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.

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

[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.

[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

Hi Natalia! I really enjoyed reading your post, however, i have several critical remarks: it would have been even better with a conclusion or a summarising discussion of the insights that you gain. You are also not revealing anything about your motivation to find out about crowdsourcing in math, which would have enriched the reading a lot. Last but least, it would have been important to answer the questions that you pose in the abstract and discuss how this is related to an overall idea of openness in math or science in general.

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DeleteAnd I forgot to say: mentioning "pure science" would need more explanation and context!

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