BNW010 - What are mathematicians calculating

I think different areas have a different set of language. The same word, calculation, for example, may mean different things when it's said by a Computer Scientist and a Mathematician. Because of this, it's really hard to communicate accurately. I had this realization because I asked the question "What are mathematicians calculating?"

It all started one day when my boyfriend watched a video on the proof of a theorem. It says in the video that the mathematician spent 4 years preparing and 1 year calculating ("计算" I'm not sure if the translation between Chinese and English caused even more misalignment in this case).

With the help of computers, I believe most "calculations", from simple additions to matrix multiplications, can be done fairly quickly. What kind of calculation takes a whole year? To find out, I turned to my dad, who studied mathematics in college and works in a related field.

This was actually the second time I had asked him this question. Maybe because I didn't really understand what he was saying the first time, his answer miraculously disappeared from my memory. I remember how and where I asked him, and I remember the setting, but when I tried to remember the content, it's just blank.

This time, what I did get from our conversation is within mathematics, you can use different symbols and different systems to represent the same thing. But that leads to different ways of deduction and outcomes. For example, when working on a matrix, we can use variables such as a, b, c to represent the entries. But we can also use a1, 1, a1, 2, a1, 3. The latter notation is better and leads to more generalized conclusions. So maybe the "calculation" is actually trying to find the proper notations and abstraction system to solve the problem.

I find it both fascinating and frustrating when trying to convey my ideas, as I lack the proper language to articulate my thoughts clearly. Additionally, my ideas can be vague and uncertain in the first place, which makes it even more difficult to communicate effectively.

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