Newsworthy Math

This piece was written around 1992. Most of it has dated well – despite the fact that this predated the public appearance of the world wide web the section on outreach makes sense for the most part. (Though clearly, and unfortunately,  none of this was written for the web. I’m still verbose, but less so.) There are many things I would change now – my cost estimates and my slightly optimistic scheduling guesses are embarrassingly off. But this is what I thought then. Except for the occasional spelling and grammatical edit this is unchanged since 1992.

---

Contents

1. Introduction
2. Why do we need a museum of mathematics?
3. What would our museum be like?
4. Outreach and Education
5. Funding and Finance
6. Conclusion
7. Appendix:  Some sample exhibits for a a museum of mathematics

Introduction

I propose to set up in New York City a permanent exhibition space devoted to mathematics: The New York Museum of Mathematics. Such a museum could take a number of forms and sizes, what will determine its influence is the guiding style and philosophy of the museum. While there should be much to interest math graduates, the museum should be aimed at non-specialists, in particular its primary audience should be children and its main purpose should not be to teach mathematics but to inspire children to learn, and to improve the image of the subject. The museum should, above all, be a place of beauty, and excitement. It should present mathematics to children, teachers, parents and post doctoral researchers, as something which is already a part of their lives, as something  which becomes more interesting the more one knows about it. It should show that the history of mathematics is a fascinating and central part of the history of the human race. A vast amount of time and money is already spent teaching children mathematics, the museum would be a place, the only place in the United State dedicated to answering the perennial question: What’s the point of learning math?”

Why do we need a museum of mathematics?

The importance of mathematics to the future prosperity of our society is hardly in dispute. While the United States produces its share of mathematic graduates, and of doctoral theses in mathematics and related subjects, what does, and should, cause concern is the significantly low low level of mathematical skills of the “average” student. While comparisons across cultures and generations are notoriously difficult there are few advocates for complacency. There is evidence that some groups consistently underachieve in mathematics, for example the mathematical education of girls is a source of concern to many. But what can be done? Students already spend a significant proportion their school time being taught mathematics, most of them would hardly applaud “more of the same”, even if the education budget would support this. Anyone who has taught mathematics is all too familiar with the “what’s the point of this” question, and, remarkably, while our society places such a value on mathematics there is no museum dedicated to answering that question. We need a museum of mathematics because a prosperous future will depend on a high average level of mathematical competence in our young people. A fundamental obstacle to this being realized is the predominantly negative image of mathematics among the general public, including parents, teachers, broadcasters and politicians. There is no public celebration of math. While theater, music, dance and film are public forms, which rely for their continued existence on persuading people that they are interesting, important and enjoyable, the unquestioned utility of mathematics means that this case is rarely made for it. All too often the default assumption is that the case can not be made. The effect of this on the motivation of children, on the interest and enthusiasm they bring to their learning and on the quality of that learning is enormous. In the USA thousands of millions of dollars are spent teaching mathematics, and next to nothing showing why it is worth learning. New York has some of the finest museums in the world, there are museums of art, of broadcasting, there is a museum of colored glass. If we are going to continue to tell children how important mathematics is, how worth while it is, how important that they work hard at it, then we need to make an effort to show that it is of some relevance to them. Utility and future employment are important, but they are poor motivation to a 14 year old. Schools can teach children, but the children’s interests and values are formed by what they see outside school. In New York they can see the best theater, dance and sport in the world, it is time New York had a museum where they could see something of he beauty of mathematics, something of its history, and something of its relevance to their lives.

What would our museum be like?

One of the problems with math education is the poor image of the subject, but what could be in our museum of mathematics to help change this? I envisage three types of exhibits in the museum:

• “the informational display” on the model of many exhibits in the Natural History Museum.
• “the artwork”, mathematics lends itself to impressive and elaborate models which need no explanation to be enjoyed = consider the Mandlebrot set, the Kepler-Poinsot solids (although these often motivate a desire for more understanding.)
• “the hands=on” or participatory exhibit, on the model of interactive science museums. (This should not entail a preponderance of puzzle type exhibits. Puzzles are excellent ways of learning, and are one of the most successful popular manifestations of mathematics, but a museum, with its high public exposure and pressure to move on in a short space of time, is not the best place to do puzzles.)

These three types are not mutually exclusive, nor are they exhaustive. Exhibits should generally be large scale and impressive, and production values should, as a matter of policy, be as high as possible. If one is already interested then a 30 cm cardboard model of five intersecting cubes is a thing of great fascination, but if  one is trying to get the visitor to look in the first place, a  meter model in iridescent Perspex will be more effective. While science and technology museums have become more numerous, and remain deservedly popular (20% of museums are science based, but 45% of visits are to science museums)there have been relatively few attempts to create exhibits devoted to mathematics. The reason for this may be some mistaken but popular beliefs about the nature of mathematics. Some of these beliefs are

• mathematics is ahistoric
• mathematics is abstract
• mathematics is either boring or difficult (or both)
• mathematics is absolute, either right or wrong
• mathematics has no place for opinion or value

Mathematics has a fascinating history, and the development of mathematics as had enormous and direct influence on politics, science, war, agriculture, art, medicine, architecture and more. The development of number systems and techniques of calculation, and the role of mathematics in religion and art across many cultures and periods are absorbing stories, well documented in many excellent books on the history of mathematics. These stories deserve to be much better known. Partly because of their intrinsic interest and their central importance in the development of human culture, and partly because they humanize mathematics and make the subject itself far more interesting. Children are often already intrigued by the ancient Egyptians, by astronomy, by stories of African, Indian, or Chinese culture, this interest can be made use of to tell the story of mathematics. Exhibits devoted to water clocks, number systems, calculating aides, calendars and cartography could introduce this history to a far wider audience. Mathematics is as abstract as the world we live in. Our perception is literally altered by learning math, our ability to see and imagine pattern is changed forever by our familiarity with circles, right angles, and reflective symmetry. There are many other concepts which are less well known but which are accessible and easily modeled: moebius bands; regular compound solids; the varieties of symmetry; chirality; curves of constant diameter; dissections of triangles and other shapes; saddle points; vertex regular solids, even the platonic solids are unfamiliar to most people. Any mathematics which can be conceived can be represented and modeled. A memorable, vivid and concrete representation of a million, billion or trillion would of itself be a valuable assistance to many adults trying to comprehend the realities of government budgets. The mathematics of risk has always been interesting: given the national and global AIDS crisis the need for us all to have a coherent understanding of epidemiology is more pressing than ever. An interactive exhibit on the probable effects of individual and average behavior choices could help get across a very important message. Mathematics is no more morally neutral than physics or medicine. Mathematical arguments have been used to justify genocide, to prove and disprove the existence of God and as evidence for astrology. The mathematics of codes is currently at the heart of a dispute  between Federal government, the telephone companies and the designers of computer interface protocols. Mathematical discoveries have led to the introduction of CAT scans and to more efficient anti-personnel bombs. There are many moral and emotive issues in our world which cannot be understood without a grasp of the underlying mathematics. Our children need to be told this about math, and we ought to do what we can to make these issues as clear as possible. In many cases a physical exhibit could serve as the first stage in the process of visualization, imagination and understanding. Learning mathematics is hard work which requires perseverance and courage, a visit to the math museum will never substitute for that. But even if the museum did no more than acquaint people first hand with some of the things which are part of their lives, and are possible only because somebody understands the math involved, it would provide a unique service. I believe the museum can do more than that. By showing models of a quality and size that are unlikely to be matched elsewhere (given the constraints of time and money) the museum can make a lasting impact and can provide its visitors with an image which enlarges their understanding and makes a permanent difference to their thinking. The view that mathematics is either difficult or trivial is false. The simplest ideas of shape, number and relationship can lead to beautiful and absorbing models, toys and patterns, and many significant ‘advanced’ mathematical concepts can at least be introduced at at a fairly elementary level  – such as the idea of limit, or the amazing and uniquely mathematical idea of a proof of non-existence. These things are part of our human heritage. They deserve to be as widely known as the works of Beethoven or Picasso, and they are certainly no more difficult to understand. A museum of mathematics could introduce people to these ideas, and could further help develop an appreciation of the concepts they already have.

Outreach and education

The influence of a museum can extend far beyond the time its visitors spend enjoying the exhibits, and one of the concerns of any museum must be to maximize its influence given its level of funding and other resources. This will involve advertising and other publicity, links to educational institutions, and publishing.

the catalogue

A serious omission in many museums is the lack of a catalogue, the importance of which increases as the subject matter of the museum becomes more conceptual. The importance of the catalogue is a straightforward consequence of the nature of conceptual learning, in short- conceptual understanding requires repeated exposure in a variety of contexts; conceptual understanding can not be timetabled. It is partly for these reasons that I have emphasized that the museum is not a place for teaching mathematics – it is ludicrous to expect 1,000 visitors all to understand the nature of the sine function in the same way in a 54  second exposure to an exhibit, however well designed it may be. Visitors will be of all ages and experiences. There cannot be only one lesson, the “right lesson” to learn from any exhibit. The other, related, reason for this emphasis is that a visit to the math museum must not be an occasion of failure; there are no good or bad grades for museum visiting. But if the museum is not a place where teaching takes place it is most definitely a place about learning. For this the ideal situation is: pre-visit publicity, knowing what to expect; a visit which is enjoyable, informative and memorable; follow up materials to “unpack” the meaning of the exhibits, to expand on them and to serve as a reminder. When this is not achieved through well coordinated school visits a catalogue is an excellent means of reaching the same end. The catalogue could borrow the three part format of some science museum publications:

• this is what you saw
• this is what it is about
• here is a home activity on the same principles

One of the main purposes of a catalogue is to provide parents (and sometimes teachers) with the means to become more confident about mathematics. This is of central importance in the formation of children’s attitudes and many parents would welcome such an opportunity. Museums often claim they do not have the time or the money to publish. I believe that this is  serious mistake. A catalogue amplifies the effectiveness of a museum out of all proportion to its production costs. Beside its educational purposes a catalogue is an advertisement for the museum. It sits in houses, schools and libraries with the museum’s name writ large upon its cover. It can reach places and people physically remote from the museum. And a catalogue can be sold, paying for itself if not actually turning a profit. These considerations hold true of t-shirts, calendars, mugs, puzzles, toys, posters and many other franchise possibilities.

educational institutions

The need for a math museum is felt most deeply in schools, and the audience is enormous. (In 1991 the “Pop Maths Road Show” visited Scotland. It was fully booked with school visits for over two months.) But the influence of the museum on schools should go beyond this. The museum should be a provider of exhibits and experiences which schools cannot replicate, or do not need to have permanently on hand, but schools and colleges are a vast repository of ideas and experience. The relationship of the museum and the schools should be mutually enhancing. The museum can even act as a clearing house for ideas and educational innovation, perhaps through a newsletter. And while the exhibits should be non-didactic there is a natural place for lectures, competitions, teacher training and more. Touring exhibits and math circuses are further possibilities. Some of these things already take place, but the museum could act as a much needed public focus for mathematics.

advertising and publicity

The idea of a museum of mathematics arouses interest whenever it is raised. Reactions range from “isn’t there one?” to “what would be in it, numbers?” Bringing the museum to the public’s attention through newspapers, television and magazines should not be a problem. What may be problematic, and more difficult to control, is the positivity or otherwise of the coverage. Far too many people, including TY hosts and journalists, are happy to boast of mathematical incompetence. The image of mathematics is so bad that some coverage would undoubtedly be negative. The image of the mathematically interested child as devoid of common sense, social grace, and physical prowess is a cultural icon which the museum could, in the long run, transform.

Controlling publicity and responding to negative images would be important, indeed it would be one of the purposes of the museum.

Funding and Finance

Museums are expensive. However well judged its admission price and however successful the museum shop may be a math museum is not going to pay for itself. Expenses will include, but are not exhausted by:

• premises costs, including any necessary construction work to ensure access and safety, heat, light etc.
• construction of exhibits – this varies, but $50,000 for a new exhibit is not unusual.
• staffing costs; janitors, security, office staff, museum helpers, staff to construct the exhibits, museum shop staff, design staff.
• development and research costs.

There are ways of minimizing costs. Space and expertise could be borrowed from an existing institution, with the museum “piggy backing” in its initial stages. The museum is an idea which excites interest, many people may be persuaded to donate their time and knowledge. For example high schools and colleges may trial exhibits, seniors or even trainee teachers may find that acting as a museum helper can develop their confidence and their explanatory skills while deepening their understanding of mathematics, corporations may be persuaded to donate materials or to fund particular exhibits on an ad hoc basis. And the museum could range in size from the vastness of the Hall of Science to the modesty of a one room gallery.

But if New York is to have a Museum of Mathematics, even on a scale to rival one of the scores of small SOHO art galleries, it will cost money. Those who bemoan the state of mathematical education, and the corporations which suffer as a result of the dearth of numerate new employees, have, in the founding of the Math Museum, the opportunity to contribute financially to a better future.

Conclusion

Establishing a museum of mathematics in New York is an enormous challenge. It will be expensive, it will require imagination, enthusiasm and the gathering together of an unusual range of skills and talents. The time to face the challenge is now.

It will not, and should not, happen overnight. A network of contributors and enthusiasts needs to be established; a proper financial analysis must be done; exhibits must be built, tested and rebuilt. This can be begun on a relatively small scale, but if it is not begun, if the commitment is not made, if the enthusiasm and funding are not available, the museum will not come about by accident.

The museum’s influence in proselytizing mathematics, in providing a focus for media attention, in helping to enthuse a new generation of children, and in widening the appeal of mathematics is badly missed.

New York needs and deserves a museum of mathematics. This time next year a permanent exhibition could exist. All we need to do is to make it happen.

Appendix: Some Sample Exhibits for a Museum of Mathematics

It is easy to have ideas for exhibits (my database of possible exhibits stands at over 200). What is difficult is to have ideas that work, and are self-explanatory, or are at least enjoyable without explanation. What is most difficult of all is to produce exhibits which can stand up to the physical rigors, the curiosity and the skepticism of public display.

What follows is a small sample of what I believe are strongly mathematical, highly unusual and eminently practical exhibits. I do not expect that any  of them would reach final display in the exact form described below. I do believe that these exhibit ideas show that a math museum is a completely practical possibility.

 

exhibit 1:  The Moebius Race Track

Unknown until the 19th century the Moebius strip is a fundamental topological form which is unusual and pleasing. A racetrack with model cars which started “on opposite sides” of the track and traveled in “opposite directions” and yet could overtake each other on the “same side”, would dramatically show some of the properties of the strip. Visitors could control the speed of the cars in a variety of ways. The exhibit would be interesting to observe as well as to operate.

 

exhibit 2: Curves of Constant Diameter

That there are non-circular shapes with constant diameter is unfamiliar to most people and yet easy to grasp. An exhibit could consist of flat slabs and a set of rollers of various cross sections, some circular, some of constant diameter, and some not of constant diameter. Visitors could predict and then test which rollers would transport the slabs smoothly. A display of a “Watts Drill” for cutting squares could further illustrate the principles involved.

 

exhibit 3: The Hairy Ball & Torus

An easily grasped curiosity of topology, the little known “hairy ball theorem” has as a consequence the inevitability of tornadoes. A short haired sphere & torus of reasonable dimension with a simple “try to get rid of the tornado” instruction could make the point memorably and succinctly. (A nearby video loop of real tornadoes could dramatize the display.)

 

exhibit 4: The Great Dodecahedron

There is an inexhaustible wealth of dramatic mathematical objects well suited for non-interactive display and decoration. (There is no excuse for bare walls or a lack of ceiling ornaments in a museum of mathematics.) The Great Dodecahedron, which consists of twelve connected, intersecting pentagons, and is a fully regular polyhedron which was missed by Plato, Archimedes and Kepler, is a striking and highly non-intuitive example. Although non-interactive it should be possible for visitors to touch the model to gain an easier understanding of its spatial properties.

 

exhibit 5: The Mandlebrot Wall

Although relatively well known the Mandlebrot set remains extremely popular and impressive. A wall sized display either with enlargements at various points or, ideally, with a side mounted screen showing an enlargement of an area determined by the visitor would demonstrate the beauty and complexity of mathematical constructions.

 

exhibit 6: The Life Sphere <yes, it ought to be a torus>

The simple “Life” program enjoyed great popularity among computer users because of the complexity and unpredictability of the consequences of its simple rules of survival. With a display consisting of LEDs mounted on a 2 meter diameter sphere <torus> this would be an order of magnitude more impressive. The display could be adapted to illustrate the spread of contagious diseases given various parameters set by interactive controls. (This exhibit and the previous one illustrate a philosophy of computer use in the museum: computers have transformed mathematics and will continue to make it more accessible to more and more people but computer screens and keyboards are the least impressive input and output devices and should make as little showing as possible.)

 

exhibit 7 The Tensegrity Icosahedron

Buckminster Fuller’s tensegrity principle is little known and meautifully mathematical. A successful exhibit of a tensegrity chair to take apart and rebuild has been used in interactive science museums before, the tensegrity icosahedron belongs in the Math Museum.

 

There are many, many other possibilities.

On the following page is a sample of an evaluation sheet which could be used to judge exhibits both before and after their construction. The reader may wish to gauge the ideas above against the criteria on the sheet.

 

An evaluation sheet for planning and assessing exhibits

Name of Exhibit

Concept

Outline

 

Reference

Do plans/evaluations for this exist? Yes No

Comments

 

Safety  easy to make safe    difficult to make safe

Interaction highly interactive not interactive

Novelty highly unusual commonplace

Fun Quotient very high very low

Concept central idea frivolous

Clarity easy to understand obscure

Sociability highly social solo

Diversity divergent only one lesson

Resources expensive inexpensive

Maintenance high low

 

Overall Rating Excellent Poor