The role of mathematics in physics

[PeroK]

I've been reading a brief history of mathematics, from the ancient civilisations onwards and found the following striking quotation from Roger Bacon (1214-94):

Mathematics reveals every genuine truth, for it knows every hidden secret and bears the key to every subtlety. Whoever then has the effrontery to study physics while neglecting mathematics should know from the start that he will never make his entry through the portals of wisdom.

I assume that Roger Bacon would not be impressed by the modern trend in popular science of villifying mathematics.

 

[Mayhem]

A lot of pop sci is just hard science fiction.

 

[S.G. Janssens]

Thank you, perhaps even more for reminding me about Bacon than for the quote itself. (It does make me wonder what he as a Franciscan would have thought about the modern trend in (popular) science of villifying religion. Although that is another matter.)

 

[mcastillo356]

Villifying or vilifying? I can't find villify anywhere

 

[gleem]

"Mathematics is the Queen of the Science and Arithmetic the Queen of Mathematics. She often descends to render service to astronomy and the other natural sciences, but under all circumstances the first place is her due." C. F. Gauss.

The first statement in Chapter 1 of Eric T. Bell's book (Mathematics Queen and Servant of Science), a discussion of the contributions of mathematics (both pure and applied) to the sciences (mostly astronomy and physics) up until about 1950. I highly recommend it.

 

[fresh_42]

"I think that modern physics has definitely decided in favor of Plato. In fact, the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language." ~ Werner Heisenberg

 

[nuuskur]

The vilifiers likely don't know much about math so they need not be heeded. I would love to see a specific example of said vilification, though. I don't keep track of pop science releases, myself.

 

[mcastillo356]

The vilifiers likely don't know much about math so they need not be heeded. I would love to see a specific example of said vilification, though. I don't keep track of pop science releases, myself.

https://www.wiley.com/network/resea...opular-culture-the-good-the-bad-and-the-bogus

 

[gleem]

Is this an example of the vilification of math or is constructive criticism?

Teaching math bolsters white privilege:
https://www.foxnews.com/us/white-privilege-bolstered-by-teaching-math-university-professor-says

 

[BWV]

Of course its just as easy to BS a non-expert with math as it is with jargon - math just a tool that works better in some situations than others

 

[gleem]

Even mathematicians can vilify their own profession or aspects of it. "A Mathematician's Apology" by Godfrey H. Hardy takes applied math to task. An article in the American Scientist discusses his view that abstract mathematics should be a" true" mathematicians (my characterization) concern and that applied math is dull and trivial and implies it is for second-rate minds.

 

[nuuskur]

https://www.wiley.com/network/resea...opular-culture-the-good-the-bad-and-the-bogus

I more so read about potential inaccuracies in the depiction of math, not slander toward math. At any rate, most notable to me is

While many academics are willing to accept mathematical inaccuracies in films, TV, books and plays, depictions of practitioners as eccentric and socially awkward could damage the subject's appeal among young people.

I am increasingly annoyed with this fixation that a movie (or a novel, for that matter) is necessarily representing reality in some way or form. It's a movie and the script is depicting the author's understanding of some aspect of reality. We should keep in mind the movie's purpose is to entertain. There has to be some drama or intrigue to drive the plot.

The young folk ought to be constantly reminded that fiction is just that - fiction. It need not have any ties to real life. Something about propositional logic and valid forms of inference ..and some such mumbo jumbo..

Teaching math bolsters white privilege:
https://www.foxnews.com/us/white-privilege-bolstered-by-teaching-math-university-professor-says

Oh Lord, that lady is an idiot or got paid well enough to write such gibberish.

Mathematics itself operates as Whiteness.

What does this even mean?!

According to the website, Gutierrez adds that there are so many people who “have experienced microaggressions from participating in math classrooms… [where people are] judged by whether they can reason abstractly.”

These 'microaggressions' occur, regardless of subject. Kids are being kids, this is normal.

Ok, it's criticism in some way. But not constructive. The connection of various observations to race or mathematics is not explained whatsoever.

The main takeaway to me is that there is an advantage in being vague. For if they don't specify what they mean, then no one can test their claims reliably. This is strictly pseudo-science territory.

 

[StatGuy2000]

I assume that Roger Bacon would not be impressed by the modern trend in popular science of villifying mathematics.

I have a difficult time accepting the premise of your argument. I don't particularly see a trend in popular science these days of vilifying mathematics (to the extent that popular culture even thinks much about mathematics, or any other variety of science).

 

[StatGuy2000]

Is this an example of the vilification of math or is constructive criticism?

Teaching math bolsters white privilege:
https://www.foxnews.com/us/white-privilege-bolstered-by-teaching-math-university-professor-says

It is entirely possible that this particular professor's views have been misconstrued or taken out of context to portray her as suggesting that math knowledge on its own is "white privilege".

 

[Astronuc]

It is entirely possible that this particular professor's views have been misconstrued or taken out of context to portray her as suggesting that math knowledge on its own is "white privilege".

Or interpreted. However, one can read her article and decide for oneself.
https://www.mtholyoke.edu/~ahoyerle/math101/Gutierrez-Annotated.pdf (see page 8 ff.)

The article states:

On many levels, mathematics itself operates as Whiteness. Who gets credit for doing and developing mathematics, who is capable in mathematics, and who is seen as part of the mathematical community is generally viewed as White. School mathematics curricula emphasizing terms like Pythagorean theorem and pi perpetuate a perception that mathematics was largely developed by Greeks and other Europeans. Perhaps more importantly, mathematics operates with unearned society, just like Whiteness.

Mathematics is a tool. People use tools. People are political (late Middle English: from Old French politique ‘political’, via Latin from Greek politikos, from politēs ‘citizen’, from polis ‘city’.).

Maybe take people out of the equation.

https://en.wikipedia.org/wiki/History_of_algebra
Claim: "The origins of algebra can be traced to the ancient Babylonians, who developed a positional number system that greatly aided them in solving their rhetorical algebraic equations."

Claim: "Ancient Egyptian algebra dealt mainly with linear equations while the Babylonians found these equations too elementary, and developed mathematics to a higher level than the Egyptians."

See also -
https://en.wikipedia.org/wiki/History_of_algebra#Greek_mathematics
https://en.wikipedia.org/wiki/History_of_algebra#China

I remember learning algebra with word problems in grade 5, but I don't remember the term algebra being used. Algebra came later about 8th grade, but it was 8th grade math. Algebra I, in grade 9, was the first formal 'Algebra' class. For me, it seem grades 5 through 8 were largely redundant. Systems of proofs and set theory were often introduced at the beginning of class. I generally found mathematics education disjoint, and somewhat disconnected from science classes.

 

[hutchphd]

I know for certain that I was taught about the historic origins of the Pythagorean theorem in high school but was left totally ignorant as to the etymology of the term "algebra". I think the history at high school level is important, and better it be taught by the math person.

 

[Astronuc]

I know for certain that I was taught about the historic origins of the Pythagorean theorem in high school but was left totally ignorant as to the etymology of the term "algebra". I think the history at high school level is important, and better it be taught by the math person.

I was trying to remember when I first encountered the Pythagorean theorem (it's been 5 decades at least). I think it was in conjunction with 3,4,5 and 5,12,13, and starting to learn basic geometry (triangles) and particularly right triangles. I was probably studying World History in parallel. As far as I knew, Pythagoras was an ancient Greek, which were among a bunch of ancient civilizations at the time.

In elementary (primary) school, we had the one teacher teaching math, english, history, science, . . . , and we had specialists teaching music, art and language (Spanish). It wasn't until junior high school (middle school), grade 7, that I encountered separate teachers for each subject.

 

[Astronuc]

However, one can read her article and decide for oneself.
https://www.mtholyoke.edu/~ahoyerle/math101/Gutierrez-Annotated.pdf (see page 8 ff.)

I haven't read through all of the article, but I feel Professor Gutierrez makes some valid points. I haven't found constructive criticism yet.

On the other hand, here is a positive example - How one professor and mathematician Federico Ardila-Mantilla changed the culture of mathematics for his students.
https://www.theatlantic.com/education/archive/2021/09/bias-math-sexism-racism/620207/

To avoid perpetuating macho aggressiveness and instead make the classroom a place where students would feel comfortable and supported, he devised a class agreement. Students were asked to commit to taking “an active, patient, and generous role” in their learning and that of their classmates. Achieving the right tone also meant rethinking how he spoke about math. Mathematicians frequently use phrases like It’s obvious or It’s easy to see, which can be profoundly discouraging for a student who does not immediately find a concept simple. In math, grappling with extremely difficult problems is part of the learning process. “A challenging experience,” Ardila told me, “can easily become an alienating one.” It’s especially important to make sure that students are not discouraged during early challenges—what’s hard to see now may become easier in time. He struck this typically demoralizing math language from his teaching.

Other changes followed. Ardila observed that only a few students would speak in class, so after he posed a question, he asked to see three hands before calling on anyone. The first hand usually shot up quickly, and sometimes the second. Eventually, a third hand would rise, tentatively. Then Ardila would ask students to share their ideas in reverse order. They eventually caught on, he told me, but in the process, they understood that all their voices were welcome and encouraged. Classes that began the semester with only a sliver of vocal participants would end with everyone talking.

For a final project in Euclidean and non-Euclidean geometry, for instance, one student of Mexican and Indigenous descent wanted to learn how his ancestors did math. The student built a replica of the Chichén Itzá temple of Kukulcán, the Mayan snake god. The temple was designed so that at the equinox, the light and shadow cast by the setting sun appears like a serpent slithering from the top of the stairs to the bright snake head at the bottom. The student uncovered the math needed to re-create the structure, complete with the undulating light of the serpent. The project was, Ardila said, of a noticeably higher caliber than the student had demonstrated before. “When students see themselves reflected in the curriculum, it qualitatively changes the kind of work they can do. It’s really moving.”

In the case of Ardila’s students, inclusion has had an astonishing impact. Of the 21 students in the first joint math class with the Universidad de los Andes, 20 went on to get graduate degrees in math and related fields. Half of these students were from San Francisco State. Fifteen went on to seek Ph.D.s in math and related fields, and 14 are already professors. This would be an astounding number even at an elite university, but at a non-Ph.D.-granting state school such as SFSU, it’s unprecedented. Many of the students originally had no intention of pursuing math Ph.D.s. Of the 200 students who have participated since the program’s founding, 50 have gone on to get doctorates in math. Almost all the U.S. participants are women or from historically underrepresented ethnic-minority backgrounds.