How to solve problems efficiently? Think like a mathematician!

Have you ever met a mathematician before? You may have most probably noticed some “peculiarity.” This is not a stereotype; however, there is a specific way in which mathematicians think. This is not innate either, it is mathematics which makes them think in such way. If we can learn to think like a mathematician, then you might find that this is very beneficial!

Below are two real conversations that I personally know of.

Example 1
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Example 2
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Do you see the difference? Mathematicians are very specific in what they say. If you ask them a question, or make a statement, it is most likely that you will get a question back, and it is usually of the form: "What do you mean by...."

Interestingly enough, it is not mathematicians who are specific themselves, it is mathematics which taught them to be specific. Ngoc, an honours mathematics student confessed to us:

“After two semesters of Math at university, I could feel that something is different in the way I think. I realized that I ask more questions, especially “what is...?” After I obtained my bachelors in Mathematics, my brain learned to function in two different modes: the mathematical mode, and the daily life mode. It is difficult to carry on a normal conversation in math mode, since I would over-analyze and over-criticize my friends' choice of words and what they mean. Vice versa, it is difficult to do research in math without being specific. This is one of the characterizations of a good mathematician.”

But why does being specific help in mathematics?
What is “mathematics” about?
According to the Britannica concise dictionary, Mathematics is the “Science of structure, order, and relation that has evolved from counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation.” In other words, to solve a problem, mathematics takes in information (definitions, data, clues), and uses logic and calculations, to give out results (theorems, solution, answer). So it is of utmost importance that we have the correct information! So when mathematicians are asking for definitions, they are trying to make the information absolutely precise. Only then can logic be applied, and only then can we get logical results.

How can the mathematician's thinking be applied in our everyday life?
“When solving problems in mathematics, the hardest part I find is to translate the problem into precise terms. Once this is done, it is just a matter of applying logic and known results and theorems to arrive at the answer.”

So actually, we don't differ from mathematicians because we lack logic. Most of us are quite logical. We just lack the initial step: of making a problem absolutely precise.

“I find that if I use mathematical thinking for my everyday life, a lot of problems become much clearer! For example, if I am studying ineffectively, I stop and ask myself: why so ineffective? This is defining the problem precisely. This thinking points me to the exact bottleneck of the problem, and from then I can devise solutions.”

So is this how pondering on shampoo and the Moon can help you become a mathematician? Not quite.

“As I said, it is difficult to carry on a normal conversation in math mode. Such shampoo and Moon are our bursts of mathematics in life, which results in nice comic strips.”

But there are ways to train yourself into this mindset. Here are some tips we gathered from mathematics students and mathematicians:

• Questions to ask when you get stuck:
• What is the problem / What is the cause of the problem?
• Can you write down a statement of the problem?
• Does the statement “make sense?”
• How would you explain your problem to other people?
• Think of how you would solve the problem. Why isn't your solution working?

This can be applied for everyday-life problems too!

Ping's example

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Try for yourself! Are you currently facing any challenges?