William Rowan Hamilton (1805 – 1865)
Great talent from a very young age, especially in linguistics and mathematics. He was brilliant enough to get the astronomy professorship at 23 without even applying. He reformulated Newton’s mechanics, he discovered quaternions, unfortunately forcing their interpretation as vectors. In the GA perspective, now we clarify their interpretation as bivectors and therefore generators of rotations.
Hermann Grassmann (1809 – 1877)
The father of external algebra and the living demonstration of how a non-linear, even self-taught path can lead to fame. Posthumous fame, unfortunately for him. Teacher and far from the academic career, in life he was known as an expert in Sanskrit, to say that his mathematical ideas were so advanced as to be incomprehensible. Grassmann, however, put his own into it: his writings were really obscure and it is worth remembering that if you want to convey an idea, clarity is a must !
William Kingdon Clifford (1845 – 1879)
A great promise in mathematics, a very young Cambridge professor destined for fame, struck down by pneumonia at the age of 34. His work of synthesizing the ideas of Grassmann and Hamilton was rediscovered and enhanced by Hestenes from the 1960s.
We will hear more and more about it.
Oliver Heaviside (1850 – 1925)
Virtually unknown to the public, he is the god of engineers in the electronics and telecommunications branch. If you are reading these lines, in practice, you have to thank him.
Self-taught, the family did not succeed in making him continue his studies and at 16 he began to work in a telegraph company. He never stopped studying while at work and in fact, at 22, he published his first article, which gained the appreciation of none other than Maxwell.
He introduced complex numbers in the study of alternating current circuits and the Laplace transform to reduce complex differential equations to simple algebraic equations.
In our history of geometric algebra unfortunately he plays the role of the “enemy” because he invented – at the same time as Gibbs – the vector calculus that cut out the quaternions and therefore Clifford’s algebra from the mathematical language of the scientists of the time.
If the Nobel Prize for telecommunications had existed, Heaviside would have won a handful, along with other semi-unknown engineers of the time: Steinmetz among all.
David Hestenes (1933 -)
His father Magnus was a talented mathematician, David himself studied mathematics even though he was actually active in the field of physics.
During his studies he hypothesized a geometric interpretation of Dirac’s matrices. In the following years he became the main architect of the rediscovery of Clifford’s algebra which he developed to give it complete form under the name of Geometric Algebra and then the extension Geometric Calculus.
Hestenes studied the application of GA in almost all fields of physics, obtaining a geometric interpretation of the fundamental equations.