### “I hated math in high school”

When I meet new people at a party and mention that I am a mathematician, I sometimes hear back “I hated math in high school,” or “I always hated mathematics.” To be honest, I didn’t much like it in high school either. The mathematics I did then like factoring polynomials or trigonometry has little to do with my present research in graph theory. Nevertheless, blanket statements like that feel like a slap in the face.

If you met a writer, would say you hate reading? Imagine meeting Margaret Atwood and saying you think books are horrible. If you meet a racecar driver, would you say you hate cars? If you met a chemist, would say you hate oxi-reduction reactions?

Mathematicians may appear intimidating but the good ones love to discuss their ideas. We may not all look like Pietro Boselli (university mathematics lecturer and fashion model), but it is worth chatting with us.

The tried and true method to strike up a conversation with anyone is to ask *questions*. The featured image of this blog is Ken Ono explaining some mathematical ideas to Dev Patel on the set of the movie *The Man Who Knew Infinity *(see my review). Patel looks at ease and engaged!

Here are some you can ask the next time you meet a mathematician.

### Ask about their research

Don’t give them a pass: force them to explain their work in layperson’s language. Any decent mathematician can do that. For instance, do you play Sudoku? That is an example of a graph coloring problem that is computationally difficulty (i.e. **NP-**complete) for general-sized squares. That segues to one of the world’s deepest mysteries: whether **P** is equal to **NP**, which comes with a million dollar prize if you solve it. Frankly, there are easier ways to earn a million dollars.

Are you on Facebook? Twitter? These are real-world *complex networks* with evolutionary properties in common with internet architecture, and even protein networks in living cells. Cool stuff.

### Ask them about the giant problems

Mathematicians think about tough open problems. We dream about solving them.

Talk to your resident mathematician about some famous conjectures. You might hear about recent progress by Shinichi Mochizuchi on the abc conjecture, the centuries-old Riemann hypothesis, or the Goldbach conjecture whose statement can be understood by a high school math student (every integer greater than two can be expressed as a sum of two primes).

There are also great stories about the resolution of some big conjectures, such as Fermat’s Last Theorem, the Strong Perfect graph theorem, or the Poincaré conjecture.

### Ask about our glitterati

Yes, there are some incredibly talented people working in mathematics. Today, actually. Right now as you read this.

Have you heard of Terrence Tao, Andrew Wiles, Maria Chudnovsky, or John Conway? These are some of the living mathematicians who have done amazing things.

Mathematical history is long and rich. You may hear about Srinivasa Ramanujan, Emmy Noether, Paul Erdős, or Alan Turing who each had a massive impact on 20th century mathematics. Or historical figures such as Euler, Riemann, Euclid, Hypatia or Ada Lovelace. Just ask.

### Ask how mathematics relates to the arts

Many recent movies and popular books focus on mathematicians or mathematics. *The Imitation Game*, *The Man Who Knew Infinity*, or *The Theory of Everything* are example of movies with lead characters who are mathematicians (Stephen Hawking at least uses advanced mathematics for his physical theories).

There is a deep connection between mathematics and music, and between mathematics and the visual arts. I wrote a blog about these connections, citing mathematicians who sculpt, write, and make music. A famous classical example was Leonardo da Vinci, who painted the Mona Lisa but was also a gifted mathematician, writer, engineer, and inventor.

Make friends with your local mathematician. Don’t be put off by our awkwardness or shyness. There are some great discussions waiting for you.

Anthony Bonato

This is a very, very basic question, but please consider and answer. I feel it touches on how children learn to understand the world

I teach in Australia in a primary school. The maths curriculum includes a “shape” component and at year 3 level the achievement standard states that the students “Make models of three-dimensional objects and describe key features” these models are constructed of paper nets, glued together and hollow inside. At no point do the children get to see, touch or create an actual geometric 3D solid. How important do you feel it would be for their experience, understanding and thinking ( intuitive as well) to experience the actual solids – esp the Platonic solids?

Thanks, Brenda Hawke

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Hi Brenda and thanks for your question. I’m not an expert in childhood education, but I think it would be very helpful to have 3D solids. Students can get a feel for their shapes and symmetries. Mathematics is more than just number crunching and rote learning. I think having students construct and interact with the solids will definitely help their geometric intuition.

By the way, have you heard of Jump Math? This is a numeracy program for all grades, pioneered by Canadian John Mighton. Check it out: http://jumpmath.org/jump/en/jump_home

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No comment. Just another question by a puzzled layman.

Space appears to be a mystery, even in the context of special relativity. Special relativity shows that, with acceleration, time slows down for the accelerating body (from a “stationary” outside observer’s viewpoint). However, we know that the greater the speed or acceleration of a body, the “more quickly” it arrives at its destination. Common sense traditionally understood “more quickly” to mean in a “shorter time”. But it has been confirmed that time actually stretches or dilates with acceleration. Therefore, the only possible explanation for “more quickly” is a shortening of distance or length or space in the direction of motion or acceleration of the body.

This is rather weird. For one thing, it suggests that “space” is not a nothingness in which objects move about unrestricted, but is rather something. It has been described as a kind of “fabric” that can fold or alter or even tear. Maybe. But one does not expect what is outside a body to transform or alter itself in deference to that body or its motion. That’s like turning the discredited geocentric theory into a discreditable egocentric theory.

Since the acceleration is a property of the body in motion, it makes more sense to say that the body stretches or lengthens with acceleration, and reaches its destination as if space or length in the direction of motion contracted or shortened. Admittedly, this doesn’t seem to agree with experience. I hold a meter stick in my hand. A hundred-meter craft passes by me at nearly the speed of light. No sooner do I apply the meter stick to measure the craft’s length than the craft has come and gone. I measured a train that is one meter long. Thus the high acceleration or velocity of the moving body makes it appear to have contracted or shrunken, not stretched or lengthened. However, a beam of light does provide the effect of unending length. Maybe it is mass/energy that stretches, not length or space that contracts, for mass, energy, length, and time are interconnected. Such stretching would make “space” a kind of fluid rather than fabric, a fluid that imbibes an object the more that object accelerates. But fluids are solid, and space is not. The only intangible “fluid” that can find its way into an object and alter it is a field, an energy field of some sort. And since, according to relativity theory, acceleration and gravitation are equivalent, the field concerned here is most likely a gravitational field. (The claim that if you cannot tell the difference between two things – e.g. gravity and acceleration – means that they are the same strikes me as sheer egocentricity, but that is another matter.)

The upshot of all this is that there might be no such thing as “space”, and what we used to think is absolute emptiness is actually a field or fields of energy, with the gravitational the most prominent grid at the macro scale and becoming more and more pronounced the greater the motion or acceleration of a material body.

Is it fair to say that space (and perhaps time as well) is just a mental or mathematical construct, and all existence, anywhere and anytime, is really only energy and matter? If so, then the so-called expansion or inflation of space cannot exceed light speed. In which case, would it be fair to say, then, that Guth and his likes should return to the drawing board?

Thank you for your attention.

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