Guides · ISEF category
Mathematics
ISEF category MATH · difficulty for high-school students: high
Pure and applied mathematics: number theory, combinatorics, graph theory, topology, analysis, algebra, probability theory, mathematical modeling, cryptography.
How it's judged
ISEF scores 100 points across five criteria:
- Creative Ability: 30 pts
- Scientific Thought: 30 pts
- Thoroughness: 15 pts
- Skill: 15 pts
- Clarity: 10 pts
What wins
- Proving a new result in combinatorics or number theory
- Novel mathematical model of a physical or biological system with rigorous analysis
- Extension of an open or partially-solved problem with partial results
- New algorithm with provable complexity bounds
- Elegant reformulation of a known result revealing new structure
Common mistakes
- Calling a pattern observed in examples a 'proof'
- Presenting a known result as novel without comprehensive literature review
- Mathematical modeling without sensitivity analysis or validation
- Confusing numerical computation for mathematical proof
What you'll need
Pen, paper, and computer algebra system (Mathematica, Sage, or Python with SymPy). No lab required.
Ethics & approvals
Human-subjects (IRB) approval is usually not required for this category. Vertebrate-animal (IACUC) approval is usually not required.
The novelty bar
A new theorem, lemma, conjecture with evidence, or a novel application of existing mathematics. Rediscovering known results is not competitive, even if the student derived it independently.
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