Editing Good Will Hunting (section)

==Mathematics==
In an early version of the script, Will Hunting was going to be a physics prodigy, but Nobel Laureate in Physics [[Sheldon Glashow]] at Harvard told Damon that the subject should be math instead of physics. Glashow referred Damon to his brother-in-law, [[Daniel Kleitman]], a mathematics professor at MIT. [[Columbia University]] physics and math professor [[Brian Greene]] at the [[Tribeca Film Festival|Tribeca]] [[Alfred P. Sloan Foundation|Sloan]] retrospectively explained that for physics, "Having some deep insight about the universe [⁠ ⁠.⁠ ⁠.⁠ ⁠.⁠ ⁠] typically [⁠ ⁠is ⁠] a group project in the modern era", while "doing some mathematical theorem is a singular undertaking very often".<ref name="bi">{{Cite news |title=One of Matt Damon's Harvard professors gave him a small note that completely changed 'Good Will Hunting' |url=https://www.businessinsider.com/good-will-hunting-matt-damon-harvard-professor-helped-change-movie-2015-4 |url-status=live |archive-url=https://web.archive.org/web/20180510184841/http://www.businessinsider.com/good-will-hunting-matt-damon-harvard-professor-helped-change-movie-2015-4 |archive-date=May 10, 2018 |access-date=May 10, 2018 |work=Business Insider}}</ref><ref name="mit">{{Cite news|url=https://alum.mit.edu/slice/how-mit-professor-helped-good-will-hunting-get-math-right-and-landed-tiny-role-film|title=How an MIT Professor Helped Good Will Hunting Get the Math Right—and Landed a Tiny Role in the Film|access-date=May 10, 2018|last=London|first=Jay|work=MIT Alumni – Slice of MIT|archive-date=October 23, 2020|archive-url=https://web.archive.org/web/20201023051200/https://alum.mit.edu/slice/how-mit-professor-helped-good-will-hunting-get-math-right-and-landed-tiny-role-film|url-status=live}}</ref> Patrick O'Donnell, professor of physics at the [[University of Toronto]], served as the mathematical consultant for the film.<ref>{{cite web |title=Patrick O'Donnell |url=https://www.physics.utoronto.ca/people/memoriam/patrick-odonnell/ |website=Physics University of Toronto |access-date=7 October 2024}}</ref> In the spring of 1997, Damon and Affleck asked Kleitman to "speak math to us" for writing realistic dialogue, so Kleitman invited postdoc [[Tom Bohman]] to join him, giving them a "quick lecture". When asked for a problem that Will could solve, Kleitman and Bohman suggested the unsolved computer science [[P versus NP problem]], but the film used other problems. The plot was inspired by [[George Dantzig]]'s real life story.<ref>{{cite web |last1=Davis |first1=Matt |title=Remembering George Dantzig: The real Will Hunting |url=https://bigthink.com/high-culture/george-dantzig-real-will-hunting/ |website=Big Think |date=March 29, 2019 |access-date=7 October 2024}}</ref>

The main hallway blackboard is used twice to reveal Will's talent, first to the audience, and second to Professor Lambeau. Damon based it on his artist brother Kyle visiting MIT's [[Infinite Corridor]] and writing "an incredibly elaborate, totally fake, version of an equation" on a blackboard, which lasted for months. Kyle returned to Matt, saying that MIT needed those blackboards "because these kids are so smart they just need to, you know, drop everything and solve problems!".<ref>{{Cite news|url=https://news.mit.edu/2016/matt-damon-commencement-address-0603|title=Matt Damon's Commencement address|work=MIT News|access-date=May 11, 2018|archive-date=April 30, 2018|archive-url=https://web.archive.org/web/20180430161028/http://news.mit.edu/2016/matt-damon-commencement-address-0603|url-status=live}}</ref>

===The first blackboard problem===
Near the start of the film, Will sets aside his mop to study a difficult problem posed by Lambeau on the blackboard.<ref>[[Burkard Polster]] & Marty Ross (2012) ''Math goes to the Movies'', [[Johns Hopkins University Press]], page 9, {{ISBN|1-4214-0483-4}}</ref> The problem has to do with intermediate-level [[graph theory]], but Lambeau describes it as an advanced "[[Fourier analysis|Fourier]] system".

To answer the first part of the question, Will chalks up an [[adjacency matrix]]:
:<math>A=\begin{pmatrix} 0 & 1 & 0& 1 \\ 1 & 0 & 2 & 1 \\ 0 & 2 & 0 & 0 \\ 1 & 1 & 0 & 0 \end{pmatrix}.</math> 
To answer the second part, he determines the number of 3-step [[walk (graph theory)|walks]] in the graph, and finds the third power matrix:
:<math>A^3=\begin{pmatrix} 2 & 7 & 2 & 3 \\ 7 & 2 & 12 & 7 \\ 2 & 12 & 0 & 2 \\ 3 & 7 & 2 & 2 \end{pmatrix}.</math>
The third and fourth parts of the question concern [[Generating function#Example: Spanning trees of fans and convolutions of convolutions|generating functions]]. The other characters are astounded that a janitor shows such facility with [[matrix (mathematics)|matrices]].

===The second blackboard problem===
Lambeau subsequently poses a new challenge on the blackboard: state [[Cayley's formula]] and "draw all the homeomorphically irreducible trees with <math>n=10</math>". Will writes eight of the ten trees correctly before Lambeau interrupts.<ref>{{cite web|url=https://www.cantorsparadise.com/the-math-problems-from-good-will-hunting-w-solutions-b081895bf379|title=The Math Problems from Good Will Hunting, w/ solutions|author=Jorgen Veisdal|date=July 31, 2019}}</ref>{{Unreliable source?|date=January 2025|reason=Medium article that falls under [[WP:SELFPUB]]}}