Humanistic Mathematics
To humanize the teaching of mathematics means so to present the subject, so to interpret its ideas and doctrines, that they shall appeal, not merely to the computatory faculty or to the logical faculty but to all the great powers and interests of the human mind.
— Cassius Jackson Keyser (1912), American mathematician, educator, author, philosopher
Embed mathematics in the soul by embedding it in history, by embedding it in story. By showing how it is lovely and adventurous – the stuff of the best quest myths. By showing how it was created by complex, adventurous, brave, struggling human being.
…If our rationale for teaching a subject is circular – “you must learn it because it is useful, because it has uses, because it is useful, because you will need it later, because it is useful” – we won’t go a long way.
…A developing human being is many things, and chief among them a poet, an adventurer and a problem-solver. Give the poetry, the adventure and the problems, through stories, both small stories of environment and large stories of culture. Grip the heart – and the brain will follow.
— Apostolos Doxiadis (2003), contemporary Greek writer, mathematician, popularizer of mathematics
The perennial student’s question, “When will we ever use this?” is a misguided question, one to which we should not succumb.
That is not to say that we should refuse to answer it; but we should deny that the question is determinative of what is important in a person’s study of mathematics…
…We should, in short, let mathematics be, just as other disciplines are, the pursuit of ways of seeing…we should teach our students to look for mathematical analogies, to delight in them when they find them, to stretch them and test them and savor them
…We will lay the proper foundation if we teach them mathematics itself, as an independent, extant reality, whose “applications” are in fact analogies which often appear as metaphors.
— Jack V. Wales, Jr. (1988), contemporary American mathematician, educator
If we want to eliminate the misunderstanding of what mathematics is, we must change the way we teach mathematics. We must teach from a culturalogical perspective. We must view mathematics as an integral part of our culture and a significant force in our culture, and we must communicate this to students.
— Harold M. Ness, Jr. (1988), American mathematician, educator, writer
Despite the increasing mathematization of every aspect of our lives, from credit cards to medical diagnosis…the humane values that mathematics exhibits, the points of contact between mathematics and the humanities are by and large ignored by mathematical educators and hence are totally underappreciated by the wider public.
The tough minded might now ask: so what? To which I answer that we must believe that to change someone’s perception makes a difference in this world.
— Phillip Davis (1993), American mathematician, educator, popularizer of mathematics, co-author of The Mathematical Experience
The art of reasoning consists in getting hold of the subject at the right end, of seizing on the few general ideas which illuminate the whole, and of persistently marshalling all subsidiary facts round them.
Nobody can be a good reasoner unless by constant practice he has realised the importance of getting hold of the big ideas and hanging on to them like grim death.
— Alfred North Whitehead (1913), influential English mathematician, logician, philosopher, popularizer of mathematics
…A professor must make a choice. His aim may be to produce a perfect mathematical work of art, having every axiom stated, every conclusion drawn with flawless logic, the whole syllabus covered.
This sounds excellent, but in practice the result is often that the class does not have the faintest idea of what is going on. … The framework is lacking; students do not know where the subject fits in, and this has a paralyzing effect on the mind.
…To see the clear, logical ideas gradually being disentangled from vagueness and confusion is vastly more instructive than simply starting with the logical ideas.
— Walter Warwick Sawyer (1955, 1959), British mathematician, educator, author, popularizer of mathematics
To introduce students to humanistic mathematics is to introduce them to a human adventure, and adventure that humans have actually partaken in history.
— Thomas Tymoczko (1992), American philosopher, logician, educator, author
The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals.
The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.
— George Sarton (1936), Belgian-American mathematician-historian, chemist, author, popularizer of history of math/science
The mind’s deepest desire, even in its most elaborate operations, parallels man’s unconscious feeling in the face of his universe: it is an insistence upon familiarity, an appetite for clarity.
Understanding the world for a man is reducing it to the human, stamping it with his seal.
— Albert Camus (1942), French philosopher, novelist, writer, Nobel Laureate,
Students must learn that mathematics is the most human of endeavors. Flesh and blood representatives of their own species engaged in a centuries long creative struggle to uncover and to erect this magnificent edifice.
And the struggle goes on today.
On the very campuses where mathematics is presented and received as an inhuman discipline, cold and dead, new mathematics is created. As sure as the tides.
— J. D. Phillips (1995), contemporary American mathematician, educator, writer
Mathematics appreciation is more than a course. It is an attitude that we should cultivate in every mathematics course.
— Josefina Alvarez (2001), contemporary Spanish mathematician, author, popularizer of mathematics
…Mathematics doesn't just have a public relations and/or communications problem—it has real problems. Those real problems are faithfully reflected in its poor public relations and dysfunctional communications. Any meaningful discussion about how to improve the quality of communications and dialogue between the mathematics community and the rest of the world must begin there.
…The essential point is that mathematics may be an extraordinarily powerful and important intellectual discipline, tool, and adventure, but the mathematical community is not seen as particularly powerful or important in helping others acquire or appreciate math as a discipline, tool, and adventure.
…While virtually everyone in the educational establishment acknowledges the ''importance" of mathematics, there remains absolutely no agreement about how that importance should be mapped onto a curriculum.
— Michael Schrage (1997), contemporary American innovation expert, educator, author