Book Review: Mathematics for Ladies

Mathematics for ladies

“Why do they insist on thinking
that women are, by nature, foolish?
They block us from learning
and then mock us for not having learned.”

It is well known, for anyone who has been paying attention, that females have long been discouraged from pursuing a career in the STEM disciplines. This has not put off a great many women scientists throughout history who, despite the significant obstacles placed in their way, and despite their male co-workers often taking the credit, have been responsible for many remarkable and life changing advancements.

Jessy Randall has taken a cross-section of these pioneers and created a collection of poems, each focusing on aspects that affected one individual in pursuit of her interest. The tone is almost playful although the facts conveyed make for sobering reading. The costs to women in science – from family opprobrium through to the stark choice between work or children, and then myriad health issues suffered from working on experimental processes – were not enough to put off these women driven to find answers to their challenging hypotheses.

Some chose to marry although perhaps to enable a working partnership that did not draw criticism.

“The truth is I married for science,
it was a way in. Like
a radiate, I got what I wanted
without attracting undue attention.”

Others railed against the expectations placed on them despite their professional achievements.

“Stop requiring women
to be charming and delightful!
Just let us do our work.”

Although readers may be familiar with many of the names included and their discoveries (despite the barriers placed in their way) there may be others whose stories are less well known, or whose contribution has not been widely credited.

“No, I didn’t tell my husband. Why
should I have? I didn’t need his permission.
It was my money built those cars.”

In amongst the success stories are episodes of sadness, and the double standards under which women often suffer blame.

“I neglected my daughter no less
than her nihilist father did.”

Certain ‘discoveries’ are mocked by the woman credited as being typically human centric – a plant or creature previously unknown to man that nevertheless existed quietly, undisturbed, and therefore more likely to flourish.

“No, I didn’t discover the Peninsular Dragon Lizard,
except in the stupidist, most human sense.”

Women who were key in moving science forward but in collaboration with men were so often reported as mere assistants, if mentioned at all. Perhaps, it is posited, it is not the female who is the weaker sex.

“let the men have the recognition
and the fame. They need it more.
They seem to die without it.
They seem to fade.”

Sometimes there are more pertinent reasons for women stepping back when men seek to excel. Lise Meitner worked in the science labs at the University of Berlin…

“I was the mother of nuclear power
and I laughed all the way away
from the Manhattan Project, in which
I refused to participate.

In that project, the men who worried
about my hair created enough fire
to burn 200,000 bodies down to nothing.”

It is sobering to consider how some things do not change however much supposed progress is made. Prejudices remain ingrained whatever proofs exist.

“In 1949, Granville was one of only two
African-American women to earn a Ph.D.

Two years later, she was denied entry
to her national conference. The hotel was whites-only.

In mathematics we say a number is even
if we can divide it by two,

or to be more precise, if we can divide it
evenly by two. Anything can be divided

by two. Anything can be divided.”

The best poetry is as accessible as it is profound, conveying a depth of considered opinion in succinct language that is both elegant and coherent. This collection, as well as being fascinating, at times rage-inducing but always entertaining and engaging, provides a masterclass in how to bring poetry into the literary mainstream. It deserves to be widely read for the importance of the message conveyed, but more than that, for the sheer pleasure of reading such skilfully crafted stanzas. Highly recommended for all readers, especially those who may not feel they always ‘get’ poetry.

My copy of this book was provided gratis by the publishers, Goldsmiths Press.

Book Review: Fibonacci’s Rabbits

“If I have seen further, it is by standing on the shoulders of giants”

Fibonacci’s Rabbits, by Adam Hart-Davis, explains in accessible language fifty significant mathematical discoveries, from ancient times through to the present day. It is divided into seven ages and demonstrates how each featured mathematician built their propositions and then proofs informed by all who had gone before. To enjoy the book fully it may be necessary to have some interest in, if not understanding of, mathematical concepts and principles.

“In mathematics, proof is everything, whereas science cannot prove anything. Scientists can disprove ideas, but they can never prove them.”

The first section outlines the long history and need for simple tallying and recording. Standardised numerals evolved from primitive marks made when counting. The reasons for and timing of the initial move from such practical applications to more complex and abstract ideas has been lost to time but ancient civilisations throughout the world are known to have used various number systems and calculations to: produce calendars, build pyramids, and study intriguing problems such as squaring the circle. Some of the questions these early mathematicians asked have still to be answered. Others led to proofs that proved useful in practical applications far in their future.

“it is easy to get trapped by habitual ways of thinking, and different approaches can lead to new insights”

Mathematics is required to be logical and rigorous. Although many of its problems appear theoretical, discoveries are often mirrored in the real world. Key patterns, sequences and shapes turn up in: plants, animals, and their natural habitats. The intrigue of the Fibonacci sequence and associated spiral enabled many new mathematical discoveries yet it is clear that Fibonacci numbers are a reflection of the way things grow – including the reproduction of rabbits.

I particularly enjoyed the chapter on zero and the mathematical problem of defining concepts. Having accepted the usefulness of ‘nothing’ whole new fields opened up.

Looking at the importance of imaginary numbers it is clear that sometimes all that is needed is a new way of simply notating a complex idea.

“In Euclid’s system, the workings of the world are not just the whims of the gods, but follow natural rules. It showed how we can find our way to the truth through logic and deductive reasoning, evidence and proof – not just intuition.”

Mathematical problems are only regarded as solved when a verified proof is discovered and written down.

“If even a single exception is found, the conjecture fails”

“for mathematicians, ‘highly likely’ is not proof”

Being unable to find an exception does not constitute a proof, however long the search has taken. There are problems that have finally been solved after hundreds of years, and others that remain outstanding.

Chaos theory and how it developed intrigued me – how one tiny event creates ripples that can radically change outcomes.

“A very small cause, which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance.”

“Really, he argues, the weather is equally as rigidly determined as the eclipse. It is just that the operation of chance with the weather is so major that we just do not have enough knowledge to predict it. Such systems seem to be chaotic, but the normal laws of the universe are still operating entirely regularly.”

Today’s intellectually challenging, high level mathematics may have no apparent practical value. And yet, as has been shown time and again over the centuries, it may offer real world insights as future applications are developed.

Mathematics is logical but logic can be mind bending.

“This statement is false”

So many of the chapters were fascinating to read, even those whose concepts I couldn’t fully comprehend.

It was fun trying to work out why certain, apparently random objects are included in the many colourful illustrations that accompany the text. This was just one entertaining puzzle in a book that provides insights into works of genius that have laid the foundations of so many discoveries and inventions.

Mathematics is an ever evolving discipline and it is exciting to know there is still so much remaining to learn.

The congenial structure and explanations provided in this book allow the reader to appreciate how important mathematics is to a wider understanding of our world and the developments we now rely on. Readers will value the tenacity of mathematicians through the ages when they realise the impact their work has had.

My copy of this book was provided gratis by the publisher, Modern Books.

Book Review: Wonder Women


“There are so many attitudes that need to be adjusted, so many biases that need to be addressed”

Wonder Women, by Sam Maggs, is not the book for anyone who believes that a successful woman is one who is slim, beautiful, amenable and capable of snagging a husband. Successful women, like successful men, are individuals who achieve things for themselves, and this book introduces the reader to dozens of ladies whose work added significantly to their area of expertise. They were innovators, inventors and trailblazers despite the ire they encountered from the patriarchal system. Naturally, many of them were denied credit for their work. History grants accolades to straight, white men as if they are the only people born with brains and the ability to use them. As is demonstrated within these pages, that ability was often lacking when it came to dealing with the opposite sex.

The book is divided into chapters introducing the accomplishments of women of Science, Medicine, Espionage, Innovation and Adventure. Within each chapter, five women are profiled followed by a couple of paragraphs on seven more. Each chapter is rounded off with a Q&A from a current expert in the area discussing their experiences as a women working in a male dominated field.

To achieve their aims, women often had to use subterfuge. Sisters worked with their brothers, wives with husbands, professors with lesser qualified male colleagues. Ideas were willingly shared for scientific advancement leading to men claiming credit for discoveries. Papers by women detailing the exact same research and results, sometimes published years before, were ignored.

“I’m not surprised at what I’ve done. I’m only sorry I couldn’t have had as good a chance as a boy, and have been put to my trade regularly”

Men in every time, place and discipline underestimated their female colleague’s skills. In one example, a morse code operative training for a new role was magnanimously offered a booklet by her superior, that some of his boys had found helpful, as she may need its advice to proceed. He was unaware that she had written it.

I most enjoyed the chapters on areas where I have a personal interest – Science and Medicine. In Espionage and Adventure some of the women came across as morally suspect, although being nice has never been a prerequisite for achievement. There are plenty of men lauded for their contribution to the advancement of learning who may not have made the best of friends.

One statistic that I noted was that, of the 5 million US patents granted since 1790, only 5% have a women’s name on them. A sizeable number of the 95% resemble inventions conceived and developed by women that were rejected as the patent office could not believe a women capable. Expensive court cases proved that accepted ideas had been copied and stolen by male acquaintances. Many patent requests avoided mentioning gender to circumvent the ingrained belief in a women’s lack of ability.

Determined women created their own opportunities. Some disguised themselves as men, others travelled abroad to gain the training denied them at home. One women who persuaded a college to allow her to attend seminars was required to sit behind a screen lest her presence upset the roomful of men, poor lambs.

The writing is light-hearted and brisk but carries a serious message. It offers a reminder that delicate little lady brains simply need the education and experiences routinely afforded to men in order to equally achieve. Perhaps at some level men are aware of this, and that is what they fear.

My copy of this book was provided gratis by the publisher, Quirk.