Putnam Competition
The William Lowell Putnam Mathematical Competition is the principal intercollegiate mathematics competition. Administered by the Mathematical Association of America since the 1930's, it is "constructed to test originality as well as technical competence." The competition consists of twelve problems, divided into a morning session (10:00 AM — 1:00 PM) and an afternoon session (3:00 PM — 6:00 PM). It takes place every year on the first Saturday of December and lunch is provided for all the participants.
These are challenging questions: the median score is typically zero. Well over four thousand students compete every year, from some five hundred institutions. Over one hundred MIT students usually participate.
Prizes
Each competing university pre-selects a team of three students. Both team and individual performances are recognized. The first place team institution wins $25,000, and each member of the winning team wins $1000. Each of the top five individuals win $2500. View the list of prizes.
Problems
Further information, including a list of all problems from past Putnam Competitions, can be found at the William Lowell Putnam Mathematics Competition Directory.
How to participate
2024 Putnam Competition details will be posted here when they are available.
Please email Andre Dixon for questions.
Past Competitions
2023 Competition
The MIT team, consisting of Ankit Bisain, Papon Lapate, Luke Robitaille, placed first.
The Putnam fellows were Ankit Bisain, Jiangqi Dai, Papon Lapate, Brian Liu, andLuke Robitaille.
Eight of the next 11 highest-ranking individuals were MIT students: Mingyang Deng, Sean Li, Derek Liu, Maximus Lu, Zhao Yu Ma, Aloysius Ng, Eric Shen, and Tomasz Slusarczyk.
Seven of the next 10 highest-ranking individuals were MIT students: Reagan Choi, Rishabh Das, Huaye Lin, Brandon Wang, William Wang, Daniel Xia, and Rowechen Zhong.
Honorable Mentions:
Serena An,
Nithid Anchaleenukoon,
Daniel Benavides,
Tomas Cantu,
Tristan Chaang,
Alvin Chen,
Brandon Chen,
Jeffrey Chen,
Raphael Dylan Dalida,
Sanjana Das,
Raymond Feng,
Gopal Goel,
Ram Goel,
Alex Gu,
Thomas Guo,
Daniel Hong,
Vidur Jasuja,
Benjamin Kang,
Aaron Alvarado Kristanto Julistiono,
Daeho Lee,
Zhening Li,
Jason Liu,
Evan Lu,
Kevin Min,
Holden Mui,
Atul Shatavart Nadig,
Gregory Pylypovych,
Pitchayut Saengrungkongka,
Maxwell Sun,
Rui Sun,
Kenta Suzuki,
Alan Vladimiroff,
Mateja Vukelic,
Albert Wang,
Anthony Wang,
Frank Wang,
Jaedon Whyte,
Kevin Wu,
Yichen Xiao,
Edward Xiong,
Daniel Xu,
Justin Yu,
William Yue,
Hankai Zhang,
Ethan Zhou,
Zixiang (Peter) Zhou,
Isaac Zhu, and
Isabella Zhu.
Isabella Zhu was the recipient of the Elizabeth Lowell Putnam prize.
2022 Competition
The MIT team, consisting of Mingyang Deng, Luke Robitaille, and Daniel Zhu, placed first.
The Putnam fellows were Mingyang Deng, Papon Lapate, Brian Liu, Luke Robitaille, and Daniel Zhu.
Nine of the next 11 highest-ranking individuals were MIT students: Vincent Bian, Kevin Liu, Zhao Yu Ma,Holden Mui, Carl Schildkraut, Anton Trygub, Yuxing Xia, Brandon Wang, and Binwei Yan.
Seven of the next 9 highest-ranking individuals were MIT students: Raymond Feng, Daniel Hong, Victor Rong, Pitchayut Saengrungkongka, Tomasz Slusarczyk, Pranjal Srivastava, and William Yue.
Honorable Mentions:
Adam Ardeishar,
Daniel Benavides,
Nikoloz Birkadze,
Ankit Bisain,
Andres Buritica Monroy,
Brandon Chen,
Reagan Choi,
Rishabh Das,
Sanjana Das,
Gopal Goel,
Thomas Guo,
Garrett Heller,
Vincent Huang,
Mohit Hulse,
Vidur Jasuja,
Tianze Jiang,
Benjamin Kang,
Dain Kim,
John Ko,
Aaron Alvarado Kristanto Julistiono,
Daniel Li,
Jason Liu,
Steven Liu,
Kevin Min,
Ritam Nag,
Rishab Parthasarathy,
Gregory Pylypovych,
Brian Reinhart,
Paramuth Samuthrsindh,
Danil Sibgatullin,
Eric Sun,
Joel Junyao Tan,
Colin Tang,
Teimurazi Toloraia,
Noah Walsh,
Albert Wang,
Samuel Wang,
William Wang,
Jaedon Whyte,
Benjamin Wright,
Daniel Xia,
Justin Yu,
Fedir Yudin,
Stan Zhang,
William Zhao,
Rowechen Zhong,
Ziqian Zhong,
Zixiang (Peter) Zhou, and
Isaac Zhu.
Binwei Yan was the recipient of the Elizabeth Lowell Putnam prize.
2021 Competition
The MIT team, consisting of Edward Wan, Shengtong Zhang, and Daniel G. Zhu, placed first.
The Putnam fellows were Andrew Gu, Michael Ren, Edward Wan, Shengtong Zhang, and Daniel G. Zhu.
Nine of the next 10 highest-ranking individuals were MIT students: Ankit Bisain, Tianze Jiang, Dain Kim, Sean J. Li, Brian S. Liu, Kevin J. Liu, Mihir A. Singhal, Noah Walsh, and Rui Yao.
Nine of the next 12 highest-ranking individuals were MIT students: Swapnil Garg, Thomas Guo, Zhao Yu Ma, Holden Mui, Kevin Ren, Victor Rong, Carl Schildkraut, Tristan Shin, and Guanpeng A. Xu.
Honorable Mentions:
Adam Ardeishar, Krit Boonsiriseth, Sanjana Das, Gopal K. Goel, Joseph W. Heerens, Daniel X. Hong, Vincent Huang, Aaron Alvarado K. Julistiono, John S. Ko, Nitin A. Kumar, Saba Lepsveridze, Daniel Li, Unubold Munkhbat, Ritam Nag, Quan M. Nguyen, Misheel Otgonbayar, Alan Peng, Gregory Pylypovych, Timothy Qian, Brian E. Reinhart, Tomasz Slusarczyk, Kenta Suzuki, Colin S. Tang, Vittal Thirumalai, William Wang, Xunjing Wei, Daniel Xu, Zhening Li, Andrew Y. Lin, James H. Lin, Jason Liu, Steven Liu, Jeffrey Lu, Binwei Yan, Andrew Yao, Zi Song Yeoh, Justin Y. Yu, Fedir Yudin, Ethan A. Zahid, and Honglin Zhu.
Dain Kim was the recipient of the Elizabeth Lowell Putnam prize.
2019 Competition
The MIT team, consisting of Ashwin Sah, Shengtong Zhang, and Daniel Zhu, placed first.
The Putnam fellows were Ashwin Sah, Kevin Sun, Yuan Yao, Shengtong Zhang, and Daniel Zhu.
Nine of the next eleven highest ranking individuals were MIT students: Adam Ardeishar, Andrew Gu, Allen Liu, Junyao Peng, Qiuyu Ren, Carl Schildkraut, Mihir Singhal, Rui Yao, and William Zhao.
Eight of the next twelve highest ranking individuals were MIT students: Jiyang Gao, Dain Kim, Tingchun Lin, Daniel Liu, Kevin Liu, Eshaan Nichani, Michael Ren, and Victor Rong.
Raul Alcantara, Vincent Bian, Krit Boonsiriseth, Merrick Cai, Kaan Dokmeci, Swapnil Garg, Vincent Huang, Sebastian Jeon, Aksha Kadaveru, Jeffery Li, Andrew Lin, James Lin, Dylan Liu, Steven Liu, Michael Ma, Srijon Mukherjee, Qi Qi, Car Joshua Quines, Brian Reinhart, Kevin Ren, Mehtaab Sawhney, Tristan Shin, Colin Tang, Michael Tang, Anton Trygub, Saaketh Vedantam, Shihyu Wang, Stanley Wang, Zhuofan Xie, Chris Xu, Guanpeng Xu, Richard Yi, and Hung-Hsun Yu received honorable mentions.
Qi Qi was one of the three winners of the Elizabeth Lowell Putnam Prize.
2018 Competition
The MIT team, consisting of Junyao Peng, Ashwin Sah, Yunkun Zhou, placed second.
The Putnam fellows were Yuan Yao and Shengtong Zhang.
Nine of the next ten highest ranking individuals were MIT students: Jiyang Gao, Andrew Gu, James Lin, Michael Ma, Ashwin Sah, Kevin Sun, Danielle Wang, Hung-hsun Yu and Yunkun Zhou.
Six of the next twelve highest ranking individuals were MIT students: Allen Liu, Junyao Peng, Brian Reinhart, Michael Ren, Mihir Singhal and Zhuofan Xie
Raul Alcantara, Zachary Chroman, Kaan Dokmeci, Swapnil Garg, Andrew He, Calvin Hsu, Brice Huang, Akshaj Kadaveru, Alexander Katz, Andrew Lin, Lingjie Mei, Jeet Mohapatra, Eshaan Nichani, Saranesh Prembabu, Qi Qi, Nikhil Reddy, Qiuyu Ren, Kevin Ren, Maya Sankar, Mehtaab Sawhney, Christopher Shao, Michael Tang, Anton Trygub, Jianqiao Xia, Yinzhan Xu, Chris Xu, Allen Yang and Richard Yi received honorable mentions.
Danielle Wang was the recipient of the Elizabeth Lowell Putnam prize.
2017 Competition
The MIT team, consisting of Allen Liu, Sammy Luo, and Yunkun Zhou, placed first.
The Putnam fellows were Omer Cerrahoglu, Jiyang Gao, Junyao Peng, Ashwin Sah, and Yunkun Zhou.
Five of the next nine highest ranking individuals were MIT students: Andrew He, Brice Huang, Allen Liu, Yuan Yao, and Hung-Hsun Yu.
Seven of the next ten highest ranking individuals were MIT students: Calvin Lee, Yang Liu, Sammy Luo, Linjie Mei, Sung Gi Park, Kevin Sun, and Jianqiao Xia.
Ryan Alweiss, Henrik Boecken, Evan Chen, Calvin Hsu, Aleksa Konstantinov, Michael Kural, Ting-Chun Lin, Peter Mizes, Jeet Mohapatra, Max Murin, Weerachai Neeranartvong, Eshaan Nichani, Nipun Pitimanaaree, Qi Qi, Sushrutha Reddy, Tahsin Saffat, Fransisca Susan, Michael Tang, Danielle Wang, Patrick Wang, and Farrell Eldrian Wu received honorable mentions
2016 Competition
The MIT team, consisting of Robert C. Shen, David H. Yang, and Yunkun Zhou, placed fourth.
The Putnam fellow was Yunkun Zhou.
Three of the next ten highest ranking individuals were MIT students: Jiyang Gao, Allen X. Liu, and Sammy Y. Luo.
Seven of the next ten highest ranking individuals were MIT students: Evan Chen, Andrew He, Hyun Sub Hwang, Eshaan Nichani, Mark A. Sellke, Robert C. Shen, and Lingfu Zhang.
Ryan N. Alweiss, Yibo Gao, Brian H. Gu, Meghal Gupta, Brice Huang, Kritkorn Karntikoon, Samuel Korsky, Michael J. Kural, Calvin J. Lee, Justin K. Lim, Ting-Chun Lin, Yang Liu, Weerachai Neeranartvong, Sung Gi Park, Tahsin Saffat, Sean Shi, Kevin Sun, Suchan Vivatsethachai, Jianqiao Xia, David H. Yang, and Kevin Zhou received honorable mentions
2015 Competition
The MIT team, consisting of Mark A. Sellke, Bobby C. Shen, and David H. Yang, placed first.
The Putnam fellows were David H. Yang and Yunkun Zhou.
Four of the next ten highest ranking individuals were MIT students: Evan Chen, Sammy Luo, Bobby Shen, and Tianyou Zhou.
Three of the next ten highest ranking individuals were MIT students: Yang Liu, Saranesh Prembabu, and Hengyun Zhou.
Matthew W. Babbitt, Matthew S. Brennan, Brian Chen, Jingwen Chen, Ernest Y. Chiu, Alexander J. Clifton, Yibo Gao, Brice Huang, Kritkorn Karntikoon, Alexander R. Katz, Samuel Korsky, Jun Jie Joseph Kuan, Kuan-yu Lin, Patrick H. Liscio, Yutao Liu, Eric L. Mannes, Max K. Murin, Weerachai Neeranartvong, Sung Gi Park, Nipun Pitimanaaree, Mark A. Sellke, Ashwath Thirumalai, Victor Y. Wang, and Kevin Zhou received honorable mentions.
Danielle Wang was the recipient of the Elizabeth Lowell Putnam prize.
2014 Competition
The MIT team, consisting of Mitchell M. Lee, Zipei Nie, and David H. Yang, placed first.
The Putnam fellows were Zipie Nie, Mark A. Sellke, Bobby C. Shen, David H. Yang and Lingfu Zhang.
Five of the next ten highest ranking individuals were MIT students: Ofer Grossman, Benjamin Gunby, Mitchell M. Lee, Nat Sothanaphan, and Victor Y. Wang.
Six of the next eleven highest ranking individuals were MIT students: Eunsoo Jee, Yutao Liu, Sammy Y. Luo, Anderson S. Wang, Hengyun Zhou, and Tianyou Zhou.
Omer Cerrahoglu, Yongyi Chen, Alexander J. Clifton, Vahid Fazel-Rezai, Yibo Gao, Yuzhou Gu, Benjamin J. Kraft, Weerachai Neeranartvong, Edward S. Park, Nipun Pitimanaaree, Sagnik Saha, Jeffrey D. Shen, Gaurav J. Singh, Lawrence J. Sun, Jonahtan B. Tidor, and Dai Yang received honorable mentions.
2013 Competition
The MIT team, consisting of Benjamin Gunby, Mitchell Lee, and Zipei Nie, placed first.
The Putnam fellows were Mitchell Lee, Zipei Nie, Bobby Shen, and David Yang.
Six of the next fourteen highest ranking individuals were MIT students: Brian Hamrick, Travis Hance, Qinxuan Pan, Ka Yu Tam, Szu-Po Wang, and Tianyou Zhou.
Five of the next six highest ranking individuals were MIT students: Matthew Brennan, Michael Cohen, Benjamin Gunby, Jiaoyang Huang, and Victor Wang.
Dhroova Aiylam, Joshua Alman, Robi Bhattacharjee, Yongyi Chen, Ping Ngai Chung, Alexander Cole, Carlos Cortez, Vlad Firoiu, Yibo Gao, Supanat Kamtue, Carl Lian, Jeffrey Shen, Lawrence Sun, Jonathan Tidor, Max Timmons, Georgios Vlachos, Tianqi Wu, Patrick Yang, Qian Yu, and Alex Zhu received honorable mentions.
2012 Competition
The MIT team, consisting of Benjamin Gunby, Brian Hamrick, and Jonathan Schneider placed second.
The Putnam fellows were Benjamin Gunby, Mitchell Lee and Zipei Nie.
Five of the next eleven highest ranking individuals were MIT students: Whan Ghang, Sung Park, Szu-Po Wang, Tianyou Zhou, and Alex Zhu.
Four of the next nine highest ranking individuals were MIT students: Joshua Alman, Holden Lee, Jeffrey Shen, and Ka Yu Tam.
Robi Bhattacharjee, Justin Brereton, Lucas Camelo Sa, Kevin Chen, Alexander Cole, Michael Cohen, Zheng Fan, Brian Hamrick, Jiaoyang Huang, Hyun Hwang, Kuan-Yu Lin, Eric Mannes, Ofir Nachum, Jonathan Schneider, Brandon Tran, Mark Velednitsky, Anderson Wang, Anthony Wang, Michael Wu, George Xing, Kerry Xing, and Dai yang received honorable mentions.
2011 Competition
The MIT team, consisting of Vlad Firoiu, Colin Sandon, and Jacob Steinhardt placed fifth.
After the top five individuals, three of the next nine highest ranking individuals were MIT students: Benjamin Gunby, Brian Hamrick, and Jonathan Schneider.
Four of the next ten highest ranking individuals were MIT students: Vlad Firoiu, Vladislav Kontsevoi, Zipei Nie, and David Rolnick.
Noah Arbesfeld, Paul Christiano, Cesar Cuenca, Akashnil Dutta, Whan Ghang, Travis Hance, Yangzhou Hu, Jiaoyang Huang, Hyun Hwang, Tian-Yi Jiang, Supanat Kamtue, Reed Lafleche, Holden Lee, Timothy Reynolds, Colin Sandon, Jeffrey Shen, Xiaolin Shi, Warut Suksompong, Bogdan Veklych, Mark Velednitsky, Tianqi Wu, and Kerry Xing received honorable mentions.
2010 Competition
The MIT team, consisting of Sergei Bernstein, Whan Ghang, and Jacob Steinhardt placed second.
The Putnam fellows were Yu Deng and Colin Sandon.
Two of the next nine highest ranking individuals were MIT students: Vlad Firoiu and Jacob Steinhardt.
Three of the next ten highest ranking individuals were MIT students: Sergei Bernstein, Whan Ghang, and Alexandr Zamorzaev.
John Berman, Yu Cheng, Paul Christiano, Brian Hamrick, Travis Hance, Daniel Li, Ofir Nachum, David Rolnick, David Rush, Krishanu Sankar, Jonathan Schneider, Minseon Shin, Anthony Wang, Yinghui Wang, Chiu Wai Wong, and George Xing received honorable mentions.
Yinghui Wang was the recipient of the Elizabeth Lowell Putnam prize.
2009 Competition
The MIT team, consisting of Qingchun Ren, Bohua Zhan, and Yufei Zhao, placed first.
The Putnam Fellows for this year were Qingchun Ren and Yufei Zhao.
Three of the next ten highest ranking individuals were MIT students: Sergei Bernstein, Jacob Steinhardt, and Bohua Zhan.
Two of the next ten highest ranking individuals were MIT students: Panupong Pasupat and Colin Sandon.
Aleksandr Arkhipov, John Berman, Ivan Borsenco, Gabriel Bujokas, Paul Christiano, Yu Deng, Rishi Gupta, Jason Hoch, Shaunak Kishore, Holden Lee, Tony Liu, Ye Luo, Henrique Oliveira Pinto, David Rolnick, David Rush, Krishanu Shankar, Jonathan Schneider, Xiaolin (Danny) Shi, Cory Smith, and Qiaochu Yuan received honorable mentions.
2008 Competition
The MIT team, consisting of Qingchun Ren, Xuancheng Shao, and Yufei Zhao placed third after Harvard University and Princeton University.
The Putnam Fellows for this year were Bohua Zhan and Yufei Zhao.
Three of the next eleven highest ranking individuals were MIT students: Qingchun Ren, Colin Sandon, and Jacob Steinhardt.
Two of the next nine highest ranking individuals were MIT students: Thomas Belulovich, and Gabriel Bujokas.
Hansheng Diao, Michael Forbes, Andrei Frimu, Jeremy Hahn, Shaunak Kishore, Tony Liu, Ye Luo, Haitao Mao, Kevin Modzelewski, Thanasin Nampaisarn, Eric Price, Anand Rajagopalan, Krishanu Sankar, Xuancheng Shao, Jason Trigg, and Alexandr Zamorzaev received honorable mentions.
2007 Competition
The MIT team, consisting of Hangsheng Diao, Eric C. Price, and Yufei Zhao, placed third, after Harvard University and Princeton University.
Two of the Putnam Fellows -- this year the six highest ranked individuals -- were MIT students: Qingchun Ren and Xuancheng Shao.
Three of the next ten highest ranking individuals were MIT students: Oleg Goldberg, Yuncheng Lin, and Yufei Zhao.
Two of the next eight highest ranking individuals were MIT students: Anand R. Deopurkar and Anders H. Kaseorg.
Thirteen of the next fifty highest ranking individuals were MIT students: Aleksandr Arkhipov, Thomas D. Belulovich, Gabriel T. Bujokas, Hansheng Diao, Nate J. Ince, Hyun Soo Kim, Sungyoon Kim, Thomas J. Mildorf, Kevin P. Modzelewski, Thanasin Nampaisarn, Eric C. Price, Jason A. Trigg, Alexandr Zamorzaev, and Bohua Zhan.
2006 Competition
The MIT team, consisting of Oleg Goldberg, Daniel Kane, and Kuat Yessenov, placed third, after Princeton University and Harvard University.
Three of the Putnam Fellows — the five highest ranked individuals — were MIT students: Hansheng Diao, Daniel Kane, and Yufei Zhao.
Six of the next ten highest-ranking individuals were MIT students: Timothy Abbott, Anders Kaseorg, Sungyoon Kim, Yuncheng Lin, Kevin Modzelewski, and Eric Price.
Four of the next eleven highest-ranking individuals were MIT students: Shinn-Yih Huang, Matthew Ince, Thomas Mildorf, and Xuancheng Shao.
Thirteen of the next fifty-two highest-ranking individuals were MIT students: Oleg Goldberg, John Kim, Maria Monks, Albert Ni, Anand Rajagopalan, Shubhangi Saraf, Nikhil Savale, Charmaine Sia, Dimitar Simenov, Jason Trigg, Ilya Tsekov, Kuat Yessenov, and You Zhou.
2005 Competition
The MIT team, consisting of Timothy Abbott, Vladimir Barzov and Daniel Kane, placed fourth, after Harvard University, Princeton University, and Duke University.
Three of the Putnam Fellows — the six highest ranked individuals — were MIT students: Oleg Golberg, Matthew Ince, and Daniel Kane.
Six of the next ten highest-ranking individuals were MIT students: Timothy Abbott, Anders Kaseorg, Sungyoon Kim, Yuncheng Lin, Kevin Modzelewski, and Eric Price.
Four of the next ten highest-ranking individuals were MIT students: Thomas Belulovich, Thanasin Nampaisarn, Eric Price, and Kuat Yessenov.
Fourteen of the next fifty-one highest-ranking individuals were MIT students: Timothy Abbott, Boris Alexeev, Jongmin Baek, Po-Ning Chen, Anand Deopurkar, Nathaniel Ince, Pramook Khungurn, Sungyoon Kim, Joshua Lim, Yuncheng Lin, Thomas Mildorf, Virgil Petrea, Matthew Thibault, and David Vincent.
2004 Competition
The MIT team, consisting of Reid Barton, Daniel Kane, and Emanuel Stoica, placed first.
Three of the Putnam Fellows — the five highest ranked individuals were MIT students: Reid Barton, Vladimir Barzov, and Daniel Kane.
One of the next ten highest-ranking individuals was an MIT student: Timothy Abbott.
Three of the next eleven highest-ranking individuals were MIT students: Oleg Golberg, Daniel Gulotta, and Zhongtao Wu.
Thirteen of the next fourty-eight highest-ranking individuals were MIT students: Boris Alexeev, Po-Ning Chen, Anand Deopurkar, Adam Donovan, Karola Meszaros, Nizameddin Ordulu, Virgil Petrea, Shubhangi Saraf, Steven Sivek, Emanuel Stoica, Matthew Thibault, Ilya Tsekov, and David Vincent.
2003 Competition
The MIT team, consisting of Reid Barton, Daniel Kane, and Yevgeny Zaytman, placed first.
Two of the Putnam Fellows — the five highest ranked individuals — were MIT students: Reid Barton and Daniel Kane.
Two of the next ten highest-ranking individuals were MIT students: David Prichard and Emanuel Stoica.
Three of the next ten highest-ranking individuals were MIT students: Vladimir Barzov, Zhongtao Wu, and Yevgeny Zaytman.
Twelve of the next forty-three highest-ranking individuals were MIT students: Timothy Abbott, Nikolay Andreev, Punyashloka Biswal, Po-Ning Chen, Maksym Fedorchuk, Prumook Khungurn, Sean Markan, Virgil Petrea, Shubhangi Saraf, Nikhil Savale, David Shin, and Gary Sivek.