I listened to a COVID-safe Zoom talk from an MIT math professor. He talked primarily about a geometric optimization problem. My question:
Maybe this will be covered during the talk, but being an engineer I would like to hear what the practical applications could be if Larry solves all of the problems that he’s talked about and/or others that he’s working on. Would ChatGPT get smarter? Would Elon Musk get to Mars sooner? Would renewable energy become cheaper?
He responded that he’d never worked on any problem that he thought had a practical application, but that maybe tools developed to solve a seemingly pointless optimization problem might end up being used to solve a practical problem. He added the question was “Above [his] pay grade.”
What about the graduates? “Half of my Ph.D. students go into academia and the other half go into finance,” responded the professor. “I think it might be because the finance industry has a well-developed path for bringing in people with quantitative skills and no other knowledge.” (i.e., half the students decided that numbers were more interesting if prefixed by a dollar sign)
There are supposedly about 35,000 math professors nationwide. Maybe 10,000 are paid primarily to do research? Taxpayer-investors will need to have nerves of steel to keep paying these folks! (Figure about $350,000
I wonder if we can date the last innovation from the math researchers that is used in ChatGPT. The guys who are credited with developing “deep learning” don’t have math Ph.Ds. (Yann LeCun, Yoshua Bengio, and Geoffrey Hinton) The speaker on Zoom event said that, as far as he knew, all of the math being used in LLMs was “old”.
Separately, the Boston Globe reports that there is a narrow majority of haters within the MIT faculty:
At MIT, about 20 students, according to student organizers and professors, have been placed on interim suspension, which means they can no longer access campus buildings, participate in graduation, receive wages for student jobs, or finish their final exams and projects. Most have also been told they need to vacate their university housing. MIT declined to confirm the number of students suspended.
A handful of the suspended students were expecting to graduate this semester, and now their diplomas, post-graduation jobs, research projects, and internships hang in limbo, according to interviews with more than half a dozen students and MIT professors. The MIT encampment ended on May 10 when police cleared out the demonstration in the early-morning hours; 10 students were arrested.
Hannah Didehbani, a senior at MIT studying physics who was suspended, said she does not know when she will receive her degree, and that the university has provided little detail about how she should proceed.
“MIT is only taking these unjust, repressive actions such as suspending us, arresting us, evicting us because they are afraid of the power we have,” Didehbani said.
A majority of the MIT faculty appear to be in favor of disciplining the student protesters, however. At a faculty meeting Friday, a motion to remove punitive actions from the suspensions lost, said philosophy professor Sally Haslanger. About 190 faculty opposed removing disciplinary actions, while roughly 150 favored the idea.
Related:
- official Diversity, Equity, and Inclusion web site for the MIT math department: Members of our community come from a variety of racial, ethnic, indigenous, religious, and socioeconomic backgrounds. We are LGBTQIA+. We are women and men and non-binary. We have families and pets. We are veterans. We are immigrants. We possess a range of physical abilities. We are first-generation students. We are young and we are experienced. We are MIT Math. [Mindy the Crippler makes our household diverse, according to the geniuses at MIT, due to her Canine-American and Scottish-American background (golden retrievers hail from Scotland).]
- Out of the 74 gender IDs recognized by Science, just one is highlighted:
How do these professors even know what their graduates did? Practical use of college level math might only seem limited because it’s all being done in China. All the credits in AI models are Chinese grad students. Reviewing a list of operators in tensorflow makes a pretty intimidating math refresher. Most of the modern AI boom is actually a search for novel math operators.
Lion: you think it is surprising that they would keep in touch with their 10 or so PhD graduates from the preceding 5-10 years?
Given your background in the sciences, Phil, though not The Science, where would you place the usefulness of a math PhD along a spectrum of academic disciplines with say physics and other hard sciences at one end and race and gender studies at the other end. I define usefulness as your opinion of its ability directly or indirectly to make the world a better place.
My background is not in the sciences! When I was 14 years old, I thought I was smart so I majored in mathematics as an undergraduate and mostly learned that I wasn’t smart (also that I didn’t like being frustrated working on a problem for hours and then feeling good for a few minutes after solving the problem before moving on to the next problem and feeling frustrated again). When I went to graduate school, after a few years of working full-time, I recognized that engineering was a better match for my personality (or lack thereof). So the rest of my education was in engineering.
Leaving aside the applied math folks, the typical math Ph.D. is unable to articulate any conceivable practical application for the work done. So the actual work of a mathematician seems to be useless. I guess for the holder of a math Ph.D., though, the training might be considered useful as brain development for work in finance or physics or maybe even AI.
In recent history, mathematics meant something. Take WWII and the Moon landing. The men (and a few women) depended on mathematics to make a significant contribution to mankind. Today, mathematics is all about speculations and to make someone’s agenda look good, i.e.: there-is-no-inflation.
If you were good enough (in math and physics), you could work on what “it” was like before the Big Bang, and even before Inflation (the cosmology one, not the one that keeps Powell up at night) – https://www.quantamagazine.org/mathematicians-attempt-to-glimpse-past-the-big-bang-20240531/
Don’t you need math departments to teach basic math courses that engineers need? That should count for something when calculating math professors’ societal ROI.
Anon: The best math researchers are often the worst math teachers, partly due to a complete lack of motivation. Every minute in the classroom is perceived as a waste of time (which is, in fact, a correct perception if the professor is employed by and seeking promotion from a research university). If you wanted to breed a crop of great teachers of undergrad math you wouldn’t build anything remotely like today’s research math PhD programs.
If we believe the folks at the Great Courses (which I do), the best calculus teacher in the U.S. is Bruce Edwards of the University of Florida. See https://www.thegreatcourses.com/courses/understanding-calculus-problems-solutions-and-tips
This guy appears to have a Ph.D. in math, but his great teaching skills could be unrelated to his education in math research. He isn’t famous as a researcher, I don’t think. https://people.clas.ufl.edu/bruceedwards/mtg-3212-geometry/AboutEdwards/ shows that he has time for lots of hobbies, so I don’t think he is doing a huge amount of research: “My hobbies include reading, chess, stamps, simulation baseball games, SuDoku, KenKen, and travel.” To the extent that he does research, it seems to be applied: “My research interests include the broad area of numerical analysis. I am particularly interested in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values.” His biography says that he taught math in Colombia for four years prior to going through math graduate school (he seems to have nimbly sidestepped the Vietnam War: ” I was a mathematics major at Stanford University and graduated in 1968. I then joined the Peace Corps and spent four years teaching math in Colombia, South America. I returned to Dartmouth in 1972 and completed my doctorate in mathematics in 1976.”). So maybe he became a great teacher by doing nothing but teaching for four years while his fellow math nerds were doing research.
Most math research is useless, but geometric optimization does have a lot of practical applications, including to AI. Maybe this professor was not doing anything directly useful, but even abstract results move the field along.
If you want useless university departments, check out art, english, gender studies, and a lot of others.
It might be worth if if, as a side effect, normal people actually ended up learning math, but no, we gotta hear every year about how nobody can do their own taxes or any kind of algebra.
Meh. Math often has a hundreds of years gap between its invention (discovery?) and its unpredictable practical application.
Eg: Fourier transforms. Invented in 1822 while studying heat, just the volume of arithmetic required made them practically useless. But 200 years later they now enable digital communications, and digital sound+images+video.
Fun aside: the Fourier-slice theorem (aka projection-slice, or X-ray slice) was the most surprising bit of math I saw while studying EE + CompSci. Its used to construct CT/X-ray/MRI images from a rotating 1D beam. It took 3 years of math to prepare, but one day in a lecture the prof derived it, and the answer just popped out in an elegant 1-line expression.
I love math and one of my professors thought that I was very good at a particular subject. In many cases, new abstract math developments used decades or sometimes centuries after they were developed in pure math.
For instance, number theory used to be useless in real word, but now it is a base for computer encryption.
Abstract math is not going make taxpayers better off on short term and may even provide tools for enemy nations to build upon, but it far less destructive in both regards then our political and crony capitalist classes. It would be one of the last spending I ‘d purged from US budget.
But what about physics – much of that is useless too. For example, how astrophysics research is helping my bottom line?
I am not biased against physics – one of my professors thought that I had good physical intuition and asked whether I wanted to become his grad student.
These predictive language models are applications of machine learning, which depends on a lot of rather abstract mathematical ideas and is the subject of ongoing research¹ by mathematicians. A branch of this mathematical research applies Noether’s Theorem and its extensions, a circumstance that I imagine² would have amused Emmy Noether greatly. She cared nothing for applications of her research, pursuing mathematics for is fascination and beauty, the motivation for nearly all workers in pure math.
1 ‘Noether’s Theorem and Machine Learning’. Available from: https://lee-phillips.org/NTandML
2 ‘Einstein’s Tutor’. Available from: https://lee-phillips.org/noether
In case I failed to make my point clear in the preceding: Noether’s Theorem dates from 1917, a while before anyone was thinking about artificial intelligence, language models, or computers.
Lee: A practical application 100 years later usually works out to a low return on investment just because of the discount rate compounding over such a long period.
(Maybe this is why humans aren’t willing to do anything now, other than post some lawn signs and bumper stickers, to avoid a predicted climate problem that will occur 50 or 100 years in the future.)
philg: Note that Noether was working without pay when she proved her famous theorem, because at the tine in Germany women weren’t allowed to be paid as faculty. So the investment was 0 DM. The payoff was a new foundation for all of fundamental physics and a seemingly endless panoply of applications that no one at the time could have possibly predicted. All from pure mathematics pursued for its own sake. I don’t know how one would make the relevant return on investment calculation here.
For any worker, including one who isn’t paid, I think you look at the opportunity cost. So the cost of an unpaid mathematician’s work would be the value of what he/she/ze/they would have done if he/she/ze/they hadn’t been doing mathematics (maybe working to improve diesel engine efficiency, for example).