WHY WE WROTE ‘LOVING AND HATING MATHEMATICS’

Reuben Hersh

University of New Mexico, USA

rhersh(at)gmail.com

As usual with any great enterprise, there was more than one reason.

We did it because so many people had said to me, on learning that I am a mathematician, “Oh! Mathematics was always my worst subject!”

And because Vera’s a psychologist, I’m a mathematician, we wanted to do something together. So, how about, “the emotional side of mathematical life”?

And because we needed to refute Hardy’s too-often-quoted remark, “Mathematics is a young man’s game.” (See De Moivre, Weierstrass, Sylvester, Littlewood…)

Vera was tempted by such questions as,

“What is the culture of mathematics?”

“How does a child become a mathematician?”

“What role do mathematical communities play in mathematical life?”

I was fascinated by such amazing life stories, as that of the major contributor to measure theory and point-set theory, a president of the International Mathematical Union—whose hundreds of papers were all co-authored by his wife, although often with only his name appearing.

And Bella Abramovna Subbotovskaya, who created the Jewish People’s Mathematical University in Moscow, in the years when Jewish students were excluded from the mathematics department at the University of Moscow—and who was rewarded by a mysterious fatal encounter with a mysterious hit-and-run driver.

And the brilliant mathematical prodigy who having tried his best to escape serving in the French Army during the Second World War, was imprisoned as a draft dodger, and enjoyed his seclusion to work very productively on number theory.

And the greatest logician since Aristotle, cleverly foiling any possible attempts to poison him by starving himself to death.

And the great founder and transformer of modern algebraic geometry, who has taken refuge from the corruption and bad faith of contemporary mathematical life, by hiding in a secret remote village in the PyreneesMountains.

And the ten-year-old boy who read about Fermat’s last theorem in a popular biography book, was fascinated by it, and 30 years later, after working secretly for seven years, produced the proof.

Yes, there are countless incredible stories in the lives of the mathematicians.

Those are some of the reasons we wrote Loving and Hating Mathematics.

But over the six years that we devoted to this project, we were led to undertake much more than we had originally contemplated.

The stories of Sophie Germain, Sonia Kovalevskaya and Emmy Noether led into the stories of Jenny Harrison, Lenore Blum, Karen Uhlenbeck, and many other living women in mathematics. We found that we had the possibility to deal at some length, and at some depth, with the issues of women in mathematics today.

The story of the great racist trainer of research mathematicians, Robert Lee Moore of Texas, turned out to be fascinatingly intertwined with the story of the great Black mathematics educator Clarence Stephens of PotsdamUniversity.

And we ended up writing a final chapter called “Loving and Hating School Mathematics” where we describe the dilemmas, paradoxes and controversies of present-day mathematics education, from pre-school up through grad school. We ended up making some very simple, common-sensical proposals that are so radical they fly in the face of most of the rhetoric and self-advertising that passes for eloquence in today’s conversation about mathematics education.

So here, since I have kindly been given this platform on which to state our viewpoint, I will summarize the proposals we make in our final chapter.

First of all, the claim that everybody has to know algebra—better still, trig—better still, calculus—in order to make a decent living nowadays, is patently untrue. The claim that our country’s economic position in the world rivalry for economic domination depends on making as many people as possible competent in algebra, trig and calculus—is patently untrue.

Secondly, in mathematics as in music, athletics, art, and poetry, different people have different degrees of interest and natural aptitude and inclination. There is no more reason to make people who have great and continued difficulty learning algebra into scapegoats or victims than to so treat people who can’t learn to carry a tune or throw a ball straight. Let us offer every one a chance to learn as much math as he or she is willing and able to learn.

That means, providing first-class math teachers in every school in our country—those in poverty districts as well as those in affluent districts.

It means that students who don’t need or want algebra as teen-agers have the

opportunity to learn it if they decide after all as adults that they do want it.

It means that medical schools, business schools, architecture schools stop using irrelevant mathematical prerequisites as filters, and find appropriate ways of choosing their students.

The idea is to provide meaningful, inspiring education to increase the number who love mathematics, and to release from needless torture and punishment the ones who simply do not love it—in other words, decrease rather than increase the hatred of mathematics.

Those are the proposals we were led to, in the course of our telling about the emotional, social and political sides of mathematical life.

We ended up with a book full of life stories, offering some serious socio-cultural analysis, and proposing an approach to mathematics education so humane, simple and natural that it is very likely to be pushed aside as utopian. But so be it. We can but tell it as we see it.

Hersh, Reuben and John-Steiner,Vera (2011) Loving and Hating Mathematics, Princeton: Princeton University Press.

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