Lemma, proposition, theorem or corollary are different types of mathematical claims with different levels of importance and difficulty. Logically, these claims are same as all of them need a valid proof to be deemed true.

1. Lemma: easily proved and least interesting claim that can be used to prove other claims …

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Natural numbers are numbers that follows Peano axioms.

Peano Axiom

1. 1 is a natural number.
2. If \(n\) is a natural number then \(n++\) is also a natural number.
3. 1 is not a successor of any natural number. Hence, \(n++\neq 1\) for every natural number \(n\).
4. For two natural numbers …

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Data is collection of facts that cane used to draw conclusions, make prediction and assist in decision-making.

Role in industry

Data science: the science of working with data. Three part: Machine learning, statistics, and analytics. Data Scientist: Creating new way of modeling and understanding the unknown by using raw data …

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Similar to Hilbert’s 23 problems in mathematics, International Association of Hydrological Sciences (IAHS) compiled some of the most significant Unsolved problems in hydrology (UPH) with the help of community. The list of following 23 problems were published in a 2019 paper.¹

Time variability and change

1. Is the hydrological …

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Question:

Is the hydrological cycle regionally accelerating/decelerating under climate and environmental change, and are there tipping points (irreversible changes)?

Literature: