Mathematics has undergone three distinct stages: of Greeks, of the Renaissance, and of modernity. Early mathematics was all based on observation, but considered as separate from other sciences. Greek mathematicians transferred their knowledge to the Egyptians. These founders knew that nothing could be known with certainty, that the only certainty in life is its inevitable uncertainty.
The Abacus was the first mathematical tool, and its origins are still unknown to us today. The first major obstacle in mathematics was the use of fractions. The earliest mathematicians, however, realized the unity of a numerator made the division of fractions possible. Ultimately, the problem was solved by being further simplified, reducing the sum several fractions to a simple and singular unitary fraction. The Romans, however, maintained a numerator of 12, and reduced fractions on the basis of 12ths. The Babylonians used 60 as their constant denominator in their studies of astronomy. This removed or bypassed the difficultly of determining a functional denominator. Repeated additions were the first form of multiplication; likewise repeated subtractions were the first form of division, but early expositions were not explicit about procedures and tracing thought-processes.
Geometry is understood to have its origins in land surveying; geometry means to measure the Earth. The practical and theoretical gap in geometry is notably small. The Egyptians, by observing a point, star or sun, on the horizon, were eventually able to surmise accurate North and South Pole dividing lines of both spheres and the globe. The Egyptians perfected the method for obtaining the most accurate right angle, enabling them to draw accurately oppositional dividing lines for Eastern and Western Hemispheres. Knots within lengths of rope led to the discovery of ratios and proportionality. With knowledge of geometry, combined with ratios and proportions, trigonometry became possible and practical. Egyptians barns were defined by three linear measurements, but we know nothing of their literal, applied mathematics. With trigonometry, ratios of other dimensions were able to be measured, even if these dimensions weren’t physically measurable.
All specimens of Egyptian mathematics deal with only particular, specific, case-by-case numerical problems, rather than with general theorems. If anything was proved to be universally true, it probably was only so through wide induction. Greek geometry was, from its commencement, deductive.
Mathematics in early China follows a similar pattern of development from fundamentals to nuance. The Chinese are known to have had several geometric tools for architectural purposes, such as the ruler, compass and level, as well as the wheel and axils. They also demonstrate knowledge of the characteristics of a magnetic needle. They understood that astronomical events occur in cycles. However, evidence reflects that the Chinese made no attempt to classify this work and/or attribute it to particular causes (rational explanations).
New Math in today’s education follows the same form as its historical discovery and the noted chronological progression of accounts noted here. All has been logical outgrowths of basic to more complex functions. Our knowledge of mathematics is very limited since proceeding from the Greeks. It is possible that, this sums up their indebtedness to other races.