We cannot help but react to numbers, but why are odds masculine and evens feminine? Why were Levi's 501s and WD-40 given those names? And is number 3 really 'warm' and 'friendly'? Alex Bellos does the maths

Jerry Newport asks me to pick a four-digit number.

"2761," I say. "That's 11 x 251," he replies, reciting the numbers in one continuous, unhesitant flow. "2762. That's 2 x 1381. 2763. That's 3 x 3 x 307. 2764. That's 2 x 2 x 691."

Jerry is a retired taxi driver from Tucson, Arizona, who has Asperger syndrome. He has a ruddy complexion and small blue eyes, his large forehead sliced by a diagonal comb of dark-blond hair. He likes birds as well as numbers, and when we meet he is wearing a flowery red shirt with a parrot on it. We are sitting in his living room, together with a cockatoo, a dove, three parakeets and two cockatiels, which were listening to, and occasionally repeating, our conversation.

As soon as Jerry sees a big number, he divides it up into prime numbers. This habit made his former job driving cabs particularly enjoyable, since there was always a number on the licence plate in front of him. When he lived in Santa Monica, where licence numbers were four and five digits long, he would often visit the four-storey car park of his local mall and not leave until he had worked through every plate. In Tucson, however, car numbers are only three digits long. He barely glances at them now. "If the number is more than four digits I'll start to pay attention to it. If it's four digits or less, it's roadkill. It is!" he remonstrates. "Come on! Show me something new!"

Asperger's is a psychological disorder in which social awkwardness can coexist with extreme abilities, such as, in Jerry's case, an extraordinary talent for mental arithmetic. In 2010, he competed at the Mental Calculation World Cup in Germany having done no preparation. He won the overall title of most versatile calculator, the only contestant to score full marks in the category where 19 five-digit numbers have to be decomposed into their constituent primes in 10 minutes. No one else even got close.

Jerry's system for breaking down large numbers is to sieve out the prime numbers in ascending order, extracting a 2 if the number is even, extracting a 3 if it divides by three, a 5 if it divides by five and so on. He raises his voice to a yell: "Oh yeah, we're sievin', baby! Yeah! Jerry and the sievers!"

His wife, Mary, who is sitting on the sofa next to us, a musician and former Star Trek extra, also has Asperger's, which is much less common in women than it is in men. A marriage between two people with Asperger's is rare, and their unconventional romance was turned into the 2005 Hollywood film Mozart and the Whale.

Sometimes Jerry cannot extract any primes from a large number, which means the number is itself prime. When this happens it gives him a thrill: "If it's a prime number I've never found before, it's kinda like if you were looking for rocks, and you've found a new rock, something like a diamond you can take home and put on your shelf." He pauses. "A new prime number – it's like having a new friend."

The earliest words and symbols used for numbers date from about 5,000 years ago in Sumer, a region in what is now Iraq. The Sumerians did not look far when coming up with names. The word for one, ges, also meant man, or erect phallus. The word for two, min, also meant woman, symbolic of the male being primary and the woman his complement, or perhaps describing a penis and a pair of breasts.

Initially, numbers served a practical purpose, such as counting sheep and calculating taxes. Yet they also revealed abstract patterns, which made them objects of contemplation. Perhaps the earliest mathematical discovery was that numbers come in two types: even – those that can be halved cleanly, such as 2, 4 and 6 – and odd – those that cannot, such as 1, 3 and 5. Pythagoras, who lived in the sixth century BC, echoed the Sumerian association of one with man and two with woman by proclaiming odd numbers masculine and even numbers feminine.

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Resistance to splitting in two, he argued, embodied strength, while susceptibility to splitting in two was a weakness. He gave a further arithmetical justification: odd was master over even, just as man is master over woman, because when you add an odd number to an even number, the answer remains odd.

Pythagoras is most famous for his theorem about triangles, but his belief about number gender has dominated western thought for more than 2,000 years. Christianity embraced it within its creation myth: God created Adam first and Eve second. One signifies unity, and two is the "sin which deviates from the First Good". For the medieval church, odd numbers were stronger, better, more godly and luckier than even, and by Shakespeare's time, metaphysical beliefs about odd numbers were common: "They say there is divinity in odd numbers, either in nativity, chance or death," Falstaff declares in The Merry Wives of Windsor. These superstitions remain. Mystical numbers still tend to be odd, notably the "magic" three, the "lucky" seven and the "unlucky" 13.

Shakespeare is also responsible for the modern meaning of "odd". Originally, the word only had a numerical sense. It was used in phrases such as "odd man out", the unpaired member of a group of three. But in Love's Labour's Lost, the farcical Spaniard Don Adriano de Armado is described as "too picked, too spruce, too affected, too odd, as it were". "Odd" has meant "peculiar" ever since.

It is human nature to be sensitive to numerical patterns. These patterns provoke subjective responses, sometimes extreme ones, as we saw with Jerry, but also more generally, leading to deeply held cultural associations.

Researchers James Wilkie and Galen Bodenhausen decided to investigate whether there was any psychological basis to the ancient belief that odds are male and evens are female. They showed respondents randomly assigned pictures of the faces of young babies, each next to a three-digit number that was either odd-odd-odd or even-even-even, and asked them to guess the baby's sex. This experiment sounds absurd, and it would have been forgotten had it not achieved a striking result: the choice of number had a significant effect. Respondents were about 10% more likely to say that a baby paired with odd numbers was a boy, than if the same baby was paired with even numbers.

Wilkie and Bodenhausen concluded that the Pythagoreans, medieval Christians and Taoists were right. The ancient, cross-cultural belief that odds are associated with maleness and evens with femaleness was supported by the data. They were unable to explain, however, why odd is masculine and even is feminine, rather than vice versa.

Culture, language and psychology play a role in the way we understand mathematical patterns; numbers have a fixed mathematical meaning – they are abstract entities signifying quantity and order – yet they also tell other stories.

The influential German theologian Hugh of Saint Victor (1096–1141) provided an early guide to numbers: 10 represents "rectitude in faith", nine, coming before 10, "defect among perfection", and 11, coming afterwards, "transgression outside of measure". If Hugh were alive today he would undoubtedly find lucrative employment at the Semiotic Alliance. I met its founder, Greg Rowland, in London. Greg advises multinational companies on the symbolism of their brands, which involves the cultural associations of numbers. His clients include Unilever, Calvin Klein and KFC.

The number 11, for example, is an essential element of KFC's corporate mythology: its signature dish is fried chicken seasoned with Colonel Sanders's secret original recipe of 11 herbs and spices. "This is the key mystical use of the number 11 in commercial culture," says Greg. The number represents transgression, he adds, in this case an extra ingredient, one beyond the ordinary. "Eleven has just gone that one past 10. It has recognised that there is an order to things, and now it is exploring the distance beyond. Eleven is opening the door to the infinite, but it's not going too far. It is … rebellion at its most finite." I ask if Colonel Sanders was therefore no different from the rocker in Spinal Tap whose amp went up to 11 so it could be louder than amps labelled to 10. Greg laughs: "Yes! But I actually believe it. I believe that 11 is more interesting than 10."

The Spinal Tap-style extra 1, he adds, is a common meme. A classic example is Levi's 501 jeans. "This raises the expectation but doesn't overplay it. It's that extra little bit, and that is what Levi's is always doing, or in its glory days always did: adding an extra little button here or a new piece of sewing there. And it works well with the big decimals: the film 2001: A Space Odyssey, the 101 drum machine, Room 101. It wasn't Room 100 – who'd be scared of that?"

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The significance of the extra 1 is an established part of Indian culture. Shagun is the custom of giving a round sum of money as a gift, with one rupee added. Gift envelopes in wedding shops, for example, come with a one rupee coin glued to them, so you don't forget it. While there is no single explanation for the practice – some say the one is a blessing, others that it represents the beginning of a new cycle – it is accepted that the symbolic value of the extra one is as important as the monetary value of the notes inside.

In business, as in religion, a good number is fundamental. The number 10 – "rectitude in faith" – strengthens faith in the anti‑acne cream Oxy 10: "Ten is about balance, security, returning to the norm. It's the absolute decimal," says Greg. "There is no argument with 10." I asked him if he thought the all-purpose lubricant WD-40 would have been as successful if it had been called WD-41. "WD-41 would not be reliable," he insisted. "WD-41 would have more stuff in it than you would want. WD-40 is not over-claiming. It is a simple, humble enhancement." (According to company legend, the brand owes its name to the chemist Norm Larsen. He was trying to invent a liquid that would prevent corrosion, hence "Water Displacement" in the name. WD-40 was his 40th attempt.)

Academic research corroborates Greg's semiotic evaluation: for household products, divisible numbers are more attractive to consumers than indivisible ones. In 2011, Dan King of the National University of Singapore and Chris Janiszewski of the University of Florida demonstrated that an imaginary brand of anti-dandruff shampoo was better liked when it was called Zinc 24 than when it was called Zinc 31. The respondents preferred Zinc 24 so much that they were willing to pay 10% more for it. King and Janiszewski argued that customers prefer 24 because they are more familiar with the number from their schooldays, when the lines 3 x 8 = 24 and 4 x 6 = 24 were drummed into them by rote. By comparison, 31 is a prime number and does not appear in any school multiplication table. Greg was not surprised at the results, but he had a different take: "Zinc 24 fits our sense that even-numbered products bring us back to a sense of normalcy, to a sense of things as they should be," he says. "Odd numbers provide extra room for a bit of emotional negotiation, which is why there is more mysticism around them." And why, he added, we don't want them in our hair.

To reinforce their hypothesis that processing fluency increases brand preference, King and Janiszewski designed a follow-up experiment that subtly included a multiplication sum in the advertisement for a numbered brand. They first decided on the products, Solus 36 and Solus 37, two fictitious lines of the real contact lens brand Solus. They then created four ads: one for Solus 36, one for Solus 37 and one for each product with the tag line "6 colours. 6 fits". When there was no tag line, the participants preferred Solus 36 over Solus 37, as would be expected. But when the researchers included the tag line, Solus 36 increased in popularity and Solus 37 became even less popular. King and Janiszewski argued that our familiarity with 6, 6 and 36, from the six times table sum 6 x 6 = 36, increases our fluency in processing the numbers, just as the unfamiliarity of 6, 6 and 37, which are not arithmetically related, decreases it. The pleasure rush that comes from subconsciously recognising a simple multiplication makes us feel good, they said, and we misattribute the buzz as satisfaction with the product. We are always sensitive to whether a number is divisible or not, and this sensitivity influences our behaviour. We are all a bit like Jerry Newport, the taxi driver from Tucson, who cannot see a number without dividing it up into primes.

Another response to numbers is affection. I had not realised the depth of our collective number love until I conducted an online experiment asking members of the public to nominate their favourite numbers and explain their choices. More than 30,000 people took part in the first few weeks. Here is an idea of the words they used. Number one: independent, strong, honest, brave, straightforward, pioneering, lonely. Two: cautious, wise, pretty, fragile, open, sympathetic, quiet, clean, flexible. Three: dynamic, warm, friendly, extrovert, opulent, soft, relaxed, pretentious. Four: laid-back, rogue, solid, reliable, versatile, down-to-earth, personable. Five: balanced, central, cute, fat, dominant but not too much so, happy. Six: upbeat, sexy, supple, soft, strong, brave, genuine, courageous, humble. Seven: magical, unalterable, intelligent, awkward, overconfident, masculine.

King and Janiszewski conducted an experiment in which the participants indicated whether they liked, disliked or felt neutral about every number from 1 to 100. The results showed that our liking of numbers follows clear patterns. Most striking, however, was the unpopularity of numbers ending in 1, 3, 7 and 9. When I saw the results, I instantly thought of Jerry and realised we all sieve prime numbers. The primes are significant features of our internal landscape of numbers, not just for savants like Jerry, but for the rest of us, too. Our brains are always switched on to arithmetic.

• Alex Bellos's Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life is out from Bloomsbury on 10 April.