Faculty members are encouraged to highlight the connection between the courses we teach and climate change, and raise awareness of the issue in our lectures, across subjects in my university. I am wondering what is usually done in that respect in mathematics. To formulate a question (answers to any of the three variants are welcomed) :

  • What are the mathematics of planet earth initiatives that can be retold within undergraduate and graduate classes?

  • Outside of optimization / numerical analysis, are there other areas where net impact on energy via mathematics can be highlighted and has been investigated (cryptography perhaps at a graduate level)?

  • Has anyone tried to convert (negative) powers of $n$ in error estimates into KW, or given examples of the impact of optimization / numerical analysis in terms of reduction of energy usage?

I first asked this question on Math SE, but it received a -3 vote in a few minutes, so I removed it. Maybe this is a more adequate place to ask.

To clarify : more than (sets of) lectures on the mathematics of climate change, or awareness lectures, I was wondering whether some examples can be found that could be embedded in run of the mill Calculus classes, Algebra classes, or other classes taught in many universities.

To clarify even further. What we are encouraged to do is to include in our curriculum elements concerning adaptation to climate change. It can take many forms, such as adding additional lectures to the common core modules, possibly coming from other disciplines; it can also be of the form described above. Since this is the part relevant to MO, that is the focus of this question. The lively debate in the comments about the motivations of such a question and /or politics within mathematics wasn't intended. I should have worded it perhaps in terms of adapting traditional "real world" examples that appear in many classes to climate change.

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    $\begingroup$ What is the purpose? Can't relevant courses in the applied sciences cover this topic, while drawing on whatever mathematics is needed? Does every subject need to justify its existence according to some political perspective? $\endgroup$ Oct 7, 2022 at 15:06
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    $\begingroup$ @efs I guess you mean, "It's proven science, not politics!" Sure ok. But the idea that we have to devote all our time to being climate activists is politics, not science. $\endgroup$ Oct 7, 2022 at 15:29
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    $\begingroup$ @Monroe Eskew I also don't see how emphasising one area of application across all disciplines is helpful to mathematics, and why mathematics of all things has to be 'green washed'. Still, the question presented to MathOverflow is interesting, in spite of the university's questionable policy decision. $\endgroup$
    – Enforce
    Oct 7, 2022 at 16:41
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    $\begingroup$ @MonroeEskew "devote all our time"? You are catastrophizing. It is not time consuming to make occasional mention of various applications, or even to devote one whole class period. Other more relevant applied science courses should certainly discuss the connections, but from an educational standpoint is is very helpful to encounter the same information in multiple contexts and perspectives. Also, from my experience with students, math education really benefits from highlighting relevance to "the real world". $\endgroup$ Oct 7, 2022 at 21:13
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    $\begingroup$ @SomaticCustard Should math classes also devote one whole class period to each of world hunger, poverty, economics, authoritarian regimes, history, psychology, personal finance, health and medicine, the law, the justice system, and countless other topics instead of teaching math? $\endgroup$
    – user76284
    Oct 10, 2022 at 20:33

2 Answers 2


Tom Murphy has written an open textbook called Energy and Human Ambitions on a Finite Planet.

He uses this course to teach a "gen ed" class in his physics department for non-majors.

I think that the book could be similarly used to run a "quantitative reasoning" course in most math departments. These courses often focus on skills like estimation, modeling with linear, polynomial, and exponential fucntions, and the use of logarithms. The book is about such skills in the context of asking "big questions" about our world.

Example problems from the text:

  1. In one day, a typical residential solar installation might deliver about 10 kilowatt-hours of energy. Meanwhile, a gallon of gasoline contains about 37 kWh of thermal energy. But the two ought not be directly compared, as burning the gasoline inevitably loses a lot of energy as heat. Correcting the solar output to a thermal equivalent (using the 37.5% factor discussed in the text) how many gallons per day of gasoline could it displace?

  2. Let’s say that the U.S. were willing to divert a one-time investment of 10 qBtu out of its 100 qBtu annual energy budget toward building a new energy infrastructure having a 10:1 EROEI and a 40 year lifetime. How many qBtu will the new resource produce in its lifetime, and how much per year? How many years before the amount of energy put in is returned by the output?

  3. In the spirit of outlandish extrapolations, if we carry forward a 2.3% growth rate (10 × per century), how long would it take to go from our current 18 TW ($18 × 10^{12}$ W) consumption to annihilating an entire earth-mass planet every year, converting its mass into pure energy using $E = mc^2$?

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    $\begingroup$ "converting its mass into pure energy using $E=mc^2$" This is likely impossible (assuming we are only counting extracted work) due to the carnot limit. $\endgroup$
    – PyRulez
    Oct 8, 2022 at 2:21
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    $\begingroup$ It is likely impossible because humans will never become intergalactic demigods. The problem is still a fun one to think about. $\endgroup$ Oct 8, 2022 at 10:49
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    $\begingroup$ You can get close to $E = mc^2$ using a black hole heat engine (which converts matter directly into hot radiation). Background radiation is pretty cold, so the carnot limit is pretty close to 100% anyways if you use it as the cold reservoir. $\endgroup$
    – PyRulez
    Oct 8, 2022 at 13:37
  • $\begingroup$ Excellent reference, thank you very much! $\endgroup$
    – username
    Sep 15 at 20:50

My former colleague David Mond at Warwick has developed some materials on this issue. He has some talks (at school and u/g level) on Climate change and game theory. He also lists some links there, to a page by John Baez, and an MSRI document, even if both of these are somewhat old now.

  • $\begingroup$ Thank you very much for these links. David Mond's material is much more in the direction I was thinking about, in the sense that I was thinking of examples that could be embedded in current courses, rather than awareness lectures. $\endgroup$
    – username
    Oct 7, 2022 at 11:41

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