notices]]''.<ref name="Wright" /><ref name="Larsen 2022 p.">{{cite journal | last=Larsen | first=Daniel | title=Bertrand’s Postulate for Carmichael Numbers | journal=International Mathematics Research Notices | publisher=Oxford University Press (OUP) | date=2022-07-20 | issn=1073-7928 | doi=10.1093/imrn/rnac203 | page=| arxiv=2111.06963 }}</ref>

==References==
{{reflist}}

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

Daniel Larsen (mathematician) - Revision history

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