
Math TOK 1: Proofs
Authored by Sagar Sagar
Mathematics
11th Grade
Used 1+ times

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7 questions
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1.
MATCH QUESTION
1 min • 5 pts
Match the following:
Theorem
An explanation of the mathematical meaning of a word
Lemma
A statement that has been proven to be true.
Definition
A less important but nonetheless interesting true statement.
Corollary
A true statement used in proving other true statements (that is, a less important theorem that is helpful in the proof of other results).
Proposition
A true statment that is a simple deduction from a theorem or proposition.
2.
MATCH QUESTION
1 min • 3 pts
Match the following:
Conjecture
The explanation of why a statement is true.
Proof
A statement believed to be true, but for which we have no proof. (a statement that is being proposed to be a true statement)
Axiom
A basic assumption about a mathematical situation. (a statement we assume to be true).
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does the idea of "proof" define the boundaries of mathematical knowledge? (Scope)
Proofs are unnecessary for mathematical knowledge
Proofs define what counts as knowledge in mathematics, setting strict boundaries
Mathematics accepts any intuitive explanation as valid proof
Boundaries in mathematics are defined by physical experiments
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What distinguishes the inductive method in science from mathematical induction? (Method and Tools)
Scientific induction is based on logical deduction, mathematical induction is based on guesswork
Both are forms of deductive reasoning
Scientific induction generalizes from observations, while mathematical induction is a formal deductive method
Both rely on empirical data
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
From different perspectives, how might certainty in mathematical knowledge be viewed?
(Perspectives)
All people see mathematics as completely uncertain
Certainty in mathematics is determined by experimentation
Mathematical certainty is always equivalent to scientific certainty
Some view proofs as absolute certainty, while others see them as dependent on axioms and logical systems.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When using computer-assisted proofs like in the Four Colour Theorem, what ethical responsibility arises in terms of accessibility? (Ethics)
https://www.youtube.com/watch?v=h7kqlYUV1l8
Ensuring the proof is easy enough for the general public to understand.
Ensuring that only experts with programming knowledge can validate the results.
Ensuring the proof process and code are openly available for scrutiny by others in the community.
Keeping the computational process proprietary to protect intellectual property.
Answer explanation
7.
OPEN ENDED QUESTION
3 mins • Ungraded
Read the article below and summarize "your views" on the same: (50-60 words)
https://www.scientificamerican.com/article/mathematicians-question-ai-performance-at-international-math-olympiad/
Link for full article:
Mathematicians Question AI Performance at International Math Olympiad _ Scientific American.pdf
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