2024 MathWorks Math Modeling Challenge - A Tale of Two Crises

It has been my pleasure to once again register our math team at CAVA to participate in the M3 Mega Math Challenge. I am happy to announce that this year - for the first time - our team was successful in triage. Our students are to be commended for this achievement. I must also express my congratulations to those students and teams who advanced further, including those who attained finalist, semi-finalist, and honorable mention prizes. In these trying times, it is especially important that the M3 Math Challenge continue in its mission to involve our top high school students in using math modeling to tackle aspects of our current, pressing crises. I would make the case that our country needs more activities of this nature. I would go further yet and declare that this is a model of how we might pivot and redirect our focus away from the excessive standardized Testing, Testing, Testing, and emphasis on Standards, Standards, Standards, and - instead - challenge our students to tackle problems in a way that their results might be utilized by our leaders to improve conditions in this country. Climate change, conversion to electric vehicles, and short- and long-term trends in telecommunication are among the topics from recent years. This year, the topic is that of solving the problem of homelessness in major cities. Here you go, young scholars- take the raw data on population and homeless figures, extrapolate a mathematical model encompassing the next 50 years, and give us the Answer to homelessness. Good luck! Ah - one of the crises facing humanity throughout this planet - homelessness. Though we often think of it as a modern urban issue, we find references to this "problem" dating as far back as the early 17th century Many of us recall having read, as required high school reading, "A Modest Proposal," the satirical essay by Irish author Jonathan Swift, suggesting that utilizing Irish babies as a food source (more bluntly, resorting to cannibalism) would be a logical remedy to poverty in Ireland. This particular essay may be especially worthwhile for my fellow left-brained readers - mathematicians, scientists, economists - who resort primarily to quantitative, math-based considerations, perhaps at the expense of missing aspects of the situation which someone with "common sense" would consider obvious. Hence, as referenced in previous posts, we have the stereotype of the "absent-minded mathematician," reminiscent of the "Wise Men of Chelm" stories. Most of us in America are also familiar with Charles Dickens' A Christmas Carol, a work which - while frequently read in school, and/or viewed (in movie version) in November and December - might be too closely associated with the holiday of Christmas in particular, and having the possible liability of missing the main point: economic inequality in Victorian England, and the plight of England's poverty-stricken and homeless citizens in particular. Ebeneezer Scrooge represents the successful British businessman, an affluent and law-abiding citizen, yet lacking in empathy and charity. His perception is that homelessness was an issue which had been resolved some time prior - in the 17th century - with the poorhouses. It is worthwhile to contemplate the exchange which occurs when he is approached by 2 men seeking charity on behalf of the poor. Scrooge replies by asking - whether with genuine or feigned surprise - whether the poorhouses are still in operation. The men reply in the affirmative. Scrooge presses them further: for those poor individuals who refuse to go there, are the prisons still opened? (The latter must surely be intended as sarcasm). The alms collectors again reply in the affirmative. In that case, declares Scrooge, he already provides for the poor through his paying his taxes (he is law-abiding, after all). The taxes he pays go to the aforementioned institutions, and those who are badly off must go there- end of discussion. The men collecting alms reply that many of the poor cannot go to these places, and many would rather die. One would think that this reply would be immune to rebuttal, but somehow Ebeneezer is sufficiently cold-hearted to press further: "If they would rather die, then they had better do it, and reduce the surplus population....." Goodness gracious, we think (hopefully); can a problem of this nature be solved with purely quantitative considerations? Is this reminiscent of the movie "Field of Dreams," in which the main character is told - referencing a baseball field he wishes to build on his ranch: "If you build it, they will come?" Build the baseball field, and somehow (magic! Or perhaps time travel coupled with teleportation?) the famous baseball players pop onto the field from the past, or from some parallel universe, and through some unspecified instantaneous transmission of information, the surrounding residents are somehow made aware of everything that is happening. Cars jam the entryway to the stadium with fans who will clearly suffice to pay off the main characters' debtors- and the financial crisis is solved. Perhaps my above digression was excessive, but hopefully it will suffice to demonstrate that mathematical models of some sort have previously been attempted by intelligent scholars for over 3 centuries (albeit with much lesser technological resources, no computers at all prior to World War II), and their results implemented. The poorhouses were a product of prior such efforts. History tells us that despite good intentions, poorhouses were ultimately discontinued due to the unsafe, unsanitary, etc. conditions in these institutions. We now have "homeless shelters" to support some of our homeless citizens, but these are usually temporary, with residents being compelled to vacate within 6 months. Also, how safe are these shelters in terms of protection from pickpockets and the like? Is there any degree of security? That being said, it is worthwhile to peruse the results and conclusions of many of the teams' solutions this year. Most of the winning teams seem to have used a logistic growth model, after first having considered linear regression, and noted a much stronger correlation of the raw data with a logistic growth function. I have previously discussed logistic growth with regard to the early part of our COVID pandemic; such a model is very useful for bacterial, viral, or human population growth. Both human population and land use have fixed carrying capacities; hence, the usefulness of a logistic growth curve is evident. As mentioned above, I am hopeful that our leaders - in government and industry - will have the wisdom to peruse the hard work of our country's motivated advanced students, who were willing to take the time and effort to provide some viable mathematical models of our homeless population and project accommodations needed for this population over the coming 50 years. At the same time, while scrutinizing students' solutions, I would strongly recommend noting their solutions for covering the cost of housing for the homeless (such as "affordable housing" solutions), as well as ensuring safe, secure, and sanitary conditions for this community.