Biology: Unifying Themes and Concepts

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.