Crowd Science in Math

Source: https://www.groton.k12.ct.us/

Carl Friedrich Gauss said that “mathematics is the queen of sciences”[1] because it is not motivated by applications in other fields of sciences but is vastly applied to them. Since mathematics is a “pure” science[2] the process of discovery in it is for the most part enclosed within a single individual researcher or a group of researchers. In this article I would like to explore the Polymath Project and the implications of how it has changed the way of doing mathematics. More specifically I would like to touch upon the question of how can crowd science become a tool for solving the most challenging (mathematical) problems?

Citizen science is overall described as scientific research that engages non-professionals in science in an active manner to work collectively on a scientific problem. One prominent form of citizen science is crowd science defined by Franzoni and Sauermann (2014) “as research that is characterised by two features: participation in a project is open to a wide base of potential contributors’ and ‘intermediate inputs such as data or problem solving algorithms are made openly available”.[3]

Scheliga at al. (2016) define the areas of application for crowd science to “be both a way of enhancing citizen participation in science through technology and a mechanism for exploiting the crowd to perform simple and repetitive tasks”[4]. Hochachka et al. (2012) and Dickinson et al. (2010) pursue the utilitarian perspective regard crowd science and describe it as a “method for collecting data or as a tool for science communication”. Without doubting all of the above mentioned researchers  presume that while crowd science yields tangible results, its impact on the way how professional scientists relate to non-professionals stays rather limited.[5][6]

I would like to argue that crowd science can be successfully utilized to solve the most challenging mathematical challenges. For this purpose, I will be exploring the Polymath Project set up by Sir Thomas Gowers in January 2009. The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. The project began in January 2009 on Tim Gowers' blog when he posted a problem and asked his readers to post partial ideas and partial progress toward a solution.

Sir Thomas Gowers described the reason of pursuing this way of solving the mathematical problem in his blog in this way: “Of course, one might say, there are certain kinds of problems that lend themselves to huge collaborations. But my question is a different one. What about the solving of a problem that does not naturally split up into a vast number of subtasks?”[7] He continues his thought by stressing the opportunity of turning away from closed collaboration in isolation to using an online discussion so that the researcher would not “spend a month thinking hard about the problem and then come back and write ten pages about it. Rather, you would contribute ideas even if they were undeveloped and/or likely to be wrong”.[8]

Sir Timothy Gowers

In this way Polymath allows a conversation on the mathematical problem proceed at a prompt but comfortable pace. A simple illustration explains how this happens: If a researcher can only transmit information through publication in journal articles, then according to Sir Timothy Gowers he “misses out on a lot of very useful informal thinking that would not be suitable for publication”[9], since he or she has to “wait a very long time for somebody to polish their ideas and get them into publishable form”[10]. Another possible solution to get round this situation is to have oral conversations with people, but mathematics is a scientific discipline that sometimes it is very hard to carry on via a conversation.

Collaboration in online space forms the unit of conversation as two or three paragraphs. Such linguistic units can be consumed , which can either be relatively easily consumed and understood “after a small amount of thought – far less than is needed for digesting a typical journal article” [11]. Another benefit online collaboration has to offer is that researchers can submit ideas in an inexact or incomplete form, get feedback from other participants, and then either leave behind these ideas or cultivate them.

Since Polymath Projects takes place online the people who decide to take part in the project are not pre-selected which has proven to be a very effective mechanism. Since the contributors are self-selected there is no need to go around looking for enthusiastic researchers. Sir Timothy Gowers described it in the following manner: “experience has shown that some of the most valuable contributors are people I would never have thought of approaching, or in some cases people I had not even heard of.”[12]

There is another efficiency gain to using online platform to run projects like Polymath. When contributors collaborate online they can choose which roles they are most effective in and use them for the overall success of the projects. This does not directly relate to their professional specialization but rather to the role they take in the process of collaboration, for instance, producing ideas, assessing potential usefulness of submitted ideas, making existing ideas more precise, summarizing what has been said so far, reformulating ideas, and so on.

Polymath Project was a complete success that resulted in solving one of the most challenging mathematical problems. This success accelerated the notion of using crowd science or open science in changing the way most difficult scientific disciplines are approached where “the entire discovery process, and not just some paper that summarizes (and to a large extent conceals) it at the end, is out in the open”. [13] The striking success of the first Polymath Project demonstrated that crowd science could become a new way of doing mathematics and other fundamental sciences.  However, the following Polymath Projects have not proved to be as successful in solving the most challenging mathematical problems. It indicates that while crowd science is an important tool for scientific collaboration, the way it is conducted still needs orchestration both in terms of platforms and organizational process. Clearly one could say that Polymath projects will occupy an important niche in scientific discovery but they will not dominate the way of doing mathematical research.

Source: http://bullseyestrategy.com/growing-a-small-business-the-art-of-perseverance/

Using the success of the Polymath Project MIT has launched and sponsored a "Crowdmath" project in collaboration with the Art of Problem Solving. This project is built upon the same idea of the Polymath project that massive collaboration in mathematics is possible and possibly quite fruitful. However, this is specifically aimed at only high school and college students with a goal of creating "a specific opportunity for the upcoming generation of math and science researchers."[14] The problems are original research and unsolved problems in mathematics. All high school and college students from around the world with advanced background of mathematics are encouraged to participate. Older participants are welcomed to participate as mentors and encouraged not to post solutions to the problems. The first Crowdmath project began on March 1, 2016.

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[1] https://en.wikiquote.org/wiki/Carl_Friedrich_Gauss

[2] http://www.richardpoynder.co.uk/Timothy_Gowers.pdf (page 7)

[3] Franzoni C, Sauermann H (2014) Crowd science: The organization of scientific research in open collaborative projects. Research Policy 43(1): 1–20. Google Scholar, page 1.

[4] http://journals.sagepub.com/doi/full/10.1177/0963662516678514

[5] Hochachka WM, Fink D, Hutchinson RA, Sheldon D, Wong W-K, Kelling S (2012) Data-intensive science applied to broad-scale citizen science. Trends in Ecology & Evolution 27(2): 130–137. Google Scholar Medline.

[6] Dickinson JL, Zuckerberg B, Bonter DN (2010) Citizen science as an ecological research tool: Challenges and benefits. Annual Review of Ecology, Evolution, and Systematics 41(1): 149–172. Google Scholar CrossRef

[7] https://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/

[8] https://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/

[9] http://www.richardpoynder.co.uk/Timothy_Gowers.pdf

[10] http://www.richardpoynder.co.uk/Timothy_Gowers.pdf

[11] http://www.richardpoynder.co.uk/Timothy_Gowers.pdf

[12] http://www.richardpoynder.co.uk/Timothy_Gowers.pdf

[13] http://www.richardpoynder.co.uk/Timothy_Gowers.pdf

[14] https://artofproblemsolving.com/polymath