## 26 Questions

Who dramatically improved the microscope and discovered spermatozoa, bacteria, and the diversity of microscopic life?

Anton van Leeuwenhoek

Which scholars of the medieval Islamic world wrote on botany and anatomy?

Al-Jahiz and Al-Dīnawarī

Who published a basic taxonomy for the natural world in 1735?

Carl Linnaeus

Whose works presented a coherent theory of evolution, predating the British naturalist Charles Darwin?

Jean-Baptiste Lamarck

Which philosophers contributed extensively to the development of biological knowledge?

Aristotle and Theophrastus

What is the primary function of energy processing in organisms?

To move, grow, and reproduce

Which unifying theme of biology explains the unity and diversity of life?

Evolution

At what levels of organization can biologists study life?

From the biochemistry of cells to the anatomy and physiology of organisms

What is the main focus of subdisciplines within biology?

The nature of their research questions and tools used

How long ago did life on Earth emerge?

3.7 billion years ago

What are the major subdisciplines of modern mathematics?

Number theory, algebra, geometry, analysis

What is the process of proving properties of abstract objects in mathematics?

Deductive reasoning

What is the essential role of mathematics in natural sciences?

Modeling and experimentation

What are the fundamental truths of mathematics independent from?

Scientific experimentation

What are the entities stipulated to have certain properties in modern mathematics called?

Axioms

What does most mathematical activity involve?

Discovery of properties of abstract objects and use of pure reason

What is the narrower and more technical meaning of the word 'mathematics' in Classical times?

Mathematical study

Which ancient Greek word means 'study' and 'science'?

Máthēma

Which group restrained the use of the word 'mathematics' to just the study of arithmetic and geometry?

Pythagoreans

What did the term 'mathematics' commonly mean in Latin and English until around 1700?

Astrology

What led to a correlated increase in the development of both mathematical innovations and scientific discoveries?

The interaction between mathematical innovations and scientific discoveries

Which problem, dating back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem?

Integer factorization

What led to a dramatic increase in the number of mathematical areas and their fields of application at the end of the 19th century?

Systematization of the axiomatic method

'Máthēma' in Ancient Greek means:

"That which is learnt"

'Mathēmatikós' (μαθηματικός) in Ancient Greek means:

"Mathematical"

In Latin, and in English until around 1700, what did 'mathematics' more commonly mean?

"Astrology"

## Study Notes

### Key Figures in Biology

- Antonie van Leeuwenhoek dramatically improved the microscope and discovered spermatozoa, bacteria, and the diversity of microscopic life.
- Scholars of the medieval Islamic world, such as Ibn Sina (Avicenna) and Ibn Rushd (Averroes), wrote on botany and anatomy.
- Carl Linnaeus published a basic taxonomy for the natural world in 1735.
- Jean-Baptiste Lamarck's works presented a coherent theory of evolution, predating the British naturalist Charles Darwin.
- Philosophers such as Aristotle and Epicurus contributed extensively to the development of biological knowledge.

### Biological Concepts

- The primary function of energy processing in organisms is to convert energy into a usable form.
- The unifying theme of biology explains the unity and diversity of life.
- Biologists can study life at multiple levels of organization, including molecules, cells, organisms, populations, communities, ecosystems, and biosphere.

### Subdisciplines of Biology

- The main focus of subdisciplines within biology is to understand the structure, function, and diversity of life.
- Subdisciplines of biology include botany, zoology, microbiology, biochemistry, ecology, and evolution.

### Origins of Life

- Life on Earth is believed to have emerged around 3.5 billion years ago.

### Mathematics

- The major subdisciplines of modern mathematics include algebra, analysis, geometry, and number theory.
- The process of proving properties of abstract objects in mathematics is called proof theory.
- Mathematics plays an essential role in natural sciences, as it provides a language and tools for describing and analyzing the world.
- The fundamental truths of mathematics are independent from human thought and perception.
- The entities stipulated to have certain properties in modern mathematics are called mathematical objects.
- Most mathematical activity involves solving problems, exploring mathematical structures, and developing new mathematical theories.

### History of Mathematics

- In Classical times, the narrower and more technical meaning of the word 'mathematics' referred to the study of arithmetic and geometry.
- The ancient Greek word 'mathema' means 'study' or 'science'.
- The ancient Greek word 'mathematikós' (μαθηματικός) means 'fond of learning' or 'studious'.
- In Latin and English until around 1700, the term 'mathematics' commonly meant the study of arithmetic and geometry.
- The development of mathematical innovations and scientific discoveries led to a correlated increase in the use of mathematical tools and methods.
- The problem of primality, dating back to Euclid in 300 BC, had no practical application before its use in the RSA cryptosystem.
- The end of the 19th century saw a dramatic increase in the number of mathematical areas and their fields of application.

Explore the unifying themes that tie together the broad scope of biology, including the role of cells, hereditary information, evolution, and energy processing in living organisms.

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