Mathnificent Word of the Week
Originally posted on
December 20, 2022
Photo by Magda Ehlers from Pexel
proof
/prüf/
noun
A formalized and concise sequence of statements that supports the truth of a given theorem.
“There was no doubt that Tatiana’s proof would be accepted, based on her consistently thorough research and documentation.”
Photo by Magda Ehlers from Pexel
“Math is a search for objective truths, while proofs are the search for subjective agreement.”
That quote is from mathematician Jay Cummings from his long-form mathematics textbook: PROOF. I think it’s a succinct observation of how math is – just like all things are, for all of us, everywhere in all our lives – always looking for and sharing affirmations to statements that we can then, collectively, move forward with as Truth (with a capital ‘T’).
I do love that the word proof is one of those words that has multiple variations on its meaning, depending on what it’s being associated with. Are we using it in mathematics? Referencing alcohol? Is it a typeset for approval? Or, in adjective form, is it to resist or repel (waterproof)? Or how about as a verb when you’re baking and using yeast?
In all the possible definitions of the word, there’s a consistent theme, and that is that there’s a definitive and absolute certainty about it that can be verified by others. And that’s why – instead of making a resolution or a goals list for 2023 – howz about making a proof? A Personal Proof.
Here’s the most basic of the basics of a proper Direct Proof:
IT HAS:
logical and crystal clear phrasing.
formality in its language.
brevity in its length (keep it under 10 sentences).
understandable everyday language.
familiar mathematical phrasing, like, “If {abc}…then {xyz}, as well as phrases like “If and only if.” It is straight forward.
IT DOES NOT HAVE:
any run-on descriptive sentences.
trivial information. Every word in every sentence has a reason to be there.
any statements that could be open to personal interpretation by the reader.
NOTE: If you are writing your Personal Proof for ‘future you’, write down what you’d consider to be the goal date for it to be True since a proof is always written in the present tense.
You start with a theorem — your proposition of what is absolutely true.
For example, you might say:
∀ I can lift 100lbs of machine weights above my head at any U.S. compliant health & fitness facility.
You follow with a statement(s) (aka a lemma) that, in consecutive statements, supports that theorem:
If I go to my neighborhood gym, then I can lift 100lbs on the hammer strength machine.
My neighborhood gym is a U.S. compliant health & fitness facility.
∴ I can lift 100lbs of machine weights above my head at any U.S. compliant health & fitness facility.
Keep in mind that your theorem does not need to be an obvious statement; go ahead, surprise other people in your life, show them how you have a thought-out logical and understandable plan-of-action that you’ll be able to say, at a pre-determined date, is the Truth.
I like the idea of writing a Personal Proof because it is a concise statement that states a commitment you’re making to yourself. If your yearly goal lists tend to have general nebulous statements, make a few Personal Proofs; it requires you to focus and be realistic about what is needed in order for you to embody your Truth with a capital T.
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